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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.


GCSE Higher

Rearrange the following formula to make \(d\) the subject:

$$ a = \frac{b - c}{d + e} $$

Circle your answer:

$$ d=\frac{b-c}{a}-e \quad \quad d=\frac{b-c}{a+e} \quad \quad d=\frac{b-c}{a-e} \quad \quad d=e +\frac{b-c}{a} \quad \quad d=e +\frac{a-e}{b-c} $$


GCSE Higher

Make \(b\) the subject of the following formula:

$$ a = \frac{5b + 2}{2b - 3} $$


GCSE Higher

The following kinematics formula can be used to work out the distance travelled (displacement) of an object travelling with constant acceleration.

$$ s = ut + \frac12 at^2 $$


(a) Rearrange the formula to make \(u\) the subject.

(b) What units would be associated with speed in this case?

(c) What units would be associated with acceleration?


IGCSE Extended
Circle in Square Diagram

A circle is drawn inside a square so that it touches all four sides of the square.

(a) If the sides of the square are each \(k\) mm in length and the area of the red shaded region is \(A\) mm2 show that:

$$4A=4k^2-\pi k^2$$

(b) Make \(k\) the subject of the formula \(4A=4k^2-\pi k^2\)


GCSE Higher

(a) Simplify the following expression.

$$ \frac{x^2 - 4}{3x^2 + 13x + 14}$$

(b) Make b the subject of the following formula.

$$ a = \frac{7(3b-c)}{b}$$

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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