1. What is the value of √144?
Solution
Correct: C
The square root of 144 is the number that multiplied by itself gives 144. 12 * 12 = 144, so √144 = 12.
2. A square has an area of 81 cm². What is the length of one side?
Solution
Correct: C
For a square, Area = side². Given Area = 81 cm², side = √81 = 9 cm.
3. If f(x) = 3x + 5, what is f(4)?
Solution
Correct: B
Substitute x = 4 into the function: f(4) = 3(4) + 5 = 12 + 5 = 17.
4. The area of a rectangle is 60 cm² and its length is 12 cm. What is its width?
Solution
Correct: B
Area = length × width → 60 = 12 × width → width = 60 ÷ 12 = 5 cm.
5. Simplify √50.
Solution
Correct: A
√50 = √(25 × 2) = √25 × √2 = 5√2.
6. A right triangle has legs 6 cm and 8 cm. What is its area?
Solution
Correct: B
Area of right triangle = (1/2) × leg1 × leg2 = (1/2) × 6 × 8 = 24 cm².
7. If g(x) = x² - 4x + 3, find g(2).
Solution
Correct: A
g(2) = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1.
8. A circle has area 154 cm². Taking π = 22/7, find its radius.
Solution
Correct: B
Area = πr² → 154 = (22/7)r² → r² = 154 × 7/22 = 49 → r = √49 = 7 cm.
9. Evaluate √2.25 without a calculator.
Solution
Correct: C
2.25 = 225/100 = (15/10)² → √2.25 = 15/10 = 1.5.
10. A triangle has base 10 cm and height 5 cm. What is its area?
Solution
Correct: C
Area = (1/2) × base × height = (1/2) × 10 × 5 = 25 cm².
11. If h(x) = 7 - x, what is h(h(3))?
Solution
Correct: B
h(3) = 7 - 3 = 4, then h(h(3)) = h(4) = 7 - 4 = 3.
12. A trapezium has parallel sides 8 cm and 14 cm and height 5 cm. Find its area.
Solution
Correct: B
Area = (1/2) × (sum of parallel sides) × height = (1/2) × (8+14) × 5 = 55 cm².
13. If f(x) = 2x² - 3x + 1, find f(-1).
Solution
Correct: C
f(-1) = 2(-1)² - 3(-1) + 1 = 2 + 3 + 1 = 6.
14. Simplify (√18 + √8)².
Solution
Correct: B
√18 = 3√2, √8 = 2√2. Sum = 5√2. Square = (5√2)² = 25 × 2 = 50.
15. A square garden of side 13 m, what is its area?
Solution
Correct: B
Area = side² = 13² = 169 m².
16. If p(x) = x/2 + 3, what is p(10)?
Solution
Correct: C
p(10) = 10/2 + 3 = 5 + 3 = 8.
17. Find the area of a parallelogram with base 9 cm and height 6 cm.
Solution
Correct: C
Area = base × height = 9 × 6 = 54 cm².
18. If q(x) = x² - 5x + 6, find the sum of q(1) and q(4).
Solution
Correct: C
q(1) = 1 - 5 + 6 = 2; q(4) = 16 - 20 + 6 = 2. Sum = 2 + 2 = 4. (Note: choices adjusted to fit correct sum)
19. If √(x - 3) = 4, what is x?
Solution
Correct: C
Square both sides: x - 3 = 16 → x = 19.
20. A rectangle has area 84 cm² and width 7 cm. Find its perimeter.
Solution
Correct: B
Length = 84 ÷ 7 = 12 cm. Perimeter = 2(12 + 7) = 38 cm.
21. If m(x) = 9 - x², find m(3).
Solution
Correct: A
m(3) = 9 - 3² = 9 - 9 = 0.
22. A rhombus has diagonals 10 cm and 12 cm. What is its area?
Solution
Correct: A
Area = (1/2) × d1 × d2 = (1/2) × 10 × 12 = 60 cm².
23. If f(x) = x² and g(x) = x + 2, find f(g(3)).
Solution
Correct: C
g(3) = 3 + 2 = 5; f(5) = 5² = 25.
24. Simplify √128 - √32.
Solution
Correct: A
√128 = 8√2, √32 = 4√2. Difference = 8√2 - 4√2 = 4√2.
25. A triangle has sides 5 cm, 12 cm, 13 cm. What is its area?
Solution
Correct: A
It is a right triangle (5² + 12² = 13²). Area = (1/2) × 5 × 12 = 30 cm².
26. If n(x) = 2x - 1 and n(a) = 11, find a.
Solution
Correct: B
2a - 1 = 11 → 2a = 12 → a = 6.
27. The area of a sector of a circle of radius 6 cm and central angle 60° is (use π = 3.14)
Solution
Correct: A
Sector area = (θ/360) × πr² = (60/360) × 3.14 × 36 = 18.84 cm².
28. If r(x) = x² - 2x + 1, find r(5) - r(3).
Solution
Correct: B
r(5) = 25 - 10 + 1 = 16; r(3) = 9 - 6 + 1 = 4. Difference = 16 - 4 = 12.
29. If √(x² + 5) = 3, what is x²?
Solution
Correct: C
Square both sides: x² + 5 = 9 → x² = 4.
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