NSMQ

NSMQ 2026 Mathematics Speed Race

Evaluate and simplify cos(π/12).

Two students are selected from a group of three boys and two girls. Find the probability that one is a girl and the other is a boy.

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Find the equation of the line perpendicular to the line 2x + 3y = 10 which passes through the point (2, -1).

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Find the solution set of the inequality (x + 4)(x − 3) < 8.

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A linear sequence has consecutive terms x + 2, 2x − 2 and 10 − x. Find the common difference.

Question 6

Express 29 as a difference of two squares.

Question 7

Find the tangent of the angle between the vectors 2i + j and i + 2j.

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Given that f(x) = x² − 5 and g(x) = 2x − 3, evaluate g(f(2)).

Question 9

Find the equation of the circle with centre in the second quadrant if the circle touches both axes and also touches the x-axis at x = −5.

Question 10

Solve the simultaneous equations 3x − 2y = 11 and 5x − 3y = 18.

Question 11

Express 125 as a sum of two squares.

Question 12

The numbers 1, 2, 3, 4, 5 are arranged in a line. Find the probability an arrangement begins with an even number and ends with an odd number.

Question 13

Solve for x, given that (2^x)^x / 8^x = 16.

Question 14

A biased coin, when tossed, has P(H) = 3/5. If it is tossed 3 times, find the probability of getting exactly 1 head.

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A circle of radius 12 cm has a chord of 18 cm. Find the distance from the centre to the chord.

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Find an integer solution of the equation x³ − 2x² = 75.

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Find P(A), given that P(A ∪ B) = 4/5, P(A ∩ B) = 1/3 and P(B) = 3/5.

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Find the component of 5i + 6j in the direction of 3i + 4j.

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Given that x = 2cos θ and y = 3sin θ, find a Cartesian equation in x and y.

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A and B are two independent events such that P(A) = 1/2 and P(B) = 1/3. Find P(A ∪ B).

Question 21

Find the coordinates of the stationary point of the curve y = x² + 16/x.

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