Math practice test, grades 11–12
10 free Math practice questions at Grades 11–12, with answers. 142 questions in the full bank, covering 7 topics.
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10 free practice questions
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- Question 1algebra
If 5x + 15 = 35, what is the value of x?
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Answer: B
5x = 35 − 15 = 20. x = 4.
- Question 2calculus
What is ∫(2x + 3)dx?
- Question 3coordinate geometry
Line g: r = (1,0,2) + t(2,1,−1). Is point P=(5,2,0) on line g?
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Answer: A
P=(1,0,2)+t(2,1,−1)=(5,2,0) → 1+2t=5 → t=2. 0+t=2 ✓. 2−t=0 ✓. Yes, P lies on g.
- Question 4geometry
The legs of a right triangle are in ratio 3:4. The hypotenuse is 25 cm. What is the shorter leg?
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Answer: B
Legs: 3k and 4k. (3k)²+(4k)²=25² → 25k²=625 → k=5. Shorter leg=3×5=15 cm.
- Question 5number theory
How many solutions does the equation sin(x) = 0.5 have in [0°, 360°]?
- Question 6probability
X~N(μ=100, σ=15). What is P(X > 130)? (Use 68-95-99.7 rule)
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Answer: A
130 = μ+2σ. By 95% rule, 95% of data is within 2σ. 5% is outside, split evenly: P(X>130)≈2.5%.
- Question 7statistics
A biased coin has P(H) = 0.6. Flipped 3 times. P(exactly 2 heads)?
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Answer: C
C(3,2)×0.6²×0.4 = 3×0.36×0.4 = 3×0.144 = 0.432.
- Question 8algebra
The product of two consecutive even integers is 168. What is the larger integer?
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Answer: C
n(n+2)=168. Try n=12: 12×14=168 ✓. Larger=14.
- Question 9calculus
What is the derivative of f(x) = x³ − 2x² + 5x?
- Question 10coordinate geometry
Vectors a=(1,2,−1) and b=(3,−1,2). What is a·b (dot product)?
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Answer: C
a·b = 1×3 + 2×(−1) + (−1)×2 = 3 − 2 − 2 = −1.
132 more questions at Grades 11–12
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algebra · calculus · coordinate geometry · geometry · number theory · probability · statistics