# Exam-Style Questions.

## Problems adapted from questions set for previous Mathematics exams.

### 1.

GCSE Higher

Rearrange the following formula to make $$d$$ the subject:

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

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

### 2.

GCSE Higher

Make $$b$$ the subject of the following formula:

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

### 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?

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

### 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.

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

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