Exam-Style Questions.

1.	GCSE Higher

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

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

Circle your answer:

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

Worked Solution

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2.	GCSE Higher

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

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

Worked Solution

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3.	GCSE Higher

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

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

where:

• \(s\) is the distance measured in metres;
• \(t\) is the time measured in seconds;
• \(u\) is the initial speed;
• \(a\) is the acceleration;

(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?

Worked Solution

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4.	IGCSE Extended

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 \(4A=4k^2-\pi k^2\)

Worked Solution

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5.	GCSE Higher

(a) Simplify the following expression.

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

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

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

Worked Solution

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