1. If f(x)=3x+7 and g(x)=x²-4, what is f(g(2))?
Solution
Correct: A
g(2)=2²-4=0, then f(0)=3·0+7=7.
2. The square root of 2.56 is
Solution
Correct: A
√2.56 = 1.6 because 1.6² = 2.56.
3. A right triangle has legs 6 cm and 8 cm. The hypotenuse is
Solution
Correct: A
Using Pythagoras: √(6²+8²)=√(36+64)=√100=10 cm.
4. Simplify √50 + √18
Solution
Correct: A
√50=5√2 and √18=3√2, so 5√2+3√2=8√2.
5. If the point (3, k) lies on the line y=2x-5, then k equals
Solution
Correct: A
k=2·3-5=6-5=1.
6. The area of a square is 50 cm². Its side length is
Solution
Correct: A
Side = √50 = √(25·2)=5√2 cm.
7. If f(x)=√x and g(x)=x²-9, for which x is f(g(x)) defined?
Solution
Correct: C
f(g(x)) defined when g(x)≥0 → x²-9≥0 → x≤-3 or x≥3.
8. Evaluate √144
Solution
Correct: A
12²=144, so √144=12.
9. A rectangle has length 9 cm and diagonal 15 cm. Its width is
Solution
Correct: A
Using Pythagoras: width=√(15²-9²)=√(225-81)=√144=12 cm.
10. Simplify (√5+√3)(√5-√3)
Solution
Correct: A
Difference of squares: (√5)²-(√3)²=5-3=2.
11. If h(x)=x²-5x+6, what is h(4)?
Solution
Correct: A
h(4)=4²-5·4+6=16-20+6=2.
12. The cube has volume 125 cm³. The length of its edge is
Solution
Correct: A
Edge = ∛125 = 5 cm.
13. Rationalize 1/√8
Solution
Correct: A
Multiply numerator and denominator by √8: √8/8 = 2√2/8 = √2/4.
14. A circle has area 81π. Its radius is
Solution
Correct: A
πr²=81π → r²=81 → r=9.
15. If f(x)=2x+3 and f(a)=11, then a equals
Solution
Correct: A
2a+3=11 → 2a=8 → a=4.
16. Simplify √(49×16)
Solution
Correct: A
√(49×16)=√49×√16=7×4=28.
17. The coordinates of the midpoint of segment AB with A(2,5) and B(6,9) are
Solution
Correct: A
Midpoint = ((2+6)/2, (5+9)/2) = (4,7).
18. If g(x)=x²-6x+9, what is the minimum value of g?
Solution
Correct: A
g(x)=(x-3)², so minimum is 0 when x=3.
19. Evaluate √0.25
Solution
Correct: A
0.5²=0.25, so √0.25=0.5.
20. A trapezoid has bases 8 cm and 14 cm and height 5 cm. Its area is
Solution
Correct: A
Area = (8+14)/2×5=22/2×5=11×5=55 cm².
21. If f(x)=x²+1 and g(x)=√x, what is f(g(16))?
Solution
Correct: B
g(16)=√16=4, then f(4)=4²+1=17.
22. Simplify √72
Solution
Correct: A
√72=√(36×2)=6√2.
23. A square garden of area 200 m² needs fencing. The length of fence required is
Solution
Correct: A
Side = √200 = 10√2 m, perimeter = 4×10√2 = 40√2 m.
24. If f(x)=5-x and g(x)=x², what is g(f(3))?
Solution
Correct: A
f(3)=5-3=2, then g(2)=2²=4.
25. The diagonal of a square with side 7 cm is
Solution
Correct: A
Diagonal = side×√2 = 7√2 cm.
26. Evaluate √(9+16)
Solution
Correct: A
√(9+16)=√25=5.
27. If h(x)=√(x-3) and h(k)=4, then k equals
Solution
Correct: A
√(k-3)=4 → k-3=16 → k=19.
28. Simplify 2√12 - √27
Solution
Correct: A
2√12=4√3 and √27=3√3, so 4√3-3√3=√3.
29. A rhombus has diagonals 10 cm and 24 cm. Its area is
Solution
Correct: A
Area = (10×24)/2 = 120 cm².
30. If f(x)=x²-4x+7, then the vertex of the parabola is
Solution
Correct: A
x= -b/2a = 4/2 = 2, f(2)=4-8+7=3, so vertex is (2,3).
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