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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.


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.


GCSE Higher

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







GCSE Higher

Show that line \(5y = 7x - 7\) is perpendicular to line \(7y = -5x + 55\).


GCSE Higher

A straight line goes through the points \((a, b)\) and \((c, d)\), where

$$a + 3 = c$$ $$b + 6 = d$$

Find the gradient of the line.


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.


GCSE Higher

A is the point (-5, -9) and B is the point (10, 1).

(a) Find the length of AB.

(b) Find the equation of the perpendicular bisector of AB.

(c) C is a point on AB.
C divides AB in the ratio 3 : 2.
Find the coordinates of C.


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.


IB Analysis and Approaches

Consider the points A(-5, 15). B(4, 6) and C(-8, 12). The line \(L\) passes through the point A and is perpendicular to [BC].

(a) Find the equation of \(L\).

The line \(L\) passes through the point (\(k\), 5).

(b) Find the value of \(k\).


IB Studies

Consider a straight line graph L1, which intersects the x-axis at A(8, 0) and the y-axis at B (0, 4).

(a) Write down the coordinates of C, the midpoint of line segment AB.

(b) Calculate the gradient of the line L1.

The line L2 is parallel to L1 and passes through the point (5 , 9).

(c) Find the equation of L2. Give your answer in the form \(ay + bx + c = 0\) where \(a, b \text{ and } c \in \mathbb{Z}\).


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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