Coordinate Geometry & Straight Lines (AQA GCSE Further Maths)

Exam Questions

58 mins19 questions
1
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3 marks

A sketch of the lines Ā y equals 2 x andĀ  y equals 6 is shown.

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Work out the area of triangle O P Q.

.................................. units2

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2
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2 marks

M is the midpoint of the line A B.

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Work out the values ofĀ p and r.

p space equalsĀ ............................ r space equals ............................

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3
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3 marks

Work out the equation of the straight line that is parallel to the line Ā 2 y equals x and intersects the x-axis at left parenthesis 4 comma space 0 right parenthesis.

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4
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2 marks

Work out the distance between the points A left parenthesis ā€“ 3 comma space 7 right parenthesis andspace B spaceleft parenthesis 5 comma space 1 right parenthesis

........................ units

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5
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1 mark

Here are four sketch graphs.

Circle the letter of the sketch graph that represents Ā 3 x space plus space 2 y space equals space 5

q3-paper1-nov2021-aqa-gcse-furthermaths

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6
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3 marks

A straight line passes through the points space left parenthesis negative 2 comma space 11 right parenthesis and left parenthesis 1 comma space 2 right parenthesis

Work out the equation of the line.

Give your answer in the form y equals m x plus c

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7
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3 marks

P is the pointĀ left parenthesis negative 12 comma space b right parenthesis
Q is the pointĀ left parenthesis a comma space 4 right parenthesis
R is the pointĀ left parenthesis 6 comma space minus 2 right parenthesis

Q is the midpoint of P R.

Work out the values ofĀ a and b.

a space equalsĀ  ..........................Ā b space equals ..........................

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8a
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1 mark

L is a straight line with equationĀ Ā Ā a x plus b y equals c where a comma space b and c are non-zero integers.

At which point does L intersect the x-axis?

Circle your answer.

open parentheses a over c comma 0 close parentheses

open parentheses c over a comma 0 close parentheses

open parentheses b over c comma 0 close parentheses

open parentheses c over b comma 0 close parentheses

8b
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1 mark

What is the gradient of a line parallel to L?

Circle your answer.

negative b over a

b over a

negative a over b

a over b

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9
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4 marks

Work out the point of intersection of the lines

2 x plus 3 y equals 11 and Ā  2 y equals 13 minus 3 x

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10
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3 marks

A triangle has vertices A open parentheses 2 comma space 5 close parenthesesĀ ,Ā Ā B open parentheses 2 comma space 0 close parenthesesĀ  Ā andĀ Ā Ā C open parentheses negative 4 comma space 3 close parentheses

Work out the area of triangle A B C.

You may use the grid to help you.

qp1-2016-paper-2-aqa-gcse-further-maths

............................ square units

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1
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4 marks

A B C spaceis a straight line withĀ A B colon B C equals 5 colon 2

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Work out the coordinates of C.

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2
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4 marks

A B C is a straight line.

A is the pointspace left parenthesis negative 4 comma space 5 right parenthesis
C is the point space left parenthesis 20 comma space minus 7 right parenthesis space
A B colon B C equals 5 colon 3

qp8-2019-paper-1-aqa-gcse-further-maths

Work out the coordinates of B.

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3
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3 marks

Here is a sketch of quadrilateral P Q R S.

M is the midpoint of P S.

qp2-2019-paper-2-aqa-gcse-further-maths

Use gradients to show that M R is parallel to P Q.

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4
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2 marks

P space left parenthesis ā€“ 3 comma space ā€“ 10 right parenthesis and Q space open parentheses a comma space b close parentheses space are points on a straight line with gradient 12

Work out one possible pair of integer values forĀ a and b.

a space equals.................. Ā b space equals....................

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5
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3 marks

A open parentheses 1 1 fifth comma space 3 4 over 5 close parentheses comma space B open parentheses 2 comma 1 4 over 5 close parentheses andĀ C open parentheses 5 comma 3 close parentheses are points on a coordinate grid.

Show that the line segments A B and B C are perpendicular.

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6
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3 marks

D open parentheses negative 6 comma space 4 close parentheses and E open parentheses negative 2 comma space 9 close parentheses are joined by a straight line.

P is a point on D E.

D P space colon space P E space equals space 3 colon 5

Work out the coordinates of P.

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1
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5 marks

A and space B spaceare points on the line y equals 3 x plus 2

B comma space C spaceand D (5, 0) are points on the line L.

space O A colon A C equals 1 colon 4 space

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Work out the x-coordinate of B.

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2
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4 marks

In the diagram,

A is the point left parenthesis 15 comma space 0 right parenthesis and B lies on the y-axis.

Anglespace A B C space equals space 90 degree and tanĀ theta =Ā 5 over 3

qp12-2018-paper-1-aqa-gcse-further-maths

Work out the equation of the line B C.

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3
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4 marks

Here is a sketch of triangle ABC.

P is a point on AB.

q8-2018-paper-2-aqa-gcse-further-maths

AP : PB is 3 : 1

Work out the length PC.

Give your answer to 4 significant figures.

Ā ................................ units

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