Mahesh

Students can go through AP SSC 10th Class Maths Notes Chapter 11 Trigonometry to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 11 Trigonometry

→ In our daily life, we can measure the heights, distances and slopes by using some mathematical techniques.

→ The mathematical techniques which come under a branch of mathematics is called ‘trigonometry’.

→ “Trigonometry” is the study of relationships between the sides and angles of a triangle.

→ Early astronomers used to find out the distances of the stars and planets from the Earth. Even today, most of the technologically advanced methods used in engineering and physical sciences are based on trigonometrical concepts.

→ Naming the sides in a right triangle:
Let’s take a right triangle ABC as shown in the figure.

Consider ∠CAB as A where angle ‘A’ is acute.
Since AC is the longest side, it is called “Hypotenuse”.

→ Now observe the position of side BC with respect to angle A. It is opposite to angle ‘A’ and we can call it as “Opposite side of angle A”.

→ And the remaining side AB can be called as “Adjacent side of angle A”.

→ Trigonometric Ratios:
The ratios of the sides of a right angled triangle with respect to its acute angles, are called Trigonometric ratios.

→ Consider a right angled triangle ABC having right angle at B as shown in the given figure.

Then, trigonometric ratios of the angle A in right angled triangle ABC are defined as follows:

→ There are three more ratios defined in trigonometry which are considered as multiplicative inverse of the above three ratios.

→ Multiplicative inverse of “sine A” is “cosecant A”.
i.e., cosec A = [latex]\frac{1}{\sin A}[/latex] = [latex]\frac{\text { Hypotenuse }}{\text { Opposite side of the angle } A}[/latex]

→ Multiplicative inverse of “cosine A” is “secant A”.
i.e., sec A = [latex]\frac{1}{\cos A}[/latex] = [latex]\frac{\text { Hypotenuse }}{\text { Adjacent side of the angle } A}[/latex]

→ Multiplicative inverse of “tangent A” is “cot A”.
i.e., cot A = [latex]\frac{1}{\tan A}[/latex] = [latex]\frac{\text { Adjacent side of the angle } A}{\text { Opposite side of the angle } A}[/latex]

Note:
i) The values of the trigonometric ratios of an angle do not vary with the lengths of the sides of the triangles, if the angle remains the same.
ii) Each trigonometric ratio is a real number and has no unit.
iii) “sin θ” is one symbol and sin, cos, tan etc., cannot be separated from θ.
iv) If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios of angle can be easily determined.
v)

→ Trigonometric ratios of some specific angles:
The values of various trigonometric ratios of 0°, 30°, 45°, 60° and 90°.

Note:
i) The values of “sin θ” and “cos θ” always lie between ‘0’ and ‘1’.
ii) In the case of tan θ, the values increase from 0 to ∞ (not determinate).
iii) In the case of cot θ, the values decrease from ∞ to 0.
iv) In the case of cosec θ, the values decrease from ∞ to 1.
v) In the case of sec θ, the values increase from 1 to ∞.

→ Trigonometric ratios of complementary angles:
Two angles are said to be complementary, if their sum is equal to 90°.
In a right angled triangle, if ∠B = 90°, then ∠A + ∠C = 90° i.e., ∠A and ∠C form a pair of complementary angles.
If ‘θ’ is an acute angle, then we can prove that
sin (90 – θ) = cos θ
cos (90 – θ) = sin θ
tan (90 – θ) = cot θ
cot (90 – θ) = tan θ
sec (90 – θ) = cosec θ
cosec (90 – θ) = sec θ

→ Trigonometric Identity: An identity equation having trigonometric ratios of an angle is called trigonometric identity. It is true for all the values of the angles involved in it.
We have three major trigonometric identities. They are
i) sin² A + cos² A = 1
ii) sec² A – tan² A = 1
iii) cosec² A – cot² A = 1
Note: sin² θ = (sin θ)² but sin θ² ≠ (sin θ)²

Students can go through AP SSC 10th Class Maths Notes Chapter 10 Mensuration to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 10 Mensuration

→ A solid is a geometrical shape with three dimensions namely length, breadth and height.
Eg:

→ A solid has two types of area namely,
a) Lateral Surface Area (L.S.A.)
b) Total Surface Area (T.S.A,)

→ In general, L.S.A. of a solid is the product of its base perimeter and height.
Eg : L.S.A. of a cuboid = 2h(l + b)
L.S.A. of a cylinder = 2πrh

→ The T.S.A. of a solid is the sum of L.S.A. and the areas of its top and base.
Eg : T.S.A. of a cylinder = 2πrh + 2πr²
= 2πr(r + h)

→ In general, the volume of a solid is the product of its base area and height.
V = A. h
Eg: Volume of a cube = a² . a = a³
Volume of a cylinder = πr² . h = πr²h

→ The volume of solid formed by joining two basic solids is the sum of volumes of the constituents.

→ Surface area of the combination of solids: In calculating the surface area of the solid which is a combination of two or more solids, we can’t add the surface areas of all its constituents, because some part of the surface area disappears in the process of joining them.

→ Surface areas and volume of different solid shapes:

→ Some solid figures and their combination shapes:

Students can go through AP SSC 10th Class Maths Notes Chapter 9 Tangents and Secants to a Circle to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 9 Tangents and Secants to a Circle

→ The locus of points which are joined by a curve and are equidistant from a fixed point is called a circle. The fixed point here is called the centre of the circle.
(or)
A simple closed curve consisting of all points in a plane which are equidistant from a fixed point is called a circle. The fixed point is its centre and the fixed distance is its radius.

→ The path followed by a circular object is a straight line.

→ The line segment joining any two points on a circle is called a ‘chord’. The longest of all chords of a circle passes through the centre and is called a diameter.

[latex]\overline{\mathrm{AB}}[/latex] is a chord and [latex]\overline{\mathrm{PQ}}[/latex] is a diameter.
[latex]\overline{\mathrm{OP}}[/latex] is the radius of the circle,
diameter = 2 × radius d = 2r
r = [latex]\frac{d}{2}[/latex]

→ There are three different possibilities for a given line and a circle.

Case (i): The line PQ and the circle have no point in common (or) they do not touch each other.
Case (ii): The line PQ and the circle have two common points (or)
The line PQ intersects the circle at two distinct points A and B. Here the line PQ is a “secant” of the circle.
Case (iii): The line PQ touches the circle at an unique point A (or) there is one and only one point common to both the line and circle.
Here [latex]\stackrel{\leftrightarrow}{\mathrm{PQ}}[/latex] is called a tangent to the circle at ‘A’.

→ The word tangent is derived from the Latin word “TANGERE” which means “to touch” and was introduced by Danish mathematician“Thomas Fineke” in 1583.

→ There is only one tangent to the circle at one point.

→ The tangent at any point of a circle is perpendicular to the radius through the point of contact.

The radius OP is perpendicular to [latex]\stackrel{\leftrightarrow}{\mathrm{AB}}[/latex] at P.
i.e, OP ⊥ AB.

→ Construction of a tangent to a circle:
Draw a circle with centre ‘O’.
Take a point ‘P’ on it. Join OP.
Draw a perpendicular line to OP through ‘P’.

Let it be [latex]\stackrel{\leftrightarrow}{\mathrm{XY}}[/latex]
XY is the required tangent to the given circle passing through P.

→ Let ‘O’ be the centre of the given circle and [latex]\overline{\mathrm{AP}}[/latex] is a tangent through A where OA is the radius, then the length of the tangent AP = [latex]\sqrt{\mathrm{OP}^{2}-\mathrm{OA}^{2}}[/latex].

→ Two tangents can be drawn to a circle from an external point.

→ Let ‘O’ be the centre of the circle and P is an exterior point. There are exactly two tangents to the circle through P.
[latex]\overline{\mathrm{PA}}[/latex] and [latex]\overline{\mathrm{PB}}[/latex] are the tangents.

Here the lengths of the two tangents drawn from the external points are equal.
[latex]\overline{\mathrm{PA}}[/latex] = [latex]\overline{\mathrm{PB}}[/latex]

→ Construction of tangents to a circle from an external point:
Step – 1: Draw a circle with centre ‘O’ and with given radius.
Step – 2: Mark a point ‘P’ in the exterior of the circle and join ‘OP’.
Step – 3: Draw the perpendicular bisector [latex]\stackrel{\leftrightarrow}{\mathrm{XY}}[/latex] to [latex]\overline{\mathrm{OP}}[/latex], intersecting at M.
Step – 4: Taking M as centre, MP or OM as radius, draw a circle which intersects the given circle at A and B.

Step – 5: Join PA and PB. PA and PB are the required tangents.

→ Consider a circle with centre ‘O’. PA and PB are the tangents from an exterior point ‘P’. Then, the centre of the circle lies on the bisector of the angle between two tangents drawn from the exterior point P.
∠OPA = ∠OPB

→ Consider two concentric circles with centre ‘O’. Let the chord [latex]\overline{\mathrm{AB}}[/latex] of the larger/ bigger circle just touches the smaller circle, then it is bisected at the point of contact with the smaller circle.
In the figure, [latex]\overline{\mathrm{AB}}[/latex] is the chord of bigger circle touching the smaller circle at P then AP = PB.

→ If AP and AQ are two tangents to a circle with centre ‘O’, then ∠PAQ = 2∠OPQ = 2∠OQP.

→ If a circle touches the sides of a quadrilateral ABCD at points P, Q, R and S then AB + CD = BC + DA.
i.e., sum of the opposite sides are equal.

→ The region enclosed by a secant/chord and an arc is called a ‘segment of the circle’.

Case (i): If the arc is a minor arc then the segment is a minor segment.
Case (ii): If the arc is a semi arc then the segment is a semi circle.
Case (iii): If the arc is a major arc then the segment is a major segment.

→ Area of a segment between the chord AB and whose arc makes an angle ‘x’ at the centre = [latex]\frac{x}{360}[/latex] × πr²

i.e., Area of the segment APB = (Area of the corresponding sector OAPB) – (Area of the corresponding triangle OAB).

Students can go through AP SSC 10th Class Maths Notes Chapter 8 Similar Triangles to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 8 Similar Triangles

→ The geometrical figures which have the same shape but are not necessarily of the same size are called similar figures.

→ The heights and distances of distant objects can be found using the principles of similar figures.

→ Two polygons with same number of sides are said to be similar if their corresponding angles are equal and their corresponding sides are in proportion.

→ A polygon in which all sides and all its angles are equal is called a regular polygon. Eg.:

→ The ratio of the corresponding sides is referred to as scale factor or representative factor.

→ All squares are similar.

→ All circles are similar.

→ All equilateral triangles are similar.

→ Two congruent figures are similar but two similar figures need not be congruent.

→ A square ABCD and a rectangle PQRS are of equal corresponding angles, but their corre¬sponding sides are not in proportion.

∴ The square ABCD and the rectangle PQRS are not similar.

→ The corresponding sides of a square ABCD and a rhombus PQRS are equal but their corresponding angles are not equal. So they are not similar.

→ If a line is drawn parallel to one side of a triangle intersecting the other two sides at two distinct points then the other two sides are divided in the same ratio.

In △ABC; DE // BC then [latex]\frac{AD}{DB}[/latex] = [latex]\frac{AE}{EC}[/latex].
This is called Basic proportionality theorem (or) Thale’s theorem.

→ If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.

In △ABC, a line ‘l’ intersecting AB in D and AC in E
such that [latex]\frac{AD}{DB}[/latex] = [latex]\frac{AE}{EC}[/latex] then l // BC.
This is converse of Thale’s theorem.

→ Two triangles are similar, if
i) their corresponding angles are equal.
ii) their corresponding sides are in the same ratio.

→ If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio or proportional and hence the two triangles are similar.

In △ABC, △DEF
∠A = ∠D
∠B = ∠E
∠C = ∠F
⇒ [latex]\frac{AB}{DE}[/latex] = [latex]\frac{BC}{EF}[/latex] = [latex]\frac{AE}{DF}[/latex]
∴ △ABC ~ △DEF (A.A.A)

→ If in two triangles, sides of one triangle are proportional to the sides of other triangle, then their corresponding angles are equal and hence the two triangles are similar.

In △ABC, △DEF
if [latex]\frac{AB}{DE}[/latex] = [latex]\frac{BC}{EF}[/latex] = [latex]\frac{AE}{DF}[/latex]
⇒ ∠A = ∠D
∠B = ∠E
∠C = ∠F
Hence, △ABC ~ △DEF (S.S.S)

→ If two angles of a triangle are equal to two corresponding angles of another triangle then the two triangles are similar.

In △ABC, △DEF
if ∠A = ∠D
∠B = ∠E
⇒ ∠C = ∠F (By Angle Sum property)
∴ △ABC ~ △DEF (A.A)

→ If one angle of a triangle is equal to one angle of other triangle and the sides including these angles are proportional, then the two triangles are similar.

In △ABC, △DEF if ∠A = ∠D, and
[latex]\frac{AB}{DE}[/latex] = [latex]\frac{AC}{DF}[/latex]
⇒ △ABC ~ △DEF (S.A.S)

→ The ratio of areas of two similar triangles is equal to the ratio corresponding sides.

→ If a perpendicular is drawn from the vertex, containing the right angle of a right angled – triangle to the hypotenuse, then the triangles on each side of perpendicular are similar to one another and to the original triangle. Also the square of the perpendicular is equal to the product of the lengths of the two parts of the hypotenuse.
In △ABC, ∠B = 90°
BD ⊥ AC

Then △ADB ~ △BDC ~ △ABC and
BD² = AD . DC

→ Pythagoras theorem: In a right angled triangle, the square of hypotenuse is equal to the sum of the squares of other two sides.

In △ABC; ∠A = 90°
AB² + AC² = BC²

→ In a triangle, if square of one side is equal to sum of squares of the other two sides, then the angle opposite to the first side is right angle.

In △ABC, if
AC² = AB² + BC² then ∠B = 90°
This is converse of Pythagoras theorem.

→ Baudhayan Theorem (about 800 BC):
The diagonal of a rectangle produces itself the same area as produced by its both sides (i.e., length and breadth).
In rectangle ABCD,

area produced by the diagonal AC = AC • AC
= AC²
area produced by the length = AB • BA = AB
area produced by the breadth = BC • CB = BC²
Hence, AC² = AB² + BC².

→ A sentence which is either true or false but not both is called a simple statement.

→ A statement formed by combining two or more simple statements is called a compound statement.

→ A compound statement of the form “If …… then ……” is called a Conditional or Implication.

→ A statement obtained by modifying the given statement by ‘NOT’ is called its negation.

Students can go through AP SSC 10th Class Maths Notes Chapter 7 Coordinate Geometry to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 7 Coordinate Geometry

→ The branch of mathematics which deals with points in a coordinate plane is called Coordinate/Analytical geometry.

→ There is a definite one-one correspondence between the position of a point in a plane and a pair of numbers called coordinates.

→ In a Cartesian plane, the position of a point P is determined by two coordinates x and y, where x is the distance of P from Y – axis and y is the distance of P from X – axis. So we denote it by P (x, y).

→ Signs of coordinates in different quadrants:

→ The point of intersection of the axes is called the- origin represented by (0, 0).

→ Any point lying on X – axis is denoted by (x, 0) as its y-coordinate is zero.

→ A point on Y – axis is denoted by (0, y) as its x-coordinate is zero.

→ Distance between any two points P(x₁, y₁) and Q(x₂, y₂) is given by
PQ = [latex]\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/latex]

→ Distance between any two points P(x₁, 0) and Q(x₂, 0) on the X – axis is | x₂ – x₁ |.
Distance between any two points P(0, y₁) and Q(0, y₂) on the Y – axis is | y₂ – y₁ |

→ The coordinates of the point P which divides the line joining of two points (x₁, y₁) and (x₂, y₂) internally in the ratio m₁ : m₂ is

→ The midpoint of a line joining any two points (x₁, y₁) and (x₂, y₂) is

→ If the ratio in which ‘P’ divides two points (x₁, y₁) and (x₂, y₂) is k : 1, then

→ The point of concurrence of medians of a triangle is called its centroid.

→ Centroid divides each median in the ratio 2 : 1.

→ If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the vertices of a triangle, then its centroid is

→ The points P, Q on a line segment [latex]\overline{\mathrm{AB}}[/latex] are said to be the points of trisection, if P and Q divides [latex]\overline{\mathrm{AB}}[/latex] into three equal points i.e., AP = PQ = QB.

→ If P, Q are points of trisection of [latex]\overline{\mathrm{AB}}[/latex], then P divides AB in the ratio 1 : 2 and Q divides AB in the ratio 2 : 1.

→ Area of a triangle AOB formed by the points origin O(0, 0), a point on X – axis A (x, 0) and another point on Y – axis B(0, y) is [latex]\frac{1}{2}[/latex]xy.

→ If (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the vertices of a triangle, then its area is

→ If three points are collinear, then the area of the triangle formed by these points is zero.

→ Let A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of a triangle △ABC, then AB = c; BC = a and AC = b and

S = [latex]\frac{a+b+c}{2}[/latex](semi-perimeter)
Then area of △ABC = [latex]\sqrt{S(S-a)(S-b)(S-c)}[/latex]
This is called Heron’s formula.

→ Let ax + by + c = 0 represents a straight line; then any pair of coordinates (x₁, y₁) satisfying the linear equation ax + by + c = 0 is called its solution, i.e., if (x₁, y₁) is a solution of ax + by + c = 0 then ax₁ + by₁ + c = 0.

→ The inclination or angle made by a straight line with positive X-axis is called the slope of the straight line. Slope of a line joining any two points (x₁, y₁) and (x₂, y₂) is m = [latex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/latex]

→ If ‘θ’ is the angle made by a line with X-axis, then slope m = tan θ.

Students can go through AP SSC 10th Class Maths Notes Chapter 6 Progressions to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 6 Progressions

→ The array of numbers following some rule is called a number pattern.
E.g.: 4, 6, 4, 6, 4, 6,…….

→ There is a relationship between the numbers of a pattern.

→ Each number in a pattern is called a term.

→ The series or list of numbers formed by adding or subtracting a fixed number to / from the preceding terms is called an Arithmetic Progression, simply A.P.
E.g.: 3, 5, 7,9, 11, ……

→ In the above list, each term is obtained by adding ‘2’ to the preceding term except the first term.

→ Also, we find that the difference between any two successive terms is the same throughout the series. This is called “common difference”.

→ The general form of an A.P. is
a, a + d, a + 2d, a + 3d,………, a + (n – 1) d.
Where‘a’is the first term, d is common difference.
Here d = a₂ – a₁ = a₃ – a₂ = a₄ – a₃ = …….. = a_n – a_n-1

→ If the number of terms of an A.P. is finite, then it is a finite A.P.
E.g.: 10, 8, 6, 4, 2.

→ If the number of terms of an A.P. is infinite, then it is an infinite A.P.
E.g.: 4, 8, 12, 16, …….

→ If d > 0, then a_n > a_n-1 and if d < 0, then a_n < a_n-1

→ The general term or nth term of an A.P is a_n = a + (n – 1) d.
E.g.: The 10th term of 10, 6, 2, -2, ……. is
Here a = 10 ; d = a₂ – a₁ = 6 – 10 = -4
∴ a₁₀ = a + (n – 1) d = 10 + (10 – 1) × -4 = 10 – 40 + 4 = -26

→ Sum of first n-terms of an A.P. is S_n = [latex]\frac{n}{2}[/latex][a + l] where a is the first term and l is the last term.
E.g.: 1 + 2 + 3 + …… + 80 = [latex]\frac{80}{2}[/latex](1 + 80) = 40 × 81 = 3240.

→ Sum of the first n-terms of an A.P. is given by, S_n = [latex]\frac{n}{2}[/latex][2a + (n – 1)d]
Also, a_n = S_n – S_n-1.

→ In a series of numbers, if every number is obtained by multiplying the preceding number by a fixed number except for the first term, such arrangement is called geometric progression or G.P.
E.g.: 4, 8, 16, 32, 64,……
Here, starting from the second term, each term is obtained by multiplying the preceding term by 2.
The first term may be denoted by ‘a’, then we also see that
We call it “common ratio”, denoted by ‘r’

→ The general form of a G.P. is
a, ar, ar², ar³, ……. ar^n-1
i.e., a₁ = a, a₂ = ar, a₃ = ar², a_n = ar^n-1.

Students can go through AP SSC 10th Class Maths Notes Chapter 5 Quadratic Equations to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 5 Quadratic Equations

→ The general form of a linear equation in one variable is ax + b = c.

→ Any equation of the form p(x) = 0 where p(x) is a polynomial of degree 2, is a quadratic equation.

→ If p(x) = 0 whose degree is 2 is written in descending order of their degrees, then we say that the quadratic equation is written in the standard form.

→ The standard form of a quadratic equation is ax² + bx + c = 0 where a ≠ 0. We can write it as y = ax² + bx + c.

→ There are various occasions in which we make use of Q.E. in our day-to-day life.
Eg : The height of a rocket is defined by a Q.E.

→ Let ax² + bx + c = 0 be a quadratic equation. A real number α is called a root of the Q.E. if aα² + bα + c = 0. And x = α is called a solution of the Q.E.
(i.e.) the real value of x for which the Q.E ax² + bx + c = 0 is satisfied is called its solution.

→ Zeroes of the Q.E. ax² + bx + c = 0 and the roots of the Q.E. ax² + bx + c = 0 are the same.

→ To factorise a Q.E. ax² + bx + c = 0, we find p, q ∈ R such that p + q = b and pq = ac. This process is called Factorising a Q.E. by splitting its middle term.
Eg : 12x² + 13x + 3 = 0
here a = 12; b = 13; c = 3
a.c = 12 × 3 = 36 = 4 × 9 and
b = 4 + 9 here p = 9 and q = 4
Now 12x² + 13x + 3 = 0
⇒ 12x² + 9x + 4x + 3 = 0
⇒ 3x(4x + 3) + 1 (4x + 3) = 0
⇒ (4x + 3) (3x + 1) = 0
Here 4x + 3 = 0 or 3x + 1 = 0
⇒ 4x = -3 or 3x = -1
⇒ x = [latex]\frac{-3}{4}[/latex] or [latex]\frac{-1}{3}[/latex]
[latex]\frac{-3}{4}[/latex] and [latex]\frac{-1}{3}[/latex] are called the roots of the Q.E. 12x² + 13x + 3 = 0 and x = [latex]\frac{-3}{4}[/latex] or [latex]\frac{-1}{3}[/latex] is the solution of the Q.E. 12x² + 13x + 3 = 0.

→ In the above example, (4x + 3) and (3x +1) are called the linear factors of the Q.E. 12x² + 13x + 3 = 0.

→ We can factorise a Q.E. by adjusting its left side so that it becomes a perfect square.
Eg: x² + 6x + 8 = 0
⇒ x² + 2.x.3 + 8 = 0
⇒ x² + 2.x.3 = -8
The L.H.S. is of the form a² + 2ab
∴ By adding b² it becomes a perfect square
∴ x² + 2.x.3 + 3² = -8 + 3²
⇒ (x + 3)² = -8 + 9
⇒ (x + 3)² = 1
⇒ x + 3 = ± 1 Now we take x + 3 = 1 or x + 3 = -l
⇒ x = -2 or x = -4

→ Adjusting a Q.E. of the form ax² + bx + c = 0 so that it becomes a perfect square.
Step – 1 : ax² + bx + c = 0 ⇒ ax² + bx = -c ⇒ x² + [latex]\frac{b}{a}[/latex]x = [latex]\frac{-c}{a}[/latex]
Step – 2 :

Step – 3 :

Step – 4 : Solve the above.
E.g: 5x² – 6x + 2 = 0

→ Let ax² + bx + c = 0 (a ≠ 0) be a Q.E., then b² – 4ac is called the Discriminant of the Q.E.

→ If b² – 4ac > 0, then the roots of the Q.E. ax² + bx + c = 0 are given by
x = [latex]\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/latex]. This is called quadratic formula to find the roots.

The nature of the roots of a Q.E. can be determined either by its discriminant or its graph.
Q.E.: y = ax² + bx + c.

Students can go through AP SSC 10th Class Maths Notes Chapter 4 Pair of Linear Equations in Two Variables to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 4 Pair of Linear Equations in Two Variables

→ An equation of the form ax + by + c = 0 where a, b, c are real numbers and where at least one of a or b is not zero (i.e, a² + b² ≠ 0) is called a linear equation in two variables x and y.

→ A pair of equations in the same two variables forms a pair of linear equations. The system of pair of equations in general a₁x + b₁y + c₁ = 0 ; a₂x + b₂y+ c₂ = 0
where a₁, a₂, b₁, b₂, c₁, c₂ ∈ R such that a₁² + b₁² ≠ 0 and a₂² + b₂² ≠ 0

→ A pair of linear equations in two variables can be represented and solved by
a) Graphical method
b) Model method
c) Algebraic methods
i) Substitution method
ii) Elimination method
iii) Cross-multiplication method.

→ Graphical method: The two linear equations in two variables are represented by two straight lines on a graph sheet.
a) If they intersect at a point, then the point gives the unique solution of the two equations. In this case the two equations are consistent.
b) If the lines coincide, then there are infinitely many solutions. Each point on the line represents a solution. In this case, we say that the pair of equations is dependent or consistent.
c) If the two lines are parallel to one another, then the pair of equations has no solution. In this case we say that the pair of equations is inconsistent. Substitution method : In this method, we make one of the variables x or y as the subject from the first equatiori. We substitute this value in the second equation and get the value of the variable involved, then by substituting this value in any of the equations we get the value of second variable.
Eg : 2x + 4y = 16 …….. (1)
3x – 8y = – 18 …….. (2)
From equation (1); 2x + 4y = 16 ⇒ 2x = 16 – 4y ⇒ x = [latex]\frac{16-4y}{2}[/latex]
Substituting x = [latex]\frac{16-4y}{2}[/latex] in the second equation
[latex]3\left(\frac{16-4 y}{2}\right)[/latex] – 8y = -18
48 – 12y – 16y = – 18 × 2
-28y = -36 – 48
y = [latex]\frac{-84}{-28}[/latex] = 3
Substituting y = 3 in (1), 2x + 4y = 16
2x + 4(3) = 16
2x = 16 – 12
x = 2

→ Elimination method: In this method we first try to eliminate one of the two variables and by reducing the system to equation in one variable. We then solve for the variable.
The following steps may be adopted:
Step – 1: Multiply both the equations by some suitable non-zero constants to make the co-efficients of one variable (either x or y) numerically equal.
Step – 2: Add or subtract one equation from other so that one variable gets eliminated. If we get an equation in one variable, proceed to step 3.
If in step – 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions.
If in step – 2, we obtain a false statement involving no variable, then the original pair of equations has no solutions, i.e., it is inconsistent.
Step – 3: Solve the equation in one variable (x or y) so obtained to get its value.

→ Cross-multiplication method: Let the pair of equations be a₁x + b₁y + c₁ = 0 ; a₂x + b₂y+ c₂ = 0

→ In every case, the obtained solutions should always be verified with the original equations.
Let a₁x + b₁y + c₁ = 0 and a₂x + b₂y+ c₂ = 0, form a pair of linear equations. Then the following situations can arise,
Case – (i): [latex]\frac{a_{1}}{a_{2}}[/latex] ≠ [latex]\frac{b_{1}}{b_{2}}[/latex] – pair of linear equations is consistent.
Case – (ii): [latex]\frac{a_{1}}{a_{2}}[/latex] = [latex]\frac{b_{1}}{b_{2}}[/latex] ≠ [latex]\frac{c_{1}}{c_{2}}[/latex] – pair of linear equations is inconsistent.
Case – (iii): [latex]\frac{a_{1}}{a_{2}}[/latex] = [latex]\frac{b_{1}}{b_{2}}[/latex] = [latex]\frac{c_{1}}{c_{2}}[/latex] – pair of linear equations is dependent and consistent.

→ There are several situations which can be mathematically represented by two equa¬tions that are not linear to start with. But we alter them so that they are reduced to a pair of linear equations.

→ The pair of values of the variables x and y for which the pair of equations is satisfied is called the solution pair.

Students can go through AP SSC 10th Class Maths Notes Chapter 3 Polynomials to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 3 Polynomials

→ Polynomial: An algebraic expression in which the variables involved have only non-negative integer power is called a polynomial.
Ex: 2x + 5, 3x² + 5x + 6, -5y, x³, etc.

→ Polynomials are constructed using constants and variables.

→ Coefficients operate on variables, which can be raised to various powers of non negative integer exponents.
, etc. are not polynomials.

→ General form of a polynomial having n^th degree is p(x) = a₀xⁿ + a₁x^n-1 + a₂x^n-2 …….. + a_n-1x + a_n where a₀, a₁, a₂,…… a_n-1, a_n are real coefficients and a₀ ≠ 0.

→ Degree of a polynomial:
The exponent of the highest degree term in a polynomial is known as its degree.
In other words, the highest power of x in a polynomial f(x) is called the degree of a polynomial f(x).
Example:
i) f(x) = 5x + [latex]\frac{1}{3}[/latex] is a polynomial in the variable x of degree 1.
ii) g(y) = 3y² – [latex]\frac{5}{2}[/latex]y + 7 is a polynomial in the variable y of degree 2.

→ Zero polynomial: A polynomial of degree zero is called zero polynomial that are having only constants.
Ex: f(x) = 8, f(x) = -[latex]\frac{5}{2}[/latex]

→ Linear polynomial: A polynomial of degree one is called linear polynomial.
Ex: f(x) = 3x + 5, g(y) = 7y – 1, p(z) = 5z – 3.
More generally, any linear polynomial in variable x with real coefficients is of the form f(x) = ax + b, where a and b are real numbers and a ≠ 0.
Note: A linear polynomial may be a monomial or a binomial because linear polynomial f(x) = [latex]\frac{7}{5}[/latex]x – [latex]\frac{5}{2}[/latex] is a binomial, whereas the linear polynomial g(x) = [latex]\frac{2}{5}[/latex] x is a monomial.

→ Quadratic polynomial: A polynomial of degree two is called quadratic polynomial.
Ex: f(x) = 5x², f(x) = 7x² – 5x, f(x) = 8x² + 6x + 5.
More generally, any quadratic polynomial in variable x with real coefficients is of the form f(x) = ax² + bx + c, where a, b and c are real numbers and a ≠ 0.
Note: A quadratic polynomial may be a monomial or a binomial or a trinomial.
Ex: f(x) = [latex]\frac{1}{5}[/latex]x² is a monomial, g(x) = 3x² – 5 is a binomial and
h(x) = 3x² – 2x + 5 is a trinomial.

→ Cubic polynomial: A polynomial of degree three is called cubic polynomial.
Ex: f(x) = 8x³, f(x) = 9x³ + 5x²
f(y) = 11y³ – 9y² + 7y,
f(z) = 13z³ – 12z² + 11z + 5.

→ Polynomial of degree ‘n’ in standard form: A polynomial in one variable x of degree n is an expression of the form f(x) = a_nxⁿ + a_n-1x^n-1 + …….. + a₁x + a₀ where a₀, a₁, a₂,…… a_n, a_n are constants and a_n ≠ 0.
In particular, if a₀ = a₁ = a₂ = …… = a_n = 0 (all the constants are zero; we get the constants zero), we get the zero polynomial which is not defined.

→ Value of a polynomial at a given point: If p(x) is a polynomial in x and α is a real number. Then the value obtained by putting x = a in p(x) is called the value of p(x) at x = α.
Ex : Let p(x) = 5x² – 4x + 2, then its value at x = 2 is given by
p(2) = 5(2)² – 4(2) + 2 = 5(4) – 8 + 2 = 20 – 8 + 2 = 14 Thus, the value of p(x) at x = 2 is 14.

→ Graph of a polynomial: In algebraic or in set theory language, the graph of a polynomial f(x) is the collection (or set) of all points (x, y) where y = f(x).
i) Graph of a linear polynomial ax + b is a straight line.
ii) The graph of a quadratic polynomial (ax² + bx + c) is U – shaped, called parabola.

→ If a > 0 in ax² + bx + c, the shape of parabola is opening upwards ‘∪’.

→ If a < 0 in ax² + bx + c, the shape of parabola is opening downwards ‘∩’

→ Relationship between the zeroes and the coefficient of a polynomial:

Note: Formation of a cubic polynomial : Let α, β, and γ be the zeroes of the polynomial.
∴ Required cubic polynomial = (x – α) (x – β) (x – γ).

→ How to make a quadratic polynomial with the given zeroes : Let the zeroes of a quadratic polynomial be α and β.
∴ x = α, x = β
Then, obviously the quadratic polynomial is (x – α) (x – β) i.e., x² – (α + β)x 4- ap.
i.e., x² – (sum of the zeroes) x + product of the zeroes.

→ Division Algorithm : If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that, p(x) = g(x) × q(x) + r(x)
i.e., Dividend = Divisor × Quotient + Remainder
where, r(x) = 0 or degree of r(x) < degree of g(x). This result is known as the division algorithm for polynomials.

→ Some useful relations:
α² + β² = (α + β)² – 2αp
(α – β)² = (α + β)² – 4αβ
α² – β² = (α + β) (α – β) = (α + β)[latex]\sqrt{(\alpha+\beta)^{2}-4 \alpha \beta}[/latex]
α³ + β³ = (α + β)³ – 3αβ(α + β)
α³ – β³ = (α – β)³ + 3αβ(α – β)

Students can go through AP SSC 10th Class Maths Notes Chapter 2 Sets to understand and remember the concepts easily.

AP State Syllabus SSC 10th Class Maths Notes Chapter 2 Sets

→ Set theory is comparatively a new concept in mathematics.

→ This theory was developed by George Cantor.

→ A well defined collection of objects or ideas is known as “set”.

→ Well defined means that:
i) All the objects in the set should have a common feature or property.
ii) It should be possible to decide whether any given object belongs to the set or not.
Example or comparision of well defined and not well defined collections:

Not well defined collections	Well defined collections
i) A family of rich persons	i) A family of persons having more than one crore rupees
ii) A group of tall students	ii) A group of students, with height 160 cm or more
iii) A group of numbers	iii) A group of even natural numbers less than 15

→ Some more examples of well defined collections:
i) Vowels of English alphabets, namely a, e, i, o, u.
ii) Odd natural numbers less than 11, namely 1, 3, 5, 7, 9.
iii) The roots of the equation x² – 3x + 2 = 0, i.e., 1 and 2.

→ Objects, elements and members of a set are synonymous words.

→ Sets are usually denoted by the capital letters like A, B, C, X, Y, Z, etc.

→ An object belonging to a set is known as a member/element/individual of the set.

→ The elements of a set are represented by small case letters,
i.e., a, b, c, , x, y, z, etc.

→ If ‘b’ is an element of a set A, then we say that ‘b’ belongs to A.

→ The word ‘belongs to’ is denoted by the Greek symbol ‘∈’.

→ Thus, in a notation form, ‘b’ belongs to A is written as b ∈ A and ‘c’ does not belong to ‘A’ is written as c ∉ A.

→ Representation of sets: Sets are generally represented by the following two methods.
i) Roster (or) Tabular form
ii) Rule method (or) Set builder form.

→ Roster (or) Tabular form: In this form, all elements of the set are written, separated by commas, within curly brackets.
Example:
i) The set of all natural numbers less than 5 is represented as N = {l,2,3,4}
ii) The set of all letters in the word “JANUARY” is represented as B = {A, J, N, R, U, Y}
Note:
a) In a set notation, order is not important.
b) The elements of a set are generally not repeated in a particular set.

→ Set builder form (or) Rule method: In this method, a set is described by using a representative and stating the property (or) properties which the elements of the set satisfy, through the representative.
Example:
i) Set of all natural numbers less than 5.
A = {x : x ∈ N, x < 5}
ii) Set of vowels of the English alphabet.
V = {x : x is a vowel in the English alphabet)
Note: It may be observed that we describe the set by using a symbol (x or y or z etc.) for elements of the set.

→ Types of set:

→ Empty set (or) Null set (or) Void set: A set, which does not contain any element is called an empty set (or) a null set (or) a void set.

→ Empty set is denoted by ∅ (or) { }

Example :
A = (x : x is a natural number smaller than 1}
B = {x : x² – 2 = 0 and x is a rational number}
C = (x : x is a man living on the moon}
Note: ∅ and { 0 } are two different sets. {0} is a set containing the single element ‘0’ while { } is a null set.

→ Singleton set: A set consisting of a single element is called a singleton set.
Examples:
{ 0 }, {- 7} are singleton sets.

→ Finite set: A set which is possible to count the number of elements of that set is called finite set.
Example – 1 : The set {3, 4, 5, 6} is a finite set, because it contains a definite number of elements i.e., only 4 elements.
Example – 2 : The set of days in a week is a finite set.

Example – 3 : An empty set, which does not contain any element (no element) is also a finite set.

→ Infinite set: A set whose elements cannot be listed, that type of set is called infinite set.

Example : i) B = {x : x is an even number}
ii) J = {x : x is a multiple of 7}
iii) The set of all points in a plane. s|s A set is infinite if it is not finite.

→ Equal sets: Two sets are said to be equal, if they have exactly the same elements.
For example: The set A and B are having same elements i.e., watch, ring, flower are said to be equal sets.

→ Cardinal number: The number of elements in a set is called the cardinal number of the set.
Example: Consider the finite set A = {1, 2, 4}
Number of elements in set ‘A’ is 3.
It is represented by n(A) = 3

→ Universal set: A set which consists of all the sets under consideration (or) discussion is called the universal set. (or) A set containing all objects or elements and of which all other sets or subsets.
It is usually denoted by ∪ (or) μ.

The universal set is usually represented by rectangles.
Example:
i) The set of real numbers is universal set for number theory.
Here ‘R’ is a universal set.
ii) If we want to study various groups of people of our state, universal set is the set of all people in Andhra Pradesh.

→ Subset: If every element of first set (A) is also an element of second set (B), then first set (A) is said to be a subset of second set (B).

→ It is represented as A ⊂ B.
Example :
Set A = {2, 4, 6, 8} is a subset of .
Set B = {1,2, 3, 4,5, 6, 7, 8}

→ Empty set is a subset of every set.

→ Every set is a subset of itself.

→ Consider ‘A’ and ‘B’ are two sets, if A ⊂ B and B ⊂ A ⇔ A = B.

→ A set doesn’t change if one or more elements of the set are repeated.

→ If A ⊂ B, B ⊂ C ⇒ A ⊂ C.

→ Venn Diagrams: Venn-Euler diagram or simply Venn diagram is a way of representing the relationships between sets.

→ These diagrams consist of rectangles and closed curves usually circles.
Example: Consider that U = {1, 2, 3, ……, 10} is
the universal set of which, A = {2, 4, 6, 8, 10} is a subset.
Then the Venn diagram is as:

→ Basic operations on sets: In sets, we define the operations of union, intersection and difference of sets.

→ Union of sets: The union of two or more sets is the set of all those elements which are either individual (or) both in common.

→ In symbolic form, union of two sets A and B is written as A ∪ B and usually read as “A union B”.

→ Set builder form of A ∪ B is A ∪ B = (x : x ∈ A or x ∈ B}

→ The union of the sets can be represented by a Venn diagram as shown (shaded portion).

→ It is evident from the definition that A ⊆ A ∪ B; B ⊆ A ∪ B.

→ Roster form of union of sets : Let A = {a, e, i, o, u} and B = (a, i, u} then A ∪ B = {a, e, i, o, u} ∪ { a, i, u} = {a, e, i, o, u}

→ Intersection of sets: The intersection of two sets A and B is the set of all those elements which belong to both A and B.

→ We denote intersection by A ∩ B.

→ We read A ∩ B as “A intersection B”.

→ Symbolically, we write A ∩ B = (x : x ∈ A and x ∈ B}

→ The intersection of A and B can be illustrated in the Venn diagram as shown in the shaded portion in the adjacent figure.

→ The intersection of A and B can be illustrated in the Roster form:
If A = {5, 6, 7, 8} and B = {7, 8, 9, 10} then A ∩ B = {7, 8}

→ Disjoint set: Consider A and B are two finite sets and if there are no common element in both A and B. Such set is known as disjoint set (or A ∩ B = ∅).
(or)
Two sets (finite) are said to be disjoint sets if they have no common elements. That is if the intersection of two sets is a null set they are disjoint sets.

→ The disjoint sets can be represented by means of the Venn diagrams as shown in the adjacent figure.

→ Difference of sets: The difference of sets A and B is the set of elements which belong to ‘A’ but do not belong to ‘B’.

→ We denote the difference of A and B by A – B or simply “A minus B”.

→ Set builder form of A – B is (x : x ∈ A and ∉ B}

→ Venn-diagram of A – B is

→ Venn-diagram of B – A is

→ A – B ≠ B – A

→ Fundamental theorem on sets:
If A and B are any two sets then n (A ∪ B) = n (A) + n (B) – n (A ∩ B) where
n (A ∪ B) = number of elements in the set (A ∪ B), also called cardinal number of A ∪ B
n (A) = number of elements in the set A also called cardinal number of A
n (B) = number of elements in the set B also called cardinal number of B

AP State Syllabus AP Board 8th Class Biology Important Questions Chapter 11 Why Do We Fall Ill

AP State Syllabus 8th Class Biology Important Questions 10th Lesson Why Do We Fall Ill

8th Class Biology 10th Lesson Why Do We Fall Ill 1 Mark Important Questions and Answers

Question 1.
What is health?
Answer:
Health is a state of physical, mental and social well – being.

Question 2.
On what factors the health of an individual depends?
Answer:
The health of an individual is dependent on his or her physical surroundings and his / her economic status.

Question 3.
What is a disease ?
Answer:
Disease is actually self – explanatory. In other words, literally means being uncomfortable.

Question 4.
What is necessary for individual health ?
Answer:
Social equality and harmony are necessary for individual health.

Question 5.
What will happen if there is a disease ?
Answer:
When there is a disease, either the functioning or the appearance of one or more systems of the body will change for the worse.

Question 6.
What are acute diseases ?
Answer:
Some diseases last for only very short periods of time and these are called acute diseases.

Question 7.
What are chronic diseases ?
Answer:
Chronic diseases have very drastic, long – term effects on people’s health as compared to acute diseases.

Question 8.
What is the cause of a disease ?
Answer:
Lack of good nourishment may be the cause of a disease.

Question 9.
What are infectious diseases ?
Answer:
Diseases where microbes are the immediate causes are called infectious diseases.

Question 10.
Which bacteria is responsible for peptic ulcers ?
Answer:
Helicobacter pylori is responsible for peptic ulcers.

Question 11.
Name the organisms that cause diseases.
Answer:
Organisms that cause diseases are virus, bacteria, fungi, protozoans and worms.

Question 12.
Name the diseases caused by bacteria.
Answer:
Typhoid, cholera, tuberculosis and anthrax are caused by bacteria.

Question 13.
What diseases are caused by protozoans ?
Answer:
Protozoans cause malaria and kalaazar.

Question 14.
What are communicable diseases ?
Answer:
Diseases that spread from an infected person to other person by many microbial agents are called communicable diseases.

Question 15.
What is the function of our immune system ?
Answer:
In our body, the immune system fight and kill the disease causing organisms that enter into our body and defend us from diseases.

Question 16.
What are vectors ?
Answer:
Many diseases transmitted by other animals. These animals carry the infecting agents from a sick person to a healthy person. Such animals are called vectors. Ex: Mosquitoes.

Question 17.
Name the diseases caused by mosquitoes.
Answer:
Encephalitis or brain fever, filaria or elephantiasismalaria, dengue etc., are caused by mosquitoes.

Question 18.
Name the disease that causes physical contact.
Answer:
AIDS disease is caused by physical contact.

Question 19.
How do we kill microbes?
Answer:
By using antibacterial and anti – viral medicines we can kill microbes and also there are drugs that kill protozoa such as malarial parasite.

Question 20.
Why making anti – viral medicines is harder than making antibacterial medicines ?
Answer:
Because viruses have few biochemical mechanisms of their own.

Question 21.
What are infectious diseases?
Answer:
Diseases where microbes are the immediate causes are called infectious diseases.

Question 22.
What are symptoms?
Answer:
Some characteristic signs or indications that appear during sickness can help us to identify the sickness are called symptoms!

Question 23.
What is manifestation?
The appearance of the symptoms of a disease is called manifestation of the disease.

Question 24.
What is immunization?
Answer:
The creation of immunity usually against a particular disease, especially treatment by vaccination of an organism for the purpose of making it immune to a particular disease.

Question 25.
What are the different means by which infectious diseases are spread?
Answer:
Infectious diseases are spread through contaminated air, water, food and vectors like mosquitoes, flies, cockroaches, snails and even lies.

Question 26.
What are the vaccines available for preventing infectious diseases?
Answer:
There are vaccines against tetanus, diphtheria, whooping cough, measles, polio and many others.

Question 27.
Who discover vaccine for small pox for the first time?
Answer:
An English physician named Edward Jenner discovered vaccine forsmall pox for the first time.

Question 28.
Why are we normally advised to take bland and nourishing food when we are sick?
Answer:
When we fall sick our normal body functions will be affected and the digestion becomes slow, so it is advised to take bland and nourishing food.

Question 29.
What is needed to be healthy?
Answer:
Proper and sufficient nourishment and clean surroundings and food helps lis to be healthy.

Question 30.
Name the diseases that do not spread.
Answer:
Non – infectious diseases like cancer, high blood pressure do not spread.

8th Class Biology 10th Lesson Why Do We Fall Ill 2 Marks Important Questions and Answers

Question 1.
What are the diseases caused by bacteria in Man?
Answer:

1. Cholera
2. Typhoid
3. Diptheria
4. Whooping cough
5. Tetanus
6. Tuberculosis
7. Leprosy

Question 2.
Name the diseases caused by viruses in man.
Answer:

1. Small pox
2. Chicken pox
3. Measles
4. Mumps
5. Poliomelitis

Question 3.
What are the diseases caused by Protozoans in Man?
Answer:

1. Malaria
2. Kala Azar
3. Amoebic Desentry

8th Class Biology 10th Lesson Why Do We Fall Ill 4 Marks Important Questions and Answers

Question 1.
Draw the picture of SARS VIRUS in your scrap book and write the size of SARS VIRUS.
Answer:
Picture of SARS VIRUS

The size of SARS VIRUS is 500 nano metres, which is half a micrometre, which is one thousandth of a millimetre.

Question 2.
Draw the picture of staphylococci bacteria. In what way it affect the health of people?
Answer:
Staphylococci Bacteria

Staphylocoecci bacteria cause acne.

Question 3.
Draw a picture showing an adult round worm and answer the given questions:
a) What is the scientific name of round worm?
b) Where does it live in human beings?
Answer:
Round Worm

a) The Scientific name of Round Worm is Ascaris lumbricoides.
b) It stays in the small intestine of human beings.

Question 4.
Draw a picture showing the air borne diseases will spread in the air.
Answer:
Spread of air borne diseases

Question 5.
Draw a flow chart which shows common methods of transmission of diseases. How the animals transmit diseases? Explain.
Answer:

We lie in an environment that is full of many other creatures apart from us. It is inevitable that many diseases will be transmitted by other animals.
These animals carry the infecting agents from a sick person to another potential host. These animals are intermediates and are called vectors.
The commonest vectors are mosquitoes. The female mosquitoes need highly nutri¬tious food in the form of blood in order to be able to lay mature eggs. In this way they can transfer diseases from person to person.

Question 6.
How does death occurs in AIDS patients?
Answer:

1. In HIV infection, the virus goes to the immune system and damage its function.
2. The body can no longer fight off with even minor infections.
3. Even mild cold becomes Pneumonia. Thus ultimately these infections kill the people suffering from HIV – AIDS.

8th Class Biology 10th Lesson Why Do We Fall Ill Important Questions and Answers

Question 1.
Prepare a pamphlet to aware people to maintain a hygienic surrounding.
Answer:
Pamphlet
“Prevention is better than cure”. So, it is better for us to prevent diseases rather than treatment. You should keep our surroundings clean and hygienic wash your hands with soap or handwash lotion thoroughly before consuming food. Wash your hands with soap after defecation. You should consume your food only when it is hot. Do exercises daily to keep you fit and healthy. Try to cultivate good habits which keep you healthy always. Use mosquito nets to avoid mosquito bites.
“SWACH BHARAT – SWASTH BHARAT”.

AP State Syllabus AP Board 8th Class Biology Important Questions Chapter 10 Not For Drinking-Not For Breathing

AP State Syllabus 8th Class Biology Important Questions 10th Lesson Not For Drinking-Not For Breathing

8th Class Biology 10th Lesson Not For Drinking-Not For Breathing 1 Mark Important Questions and Answers

Question 1.
Which department issues the pollution under control certificate?
Answer:
The pollution check up centre issues the certificate.

Question 2.
For how much time is it valid?
Answer:
It is valid for six months.

Question 3.
For which types of vehicles has it been issued?
Answer:
All types of vehicles like motor bike, scooter, car, bus, lorry etc.

Question 4.
What is emission test?
Answer:
The test conducting of the gases releasing from the vehicle is called emission test.

Question 5.
What components are tested in the pollution check up centre?
Answer:
Carbon dioxide, carbon monoxide, nitrogen, hydrocarbons, sulphur dioxide etc.

Question 6.
What will happen if harmful microorganisms or substances enter your body? How do you feel?
Answer:
If harmful microorganism enter the body the normal functioning of the body will be disrupted or disturbed. We feel sick.

Question 7.
What is the effect of rapid increase in the number of vehicles?
Answer:
With the number of vehicles increase, the pollution also increases, which causes air pollution.

Question 8.
What is pollution?
Answer:
Anything that is harmful to the environment is called pollution.

Question 9.
When do all the living organisms with in the environment will be healthy and thriving?
Answer:
When everything is working the way it should be all the living organisms with the environment including humans are healthy and thriving.

Question 10.
Name the diseases caused by air pollution.
Answer:
Diseases of the respiratory system like lung cancer, Asthma etc.

Question 11.
What do our elders talk about the environment?
Answer:
Our elders talk about the blue sky, clean water and fresh air that was available in their times.

Question 12.
What is our environment made up of?
Answer:
The environment is made up of systems, cycles and specialized relationships between living and non – living elements.

Question 13.
Name some substances which impact the health of our earth.
Answer:
Litter, car exhaust, motor oil, used tires, smoke, chemicals, disposed computer, mobile phone material etc., all of these can have an instant or a gradual impact on the health of our earth.

Question 14.
What are the four major gases in the air?
Answer:
The four major gases are nitrogen, oxygen, argon and carbondioxide.

Question 15.
Which is the essential element for survival of all living organisms?
Answer:
The atmosphere contains 21 % of oxygen which is essential for survival of all living organisms.

Question 16.
How is carbon dioxide important?
Answer:
Carbon dioxide which is 0.033% is essential for the process of photosynthesis in plants.

Question 17.
What is air pollution?
Answer:
The contamination of air by impurities which may have harmful impacts on the living organisms and the non-living components of the environment is called air pollution.

Question 18.
What are pollutants?
Answer:
Pollutants are the substances which contaminate the environment.

Question 19.
Name the main pollutants in the atmosphere.
Answer:
Suspended particulate matter, carbondioxide, carbon monoxide, oxides of sulphur and nitrogen CFCs and heavy metals.

Question 20.
Name the natural disasters in the world.
Answer:
The natural disasters in the world are volcanic eruptions, forest fires and sand storms which leads to air pollution.

Question 21.
What is the problem with airborne pollutants?
Answer:
The problem with airborne – pollutants is the way winds criss – cross the globe, picking up pollutants and carrying them all over the world. Air pollution is not just a local concern.

Question 22.
What pollutants are released by forest fires?
Answer:
Forest fires release carbon particles (ash) into the air and pollute the air.

Question 23.
What gas is released from decay of organic matter?
Answer:
Decay of organic matter releases Ammonia gas into air.

Question 24.
What gas is released from decay of organic matter lying under water?
Answer:
Decay of organic matter lying under water releases Methane gas as air pollution.

Question 25.
How do pollen grains pollute the air?
Answer:
Pollen grains released by plants remain floating in the air and pollute it.

Question 26.
What gases are produced by burning fuels?
Answer:
Burning fuels pollute the air by producing carbon – monoxide, sulphur dioxide, smoke, soot and ash.

Question 27.
What gases are emitted by vehicles?
Answer:
Sulphur dioxide, nitrogen dioxide, carbon monoxide, unburnt hydrocarbons, lead compounds and soot.

Question 28.
Name the polluted areas and the factories present in that area.
Answer:

1. Prakasam district – Granite factory
2. Macharla – Cement factory
3. Piduguralla – Lime stone

Question 29.
Name various industries that pollute the air.
Answer:
Granite, lime, cement factories pollute the air by releasing sulphur dioxide, nitrous oxide, chlorine fly ash, dust, asbestos dust etc.

Question 30.
How local people are suffering living near Parawada and Krishnapatnam Thermal Power Plants?
Answer:
The Thermal power plants release fly ash, sulphur dioxide and radio active substances into air, water and land, local people are suffering from lung cancer and skin allergies.

Question 31.
What are the problems face by the people living near the granite factory?
Answer:
The people living near the granite factory are facing several health problems like respiratory bronchitis and asthma.

Question 32.
How are Nuclear power plants dangerous?
Answer:
The two problems of Nuclear power plants are radio active waste and melt downs.

Question 33.
What are melt downs?
Answer:
Melt downs are caused by too much heat in the power plant. During melt down the power plant makes more Radio active pollution.

Question 34.
How do power plants release power?
Answer:
Power plants produce power by using water, coal and gas.

Question 35.
How do Nuclear power plants produce power?
Answer:
By using Radio active elements like uranium.

Question 36.
How agriculture pollutes land and water?
Answer:
Use of fertilizers and pesticides in agriculture pollutes not only air but also land and water.

Question 37.
What is the result of deforestation?
Answer:
The destruction of forests and woods is called deforestation. It has resulted in the reduction of indigenous forests.

Question 38.
If forests reduce what would happen?
Answer:
If forests reduce the level of carbondioxide increases resulting to global warming.

Question 39.
In which devices chloro flouro carbons are used?
Answer:
Chloro flouro carbons (CFC) are used in refrigerators, Air Conditioners and aerosol sprays. CFC pollutes air by depleting the ozone layer.

Question 40.
How is mining cause pollution?
Answer:
Mining of coal and stone releases coal dust and stone dust that cause air pollution.

Question 41.
Why do the currently cars and buses not allowed to drive to the Taj Mahal?
Answer:
The motor vehicles and the Industries located in and around Agra for rubber processing, chemicals oil refinery of Mathura, iron foundries have been responsible for the colour change of Taj Mahal from white to yellow.

Question 42.
What did the Archeological department of lndia declared towards Taj Mahal?
Answer:
The Archeological department declared that 2[latex]\frac{1}{2}[/latex] km around Taj Mahal is no drive zone.

Question 43.
What is the unforgettable tragedy of Bhopal?
Answer:
On second December 1984 about 3000 human beings died, about 5000 were paralized in just one night at Bhopal.

Question 44.
What is the reason for the tragedy at Bhopal?
Answer:
The reason for this is the leakage of Methyl isocynate into the air from an insecticide factory managed by union carbide.

Question 45.
What are the affects caused by air pollution?
Answer:
Air pollution causes certain diseases including shortness of breath, sore throat, chest pain, nausea, asthma, bronchitis and lung cancer.

Question 46.
How is like the air pollution?
Answer:
Air pollution is like a slow poison.

Question 47.
How to reduce air pollution from industries?
Answer:
Install electrostatic precipitators in the chimney of industries.

Question 48.
How to reduce pollution from vehicles?
Answer:
Reduce vehicular emission by using non-polluting fuels like CNG.

Question 49.
What is Vanamahotsav?
Answer:
We can protect plants and trees. On the day of Vanamahotsav lakhs of trees are planted in July every year.

Question 50.
Name one of the most polluted area in India.
Answer:
Patancheru, a suburban mandal in Medak district is a major industrial hub of the state is one of the most polluted area in India.

Question 51.
How are the villages badly affected by pollution?
Answer:
They are affected with some diseases like cancer, respiratory diseases and heart diseases by poisons in air, water and on land.

Question 52.
What is water pollution?
Answer:
The contamination of water with unwanted and harmful substances such as sewage, toxic chemicals, industrial waste etc., is called water pollution.

Question 53.
What is the character of normal water?
Answer:
Normal water is colourless without any smell or any unwanted substances. Water which is suitable for drinking is called potable water.

Question 54.
How Musi river got polluted?
Answer:
The people living near Musi throw large quantities of garbage, unwanted sewage, industrial waste, dead bodies, polythene bags, hot water and statues of deities and many other materials and made the river polluted.

Question 55.
What is definite source of pollution?
Answer:
Definite source of pollution is due to discharges from a single source, such as industrial site.

Question 56.
What is Biodegradable waste?
Answer:
Biodegradable waste consists of mainly human and animal waste.

Question 57.
How do plant nutrients pollute water?
Answer:
Phosphates sand nitrates – chemical fertilizers from agriculture run – off due to rain and industrial waste enter into water through sewage and pollute the water.

Question 58.
How is heat polluting water?
Answer:
As water, temperature increases, the amount of dissolved oxygen decreases. So thermal pollution often reduces the aquatic life diversity in water.

Question 59.
How is water polluted by sediment?
Answer:
Sediment pollution is formed by the sources such as constructional, agricultural, logging, flooding and city runoff.

Question 60.
What is Eutrophication?
Answer:
The enrichment of water by nutrients leading to excessive plant growth and duplication of oxygen is known as Eutrophication.

Question 61.
How is fluorine hazardous substance to ground water?
Answer:
Fluorine mixed in ground water cause dangerous disease called fluorosis.

Question 62.
What are 3R’s principles?
Answer:
The 3R’s principles are Reduce the usage of the materials, Reuse them for secondary purpose and Recycle the material again and again.

Question 63.
How should we maintain natural resources?
Answer:
We should keep the natural resources clean and healthy not only for us but also future generations.

8th Class Biology 10th Lesson Not For Drinking-Not For Breathing 2 Marks Important Questions and Answers

Question 1.
Complete this flow chart.

Answer:

1. Human activities
2. Volcanic eruptions
3. Forest fires
4. Sand cyclones
5. CFCs
6. Mining
7. Sewage
8. Industrial effluents
9. Toxic chemicals

Question 2.
Complete this flow chart.

Answer:
2) Industrial emissions
3) Atomic power plant radiation
4) Automobile exhausts
5) Fly ash

Question 3.
Heat can be a source of pollution ? How does it effect the aquatic life?
Answer:

1. As the water temperature increases, the amount of dissolved oxygen decreases.
2. Fish and plants require certain temperature and oxygen levels to survive.
3. So, thermal pollution often reduces the aquatic life diversity in the water.

8th Class Biology 10th Lesson Not For Drinking-Not For Breathing 4 Marks Important Questions and Answers

Question 1.
“It is much better to worship Ganesh Idol made of clay than Idol of Plaster of Paris” – said Kavitha. How do you support her ? How do you appreciate her attitude?
Answer:

1. I appreciate Kavitha’s attitude towards pollution free society.
2. ‘Plaster of Paris’ idol consists of different harmful chemicals. During “Nimajjanam” these are immersed in different water bodies which leads to water pollution.
3. Worshipping idols made with clay is eco-friendly.
4. Hence, I appreciate her environmental concern and eco-friendly nature.

Question 2.
Prepare some slogans which create awareness among people on air pollution.
Answer:

1. Stop pollution – Save life
2. Polluting water – Ending our lives
3. Save the nature – Nature will save you
4. Live and let live.
5. Nature is for humans need – Not for his greed.
6. Solar energy – Forever energy

Question 3.
What are the industries that cause water pollution?
Answer:

1. Textile industries
2. Chemical industries
3. Leather industries
4. Pesticide industries
5. Paint factories
6. Fertilizer industries – are causing water pollution.

8th Class Biology 10th Lesson Not For Drinking-Not For Breathing Important Questions and Answers

Question 1.
Natural resources are the divine gift for us by nature. We can use these resources in a meaningful way which helps us. If we destroy these resources human life will become an unsolvable puzzle. We should keep these resources clean and healthy not only for us but also for future generation.
Read the above paragraph and answer the questions given below.
a) How should we use our natural resources?
b) What would happen if we use natural resources injudiciously?
Answer:
a) We should use the natural resources discriminately. They are the gifts of nature. For example we should minimise the usage of fossil fuels and encourage the usage of alternative energy sources like solar energy and wind energy. We should use CNG in place of diesel and petrol in vehicles to restore fossil fuels for longer periods.
b) Man’s life on earth turns into a mysterious puzzle. Life is not possible for us.

Question 2.
Observe the above diagram and answer the following questions:

1. What does the diagram represent?
2. Which gas is more in quantity in the given picture?
3. What will happen if the percentage of carbon dioxide will increase in the atmosphere?
4. When can you say that carbon dioxide is not a pollutant?

Answer:

1. The above diagram tell us about the percentage of different gases present in our atmosphere.
2. Nitrogen.
3. The increase in CO₂ levels results in the increasing temperatures on the earth. As a result the glaciers in the polar region melt and rise in sea levels occur. It leads to submergence of many cities of the shore.
4. If CO₂ levels are below 0.03%, then it is considered as non – pollutant.

Question 3.
Read the following passage and answer the questions.
Here are two main sources of water pollution; definite sources and non-definite sources. Definite source pollution is due to discharges from a single source, such as an industrial site. It includes factories, waste water treatment facilities, septic systems, and other sources that are clearly discharging pollutants into water sources. Non definite-source pollution involves many small sources that combine to cause significant pollution. For instance, the movement of rain or irrigation water over land picks up pollutants such as fertilizers, herbicides and insecticides carries them into rivers, lakes, reservoirs, coastal waters, or groundwater. Non-definite sources are more difficult to identify, as they cannot be traced back to a particular location. Landfills can also be a non-definite source of pollution, if substances leach from the landfill into water supplies.
a) Which sources of water pollution are difficult to identify?
b) What are definite sources of water pollution? Give two examples.
Answer:
a) Non-definite
b) Definite source pollution is due to discharge from a single source such as an industrial site. Examples are factories, waste water treatment plants etc.