National 5 Mathematics

National 5 Maths Readiness Check

A short pupil-facing check across key National 5 Mathematics foundations. Use it as a starting-point guide, not a formal assessment judgement.

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Readiness snapshot

Check key skills

Answer each question, then check it. When all questions are checked, your readiness result and suggested next practice will appear.

Score: 0/10

Question 1

Simplify √63.

number skills
Choose an answer

Question 2

Simplify ×

algebraic working
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Question 3

The points A(2, −3) and B(4, −9) lie on a straight line. Find the equation of the line.

graphs and functions
Use the two points to find the gradient, then the intercept.
Maths tools

Question 4

Factorise x² − 10x + 16 and hence solve x² − 10x + 16 = 0. Show your working

quadratics
Maths tools

Question 5

A right-angled triangle has shorter sides 15 cm and 36 cm. Find the hypotenuse.

geometry
The unknown hypotenuse is opposite the right angle.
Choose an answer

Question 6

In a right-angled triangle, the hypotenuse is 17 cm and an angle is 41°. Find the opposite side to 1 decimal place.

trigonometry
The unknown side is opposite the given angle.
Choose an answer

Question 7

a = (3, 3) and b = (-2, −2). Find a + b.

vectors
Components are added separately.
Maths tools

Question 8

Find the mean of 10, 12, 14, 16.

statistics
Choose an answer

Question 9

A pupil has P(success) = on each attempt. There are two independent attempts. Find P(at least one success).

probability

Two attempts

Multiply along a path. Add separate paths for an or probability.
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Question 10

A parabola crosses the x-axis at x = −5 and x = −1. Which equation has these roots?

quadratics
Sketch shows the roots where the curve crosses the x-axis.
Choose an answer