HAPPYDAY SCHOOL SYSTEM PESHAWAR CANTT
FINAL TERM EXAMINATION 2022
Grade: 10th
Paper: Maths
Total Marks: 75
Name:________________________ Class _____ Section______ Date____________
Subject Teacher:___________________________ Class Teacher:________________
GROUP-A
SECTION-A
Q1: Choose the Correct option.
1.
2.
15
If (x +1) ( x-5) = 0 then solutions are:
O. x = -1,5
O. x = 1, -5
2
If x -x-1 = 0 then x = ____________.
−1±√5
√5
O. x = 1, 5
O. x = -1, -5
1±√5
√5
O. 2
O. −1 ± 2
O. 2
O. 1 ± 2
2
3. If the sum of the roots of (a+1)x + (2a+3)x + (3a+4) = 0.
O. 2
O. 0
O. 1
O. 3
4. The sum of the roots of a quadratic equation is 2 and the sum of the cubes of the roots
in 98. The equations is:
O. x2 - 2x -15 = 0
O. x2 - 2x +15 = 0
O. x2 - 4x + 15 = 0
O. None of these
5. Direct variation between a and b is expressed as:
1
1
O. a x b
O. a = b
O. a = 𝑏
O. a x 𝑏
6. If 𝑚 𝑥
1
𝑛
then.
𝑚
O. mn = K
O. m = kn
O. n=km
O. 𝑛 = 𝑘
7. If R = { (0,0), (8,2),(10,3),(14,12)} then dom R = ___________.
O. {0,8,10,14}
O.{0,2,3,12}
O. {8,10,4} O. {0,10}
́
8. (𝐴𝑈𝐵) = _____________.
O. 𝐴́ ∩ 𝐵́
O. 𝐴́ ∪ 𝐵́
O.𝐵́
O. 𝐴́
9. In a Set of data 63,69,66,67,69 median is _____________.
O. 66
O. 63
O. 67
O. 69
10. Cot 𝜃 = ______________.
𝐶𝑜𝑠 𝜃
𝑆𝑖𝑛 𝜃
1
1
O. 𝑆𝑖𝑛 𝜃
O. 𝐶𝑜𝑠 𝜃
O. 𝐶𝑜𝑠 𝜃
O. 𝑆𝑖𝑛 𝜃
11. A ____________ is a chord that contains the centre of a circle.
O. Diameter
O. radius
O. line
O. Angle
12. Two tangents drawn to a circle from a point outside it are of _______________ in
length.
O. Equal
O. Half
O. double
O. triple
13. The measure of the entire circle is ______________.
O. 3600
O. 1800
O. 980
O. 450
14. The measure of the external angle of a regular hexagon is _______________.
𝜋
𝜋
𝜋
O. 3
O. 4
O. 6
O. None of these
15. A circle can be drawn through given three______________.
O. Non- collinear points
O. Collinear points
O. tangents
O. None of these
SECTION-B
Note:- Attempt any nine (9) questions. All questions carry equal marks.
1. Solve by factorization:- 6x2 - 13x + 5 = 0
2. Find the disaiminant of the following quadratic equation. x2 - 4x + 13 = 0
3. Find the value of K if sum of the roots of 2x2+Kx +6 = 0 is equal to the product of its
roots.
4. Find two consecutive positive integers. Whose product is 72.
5. Find the mean proportional of 12,3?
6. Volume of gas “v” varies inversely as pressure P. P = 300 N/m2 when v=4m3. Find
pressure when v =3m3.
7. Find A\B and B\A when.
A = {1,3,5,7},
B= {3,4,5,6,7,8}
8. Using assumed mean find the mean of the following numbers: 1242, 1248, 1252,
1244 , 1249.
4
𝜋
9. If sin 𝜃 = 5 and 2 < 𝜃 < 𝜋 then find other trigonometric ratios.
10. Prove:- (Sec2 𝜃-1) Cos2 𝜃 = Sin2 𝜃.
11. A building that is 21 meters tall casts a shadow 25 meter long. Find the angle of
elevation of the sum to the nearest degree.
12. Domain of a binary relation.
R = {(𝑥, 𝑦)| 𝑦 + 1 = 2𝑥 2 } is set N. Find its range.
SECTION-C
Note:- Attempt any three (03) Questions.
1. One and only one circle can pass through three non-collinear points.
2. Equal chords of a congruent circles subtend equal angles at the corresponding
centers.
3.
If two angles subtended by two chords of congruent circles at the corresponding
centers are equal in measure, then the chords are equal in measures.
4. Inscribe a regular hexagon in a circle of radius 4cm.
HAPPYDAY SCHOOL SYSTEM PESHAWAR CANTT
FINAL TERM EXAMINATION 2022
Grade: 10th
Paper: Maths
Total Marks: 75
Name_________________________ Class _____ Section______ Date____________
Subject Teacher:___________________________ Class Teacher:________________
GROUP-B
SECTION-A
Q1: Choose the Correct option.
15
1. To apply the quadratic formula to 2x2 -x = 3.
O. a = 2, b = -1, c = -3
O. a=2,b=-1,c=3
O. a=2, b=1, c=3
O. a=2, b=-1,c=0
2 1
2. X - = 0, the solution are:
4
O. x = ±
1
O. x = ±
2
1
O. x = ±
O. x = ±
8
1
4
1
16
1
2
1
3. If a and b are the roots of 4x - 3x + 7 = 0 then the value of + .
3
−3
O.
O.
O.
7
4
4. The quadratic formula is :___________.
O. x =
5. If
𝑎
𝑏
=
𝑐
𝑑
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
O. b2-4ac
𝑎
−3
O.
7
𝑏
4
7
O. 4ac O. ax2+bx+c=0
then by alternant property .
𝑎
𝑏
𝑎−𝑏
𝑐−𝑑
𝑎
𝑐
𝑏
𝑑
O. =
O.
=
O.
=
O. =
𝑐
𝑑
𝑏
𝑑
𝑎+𝑏
𝑐+𝑑
𝑎
𝑒
6. If 7:9 :: x:27.
O. x = 21
O. x=3
O. x=7
O. x= 81
7. Which one of the following is an example of disjoint sets?
O. {0,4,8,12} and {6,10,14,18}
O. {1,2,3} and {1,2}
O. {5,2} and {1,2,3}
O. None of these
8. (𝐴𝑈𝐵)́ = _____________.
O. 𝐴́ ∩ 𝐵́
O.𝐵́
O. 𝐴́
O. ∅
9. The difference of the largest and smallest value in the data is called
_____________.
O. Range
O. Mean
O. Mode O. Standard deviation
10. The most frequent value in the data is called its ___________.
O. Mode
O. Mean
O. Median O. G. M
2
11. 1 + tan 𝜃 = __________.
O. sec2 𝜃
O. Sin2 𝜃
O. Cos2 𝜃
O. Cosec2 𝜃
12.Perpendicular from the centre of a circle on a _____________ bisect it.
O. Chord
O. Radius O. Diameter
O. None of these
13.The tangents subtend equal angles at the _______.
O. Centre
O. Radius
O. secant O. line
14.The measure of the semi circle is ________.
O. 1800
O. 2900
O. 3600
O. 900
15.Sin22 + Cos 22 = __________.
O. 1
O. 2
O. (Cos2 𝜃)2
O.Tan2 𝜃
SECTION-B
Note: Attempt any nine (9) questions. All questions carry equal marks.
Solve by quadratic formula. x2 - 8x + 15 = 0
Example the nature of the roots. 3x2 - 5x + 1 = 0
Evaluate: w2+w58+w25.
Find the value of m and n if both sum and product of the roots of the
3
equations mx2-3x-x=0 are equal to − .
5
5. Use synthetic division to find the value of k if -2 is a zero of the
polynomial x3+4x2+kx+8.
6. Pressure “P” of a gas in a container varies directly as temperature T.
When pressure is 50 N/m2. Temperature is 750C. Find pressure when
temperature is 1500.
7. Verify commutative property of union and intersection.
A = {1,2,3}, B = {4,5,6}
8. Find the mean of the weights 45,30,25,36,42,27,31,43,49 and 50 by using
short cut method.
9. Find the values of : 2sin 450 Cos450.
10.Prove the following identities.
1+𝑆𝑖𝑛 𝜃
Tan𝜃 + sec 𝜃 =
𝑐𝑜𝑠𝜃
11.A tree is 50m high. Find the angle of elevation of its top to a point, on the
ground 100m away from the foot of tree.
12.Solve the equation:
1.
2.
3.
4.
√3𝑥+2+ √𝑥
√3𝑥+2− √𝑥
=
4
1
SECTION-C
Note: Attempt any three (03) Questions.
1. Prove that: perpendicular from the centre of a circle on a chord bisect it.
2. Prove that: The two tangents drawn to a circle from a point outside it, are
equal in length.
3. If two areas of a circle are congruent then the corresponding chord are
equal.
4. Circumscribe a square about a circle of radius 5cm.