# Exam-Style Questions.

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

### 1.

GCSE Higher

The equation of the line L1 is $$y = 2 - 5x$$.

The equation of the line L2 is $$3y + 15x + 17 = 0$$.

Show that these two lines are parallel.

### 2.

GCSE Higher

Which of the following lines is parallel to the x-axis?

$$y=-7$$

$$x-y=1$$

$$x=10$$

$$x+y=0$$

$$x=y$$

### 3.

GCSE Higher

Show that line $$5y = 7x - 7$$ is perpendicular to line $$7y = -5x + 55$$.

### 4.

GCSE Higher

The straight line $$L$$ has the equation $$4y = 3x + 5$$.

The point A has coordinates $$(6,7)$$.

Find an equation of the straight line that is perpendicular to L and passes through A.

### 5.

GCSE Higher

(a) Complete the table of values for $$y=\frac{(x^3-5x)}{10}$$

 $$x$$ -3 -2 -1 0 1 2 3 4 $$y$$ 0.2 1.2

(b) On the grid below, draw the graph of $$y=\frac{(x^3-5x)}{10}$$ for values of $$x$$ from -3 to 4.

### 6.

GCSE Higher

Suppose a rhombus ABCD is drawn on a coordinate plane with the point A situated at (4,7). The diagonal BD lies on the line $$y = 2x - 5$$

Find the equation the line that passes through A and C.

### 7.

GCSE Higher

On the grid below, draw the graph of $$y = 1 - 2x$$ for values of $$x$$ from -2 to 2.

### 8.

IB Studies

The vertices of quadrilateral ABCD are A (2, 4), B (-1, 5), C (–3, 4) and D (–2, 2).

(a) Calculate the gradient of line CD.

(b) Show that line AD is perpendicular to line CD.

(c) Find the equation of line CD. Give your answer in the form $$ax+by=c$$ where $$a,b,c\in \mathbf Z$$

Lines AB and CD intersect at point E.

(d) Find the coordinates of E.

(e) Find the distance between A and D.

The distance between D and E is $$\sqrt{20}$$.

(f) Find the area of triangle ADE.

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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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