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Maths Essentials: 18 MCQs with answers

All 18 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Quick Revision · 18

Warm-up · 11 questions

Q1. Which of the following is an irrational number?

Beginner
A √2 B -3 C 1/4 D 0.5
Show answer & explanation

√2

√2 cannot be expressed as a ratio of two integers, making it irrational. The others are rational numbers.

Q2. Simplify: 3(x + 2) - 2(x - 1)

Beginner
A x + 4 B 5x + 4 C 5x + 8 D x + 8
Show answer & explanation

x + 8

Distribute: 3x + 6 - 2x + 2 = x + 8.

Q3. What is the slope of the line passing through (1, 2) and (3, 6)?

Beginner
A 4 B 3 C 1 D 2
Show answer & explanation

2

Slope = (6-2)/(3-1) = 4/2 = 2.

Q4. The sum of the interior angles of a triangle is:

Beginner
A 180° B 270° C 360° D 90°
Show answer & explanation

180°

A fundamental property of Euclidean triangles is that their interior angles sum to 180°.

Q5. What is the derivative of f(x) = x^3?

Beginner
A x^4/4 B 3x C 3x^2 D x^2
Show answer & explanation

3x^2

Using the power rule, d/dx(x^n) = n*x^(n-1), so d/dx(x^3) = 3x^2.

Q6. Which of the following is a prime number?

Beginner
A 23 B 21 C 15 D 27
Show answer & explanation

23

23 has only two distinct divisors: 1 and itself, making it prime. Others are composite.

Q7. Solve for x: 2x + 5 = 13

Beginner
A x = 4 B x = 3 C x = 6 D x = 5
Show answer & explanation

x = 4

Subtract 5 from both sides: 2x = 8, then divide by 2: x = 4.

Q8. The derivative of a constant function is:

Beginner
A 0 B 1 C The constant itself D Undefined
Show answer & explanation

0

The derivative measures rate of change; a constant has no change, so its derivative is 0.

Q9. What is the value of log₁₀(100)?

Beginner
A 100 B 1 C 10 D 2
Show answer & explanation

2

log₁₀(100) = log₁₀(10²) = 2.

Q10. The number 0 is an integer.

Beginner
A True B False
Show answer & explanation

True

Integers include all whole numbers and their negatives, so 0 is an integer.

Q11. The derivative of e^x is e^x.

Beginner
A True B False
Show answer & explanation

True

The exponential function e^x is its own derivative.

Building up · 7 questions

Q12. What is the area of a circle with radius 3 cm?

Intermediate
A 6π cm² B 12π cm² C 9π cm² D 3π cm²
Show answer & explanation

9π cm²

Area = πr² = π(3²) = 9π cm².

Q13. The limit of (sin x)/x as x approaches 0 is:

Intermediate
A 0 B ∞ C Undefined D 1
Show answer & explanation

1

This is a standard limit in calculus: lim_{x→0} (sin x)/x = 1.

Q14. Which of the following is the factored form of x² - 5x + 6?

Intermediate
A (x + 2)(x + 3) B (x - 2)(x - 3) C (x + 1)(x - 6) D (x - 1)(x - 6)
Show answer & explanation

(x - 2)(x - 3)

The factors of 6 that sum to -5 are -2 and -3, so x² - 5x + 6 = (x - 2)(x - 3).

Q15. In a right triangle, if one leg is 3 and the hypotenuse is 5, the other leg is:

Intermediate
A √34 B 4 C 2 D 8
Show answer & explanation

4

By the Pythagorean theorem: 3² + b² = 5² → 9 + b² = 25 → b² = 16 → b = 4.

Q16. What is the integral of 2x with respect to x?

Intermediate
A 2x² + C B x + C C 2 + C D x² + C
Show answer & explanation

x² + C

∫2x dx = 2*(x²/2) + C = x² + C.

Q17. The solution set of |x - 2| < 3 is:

Intermediate
A x > -1 B -1 < x < 5 C -5 < x < 1 D x < 5
Show answer & explanation

-1 < x < 5

|x - 2| < 3 means -3 < x - 2 < 3, adding 2 gives -1 < x < 5.

Q18. Which of the following is the equation of a line with slope 2 and y-intercept -3?

Intermediate
A y = 2x + 3 B y = -3x + 2 C y = 2x - 3 D y = -2x - 3
Show answer & explanation

y = 2x - 3

Slope-intercept form is y = mx + b, so m=2 and b=-3 gives y = 2x - 3.

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