Half Book 1

1

Shahid is finding the HCF of 9x³y² and 15x²y⁴. He takes the lowest powers. What is the HCF?

A 3x²y² B 3x³y⁴ C 45x³y⁴ D 3xy

2

What is the value of log₂(128)?

A 6 B 7 C 8 D 9

3

Solve: |x| = |x - 2|

A 1 B 0 C 2 D No solution

4

Express 7.2 × 10⁻⁵ in standard notation.

A 0.000072 B 0.0000072 C 720000 D 0.72

5

Mariam is given a right triangle with opposite side 8 and hypotenuse 17. What is cos θ?

A 15/17 B 8/17 C 8/15 D 17/15

6

Nimra needs the LCM of 4x³y and 6x²y². She takes the highest powers. What is the LCM?

A 12x³y² B 12x²y C 24x³y² D 2x²y

7

What is the radius of a circle if its sector has an arc length of 15 cm and a central angle of 3 radians?

A 5 cm B 45 cm C 3 cm D 10 cm

8

Tahir is checking the identity property for union. If A = {1,2} and ∅ is the empty set, what is A ∪ ∅?

A A B ∅ C {1,2,∅} D U

9

A relation R = {(1,2), (2,4), (3,6)} is defined. What is the range of R?

A {1,2,3} B {2,4,6} C {1,2,3,4,6} D {2,4}

10

What is the domain of the relation R = {(1,2), (2,3), (3,4)}?

A {1, 2, 3} B {2, 3, 4} C {1, 2, 3, 4} D {1, 3}

11

Write 0.000450 in scientific notation.

A 4.50 × 10⁻⁴ B 4.5 × 10⁴ C 45 × 10⁻⁵ D 0.45 × 10⁻³

12

Sidra is simplifying (9^2)^0.5. She first multiplies the exponents. What is the result?

A 9 B 3 C 81 D 1

13

The expression x⁻ⁿ is equivalent to:

A 1/xⁿ B -xⁿ C x/n D n/x

14

What is the value of log₇(7)?

A 0 B 1 C 7 D 49

15

What is the value of sin 90°?

A 1 B 0 C 1/2 D √3/2

16

Babar is finding the square root of 16x²/49y⁴. He takes the square root of each part. What is the result?

A 4x/7y² B 4x²/7y² C 8x/7y² D 4x/7y

17

What is the value of log₂(8)?

A 2 B 3 C 4 D 8

18

What is the square root of (x² - 2x + 1)?

A x - 1 B x + 1 C (x - 1)² D x² - 2x + 1

19

What is logₐ(a²)?

A 2 B a C 2a D 1

20

What is the square root of (4x² + 12x + 9)?

A 2x + 3 B 2x - 3 C 4x + 3 D 2x + 9

21

Nadia is factorizing x² - 7x + 12. She needs two numbers with product 12 and sum -7. What is the factorization?

A (x - 3)(x - 4) B (x + 3)(x + 4) C (x - 2)(x - 6) D (x - 1)(x - 12)

22

Any non-zero real number raised to the power of 0 is equal to:

A 1 B 0 C The number itself D -1

23

What is the value of x in √(x - 4) = 3?

A 7 B 13 C 9 D 5

24

A relation R is defined as R = {(x,y) : y = 2x + 1, x ∈ {1,2,3}}. What is the range of R?

A {3,5,7} B {1,2,3} C {2,4,6} D {1,3,5}

25

Simplify: (2a³b)⁰

A 1 B 0 C 2a³b D Undefined