KCSE Mathematics Practice

Question 1

If A = {1, 2, 3} and B = {2, 3, 4}, what is the union of sets A and B?

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Question 2

Using mathematical induction, if the statement P(k) is true for k = 1, and P(k) implies P(k+1), what can we conclude?

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Question 3

Simplify the expression (2^3)^4.

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Question 4

Express √50 in simplest surd form.

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Question 5

Find the value of log₃ 27.

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Question 6

Factorize the expression x^2 - 9.

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Question 7

Solve the quadratic equation x^2 - 5x + 6 = 0.

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Question 8

Find the 5th term of the arithmetic progression 3, 7, 11, ...

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Question 9

If matrix A = [[1,2],[3,4]] and matrix B = [[0,1],[1,0]], find AB.

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Question 10

Find the magnitude of the vector v = 3i + 4j.

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Question 11

Find the slope of the line passing through points (2,3) and (4,7).

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Question 12

Find the value of sin 30°.

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Question 13

Solve the equation 2cos x = 1, where 0° ≤ x ≤ 360°.

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Question 14

If f(x) = 2x + 3, find f^{-1}(x), the inverse function.

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Question 15

Differentiate y = 3x^2 + 5x - 7 with respect to x.

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Question 16

Integrate ∫(4x^3) dx.

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Question 17

Calculate the mean of the data set: 4, 7, 9, 10, 6.

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Question 18

Find the variance of the numbers 2, 4, 6, 8, 10.

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Question 19

A coin is tossed three times. What is the probability of getting exactly two heads?

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Question 20

In the geometric progression 2, 6, 18, ..., find the 4th term.

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Question 21

If det(A) = 5 for matrix A, what is det(3A) where A is a 2×2 matrix?

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Question 22

Find the angle between vectors a = 3i + 4j and b = 4i + 3j.

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Question 23

Find the equation of the line perpendicular to y = 2x + 3 passing through point (1, 4).

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Question 24

Prove by induction that the sum of first n odd numbers is n^2.

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Question 25

Solve the inequality x^2 - 4x - 5 < 0.

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Question 26

If f(x) = x^2 and g(x) = x + 1, find (f ◦ g)(2).

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Question 27

Evaluate the integral ∫(2x + 1) dx.

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Question 28

If P(A) = 0.4 and P(B) = 0.5, and A and B are mutually exclusive, find P(A ∪ B).

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Question 29

Find the sum of the first 10 terms of the arithmetic progression: 5, 8, 11, ...

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Question 30

Given vectors a = i + 2j + 3k and b = 4i + 5j + 6k, find a × b.

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Question 31

Find the equation of the circle with center at (2, -3) and radius 5.

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Question 32

Simplify the expression log_a (a^5).

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