Q1.
(a)
On the grid below draw the graph of y = 2x – 3 for values of x from –1 to 4.
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(3)
(b)
The line y = 4.5 crosses the line y = 2x – 3 at P.
Use the graph to work out the coordinates of P.
Answer ( ................. , ............... )
(2)
(Total 5 marks)
Page 1 of 28
Q2.
Wayne cycles from Newcastle to Ashington, a distance of 20 miles.
The diagram shows the distance-time graph of his journey.
(a)
How far from Newcastle is Wayne at 11.00?
Answer .......................................... miles
(1)
(b)
Describe what is happening between 12.00 and 13.00
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(1)
(c)
How far does Wayne travel in the first 2 hours of his journey?
Answer .......................................... miles
(1)
(d)
What is Wayne’s average speed over the first 2 hours of his journey?
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Answer ........................................... mph
(2)
(e)
Darren travels from Ashington to Newcastle by bus.
He leaves Ashington at 10.00 and arrives in Newcastle at 11.00
On the diagram draw a possible distance-time graph of Darren’s journey.
(1)
(Total 6 marks)
Page 2 of 28
Q3.
You may use the grid below to help you solve this problem.
At 9 am a man leaves point P and walks along a road at a steady speed of 6 kilometres per
hour.
At 12 noon a cyclist leaves P, on the same road in the same direction, at a steady speed
of 20 kilometres per hour.
After travelling for an hour the cyclist gets a puncture which delays her for 30 minutes.
She then continues at 20 kilometres per hour until she overtakes the walker.
(a)
At what time did the cyclist overtake the walker?
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Answer ..............................................
(3)
Page 3 of 28
(b)
A motorist leaves P, travelling at a steady speed of 50 kilometres per hour.
The motorist overtakes the walker at the same time as the cyclist.
At what time did the motorist leave P?
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Answer ..............................................
(2)
(Total 5 marks)
Q4.
An activity centre hires out road bikes and mountain bikes.
The graph shows the cost, C (£) of hiring a road bike for a number of days, d.
(a)
Circle the correct formula connecting the cost, C and the number of days, d for hiring a
road bike.
C = 2d + 5
C = 5d + 10
C = 10d + 5
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(1)
Page 4 of 28
(b)
The cost of hiring a mountain bike is given by the formula C = 5d + 15
Rowan would like to hire a mountain bike.
He thinks that a mountain bike will always cost more to hire than a road bike.
Is this true?
Yes
No
Explain your answer.
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(3)
(Total 4 marks)
Q5.
(a)
Complete the table of values for y = 2x – 1
x
–1
y
–3
0
1
1
2
3
5
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(1)
Page 5 of 28
(b)
On the grid below, draw the graph of y = 2x – 1 for values of x from –1 to +3
(2)
(Total 3 marks)
Q6.
The diagram shows the points P (0, –4) and Q (5, 2).
Find the coordinates of the mid-point of the line segment PQ.
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Answer ( ........................... , ........................... )
(Total 2 marks)
Page 6 of 28
Q7.
Here is a distance-time graph for a train journey.
(a)
For how long does the train stop on the journey?
Answer ..................................... minutes
(1)
(b)
(i)
On which part of the journey does the train travel fastest?
Put a circle around the part of the graph that shows this.
(1)
(ii)
Explain how you know.
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(1)
(Total 3 marks)
Page 7 of 28
Q8.
The graph shows a sketch of the line y = 3x + 1
Not drawn accurately
(a)
Does the point (–2, –5) lie on the line?
Yes
No
Explain your answer.
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(2)
(b)
On the graph, sketch the line y = 3x + 4
(2)
(c)
Rearrange the formula y = 3x + 1 to make x the subject.
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Answer ................................................
(2)
(Total 6 marks)
Page 8 of 28
Q9.
‘4 in a line’ is a game for two players.
Players take it in turns to place a coloured counter on a coordinate point.
The first player to place four counters in a straight line wins.
Examples of winning lines are shown on this grid.
The grid below shows an unfinished game between Ali and Sasha.
Ali has gone first and so far has placed three black counters.
Sasha is about to place her third counter at the point (4, 3).
(a)
Mark the point (4, 3) on the grid.
(1)
(b)
Explain why Sasha can be certain of winning if the counter is placed there.
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(2)
(Total 3 marks)
Page 9 of 28
M1.
(a)
Two points calculated or plotted
B1 For each point or
B1 Line through (0, –3)
B1 Line gradient 2
(–1, –5)
(0, –3)
(1, –1)
(2, 1)
(3, 3)
(4, 5)
B2
Straight line drawn
B1
Page 10 of 28
(b)
Attempt to read off at y = 4.5 or 2x = 7.5
or 4.5 as y coordinate
B1
3.75
ft Their graph
± 1 mm (
square)
B1 ft
[5]
Page 11 of 28
M2.
(a)
8
B1
(b)
Not moving
Same distance from Newcastle oe
B1
(c)
16
B1
Page 12 of 28
(d)
Their 16/2
M1
8
A1 ft
(e)
Line or curve from (10.00, 20) to (11.00,0)
B1
[6]
Page 13 of 28
M3.
(a)
Line from (9 am, 0) to (2 pm, 30)
B1
Line from (12, 0) to (1, 20) plus 30 minute break, then line from
(1:30, 20) to (2 pm, 30)
B1
2 (pm)
B1
Page 14 of 28
Alt 1
Table or list of values showing steady speed of 6 km/h for at least
3 values
eg, (10, 6), (11, 12), (12, 18), (1, 24), (2, 30)
B1
Table or list of values showing steady speed of 20 km/h with break
to at least (1:30, 20)
eg, (1, 20), (1:30, 20), (2, 30) [(2:30, 40)]
B1
2 (pm)
B1
Page 15 of 28
Alt 2
6x = 20(x – 3 – 0.5)
M1
x = 5 hours
A1
2 (pm)
A1
Page 16 of 28
(b)
Line from their ‘(2 pm, 30)’ with gradient 50 km/h
30 ÷ 50 (= 36 minutes)
M1
1:23 – 1:25 (pm)
Their (a) – 36 minutes
A1 ft
Page 17 of 28
Alt 1
Table of values back from their ‘(2, 30)’ for at least 1 hour
eg, (1, 5)
B1
1:23 – 1:25 (pm)
Their (a) – 36 mins
B1 ft
Page 18 of 28
Alt 2
30 ÷ 50 (= 0.6h = 36m)
M1
1:24 (pm)
Their (a) – 36 mins
A1ft
[5]
Page 19 of 28
M4.
(a)
C = 10d + 5
B1
(b)
Correct substitution of a value for d in formula
20, 25, 30
M1
Identifies equal pay at d = 2
M1 dep
No and cheaper at d > 2
oe
A1
Page 20 of 28
Alternate method
Plots at least two correct coordinates on graph for mountain bike
(0, 15) (1, 20) (2, 25) (3, 30)
M1
Correct line at least as far as intersection at (2, 25)
M1 dep
No and cheaper at d > 2
A1
[4]
Page 21 of 28
(a)
M5.
0 → –1 and 2 → 3
B1
(b)
Straight line passing through
(–1, –3), (0, –1), (1, 1), (2, 3) and
(3, 5) ±
small square
B1 (–1, –3), their (0, –1), (1, 1), their (2, 3) and
(3, 5) plotted correctly ±
small square
or Line through three or four correct points
B2
[3]
Page 22 of 28
M6.
or evidence of good use of grid
M1
2.5, –1
Take one or other value correct as evidence for the M1
SC1 for (–1, 2.5)
A1
[2]
Page 23 of 28
M7.
(a)
10 minutes
B1
(b)
(i)
Last section indicated
B1
(ii)
Steepest line
oe
Do not accept 20 km in 20 mins and 25 km in 50 mins
Do not accept greater distance in shorter time
B1dep
[3]
Page 24 of 28
M8.
(a) Yes and full explanation
eg, –5 = 3 × –2 + 1 or –5 = –6 + 1
or 3 × –2 + 1 = –5 or –6 + 1 = –5
E1 For Yes and partial explanation
eg, values work in equation or 3 × –2 + 1
or –6 + 1
E2
Page 25 of 28
(b)
Line ‘parallel’ to existing line
B1
Line intersects y-axis between 1
and 4 cm above x axis
B1
Page 26 of 28
(c)
3x = y – 1
M1
x=
A1
[6]
Page 27 of 28
M9.
(a)
Correct plot
B1
(b)
Can win with either (2, 3) or (6, 3) Both cannot be blocked
or Ali can only block one side, Sasha can go at the other side
Full explanation E2
Partial explanation E1
eg two possible places to win or Can win
with either (2, 3) or (6, 3)
E2
[3]
Page 28 of 28