1
1
y
4
3
L
2
1
–3
–2
–1
0
–1
1
2
x
–2
–3
–4
–5
–6
Find the gradient of line L.
...................................................
[2]
[Total: 2]
2
(a) Find the gradient of line l.
...................................................
[2]
y = ...................................................
[2]
(b) Find the equation of line l in the form y = mx + c.
2
(c) Find the equation of the line that is perpendicular to line l and passes through the point (12, −7).
Give your answer in the form y = mx + c.
y = ...................................................
[3]
[Total: 7]
3
The diagram shows a line L and two points, A and B, on a grid.
y
6
L
5
A
4
3
2
1
–6
–5
–4
–3
–2
0
–1
1
2
3
4
5
B
6
7
8
x
–1
–2
(a) Write down the coordinates of point A.
( .............................. , .............................. ) [1]
(b)
(i)
Find the gradient of line L.
...................................................
[1]
3
(ii) Write down the equation of line L in the form y = mx + c.
y = ...................................................
(c)
(i) Draw a line that is perpendicular to line L and passes through the point A.
(ii) This line crosses the x-axis at point C.
[2]
[1]
Mark point C on the grid and write down the coordinates of point C.
( .............................. , .............................. ) [1]
[Total: 6]
4
(a) Find the gradient of line L.
(b) Write down the equation of line L in the form
...................................................
[2]
y = ...................................................
[1]
.
[Total: 3]
5
The diagram shows a point P and a line L.
4
(a) Write down the co-ordinates of point P.
( .............................. , .............................. ) [1]
(b) Find the gradient of line L.
...................................................
[2]
y = ...................................................
[2]
(c) Write down the equation of line L in the form y = mx + c.
[Total: 5]
5
6
Point A has co-ordinates (1, 0) and point B has co-ordinates (2, 5).
Calculate the angle between the line AB and the x-axis.
...................................................
[3]
[Total: 3]
6
7
A is the point (4, 1) and B is the point (10, 15).
Find the equation of the perpendicular bisector of the line AB.
...................................................
[6]
[Total: 6]
8
y
NOT TO
SCALE
P
l
0
The equation of the line l in the diagram is y = 5 – x .
x
7
(a) The line cuts the y-axis at P.
Write down the co-ordinates of P.
Answer (a) ( .............................. , .............................. ) [1]
(b) Write down the gradient of the line l.
Answer(b) ...................................................
[1]
[Total: 2]
9
A has coordinates (−2, 7), B has coordinates (1, −5) and C has coordinates (5, 4).
(a) Find the coordinates of the midpoint of the line AB.
( .............................. , .............................. ) [2]
(b) Find
.
=
(c) Find
[2]
.
...................................................
[2]
8
(d) Find the equation of the line AB.
Give your answer in the form y = mx + c.
y = ...................................................
[3]
(e) Find the equation of the line perpendicular to AB that passes through C.
Give your answer in the form y = mx + c.
y = ...................................................
[3]
[Total: 12]
10
A is the point (5, 7) and B is the point (9, −1).
Find the equation of the line AB.
...................................................
[3]
[Total: 3]
9
11
(a) Find the equation of line L in the form
.
y = ...................................................
(b) On the grid, draw a line that is perpendicular to line L.
[2]
[1]
[Total: 3]
12
The line
crosses the y-axis at G.
Write down the coordinates of G.
( .................... , .................... ) [1]
[Total: 1]
13
The equation of line L is
.
(a) Find the gradient of line L.
...................................................
[2]
(b) Find the coordinates of the point where line L cuts the y-axis.
( .................... , .................... ) [1]
10
[Total: 3]
14
Find the co-ordinates of the point where the line
crosses the y-axis.
( .............................. , .............................. ) [1]
[Total: 1]
15
Line L passes through the points (0, −3) and (6, 9).
(a) Find the equation of line L.
...................................................
[3]
(b) Find the equation of the line that is perpendicular to line L and passes through the point (0, 2).
...................................................
[2]
[Total: 5]
16
Write down the gradient of the line
.
...................................................
[1]
[Total: 1]
17
Write down the co-ordinates of the point where the line
crosses the y-axis.
( .............................. , .............................. ) [1]
[Total: 1]
11
18
The points (9, a) and (b, 3) lie on the line
.
Work out the value of
(a) a,
a = ...................................................
[2]
b = ...................................................
[2]
(b) b.
[Total: 4]
19
The equation of a straight line is
.
(a) Find the gradient of this line.
...................................................
[1]
(b) Find the co-ordinates of the point where the line crosses the y-axis.
( .............................. , .............................. ) [1]
[Total: 2]
20
The diagram shows a straight line L.
12
(a) Find the equation of line L.
...................................................
[3]
(b) Find the equation of the line perpendicular to line L that passes through (9, 3).
...................................................
[3]
[Total: 6]
21
Line L has the equation
.
Write down the gradient of line L.
...................................................
[1]
[Total: 1]
13
22
Write down the gradient of the line
.
...................................................
[1]
[Total: 1]
23
Write down the co-ordinates of the point where the graph of
crosses the y-axis.
( .................... , .................... ) [1]
[Total: 1]
24
The point (k, 7) lies on the line
.
Find the value of k.
k = ...................................................
[2]
[Total: 2]
25
The equation of line L is y = 4x – 3.
Write down
(a) the co-ordinates of the point where the line L crosses the y-axis,
( .................... , .................... ) [1]
(b) the gradient of the line L,
...................................................
[1]
(c) the equation of the line parallel to line L that passes through the origin.
...................................................
[1]
[Total: 3]
14
26
Write down the co-ordinates of the point where the line y = 3x + 5 crosses the y-axis.
Answer ( .................... , .................... ) [1]
[Total: 1]
27
Write down the gradient of the line y = –3x + 4.
Answer ...................................................
[1]
[Total: 1]
28
A train passes through a station at a speed of 108 km/h.
The length of the station is 120 m.
The train takes 7 seconds to completely pass through the station.
Work out the length of the train.
................................................... m
[3]
[Total: 3]
29
Annette cycles a distance of 70 km from Midville to Newtown.
Leaving Midville, she cycles for 1 hour 30 minutes at a constant speed of 20 km/h and then stops for
30 minutes.
She then continues the journey to Newtown at a constant speed of 16 km/h.
15
(a) On the grid, draw the distance–time graph for the journey.
[3]
(b) Calculate the average speed for the whole journey.
................................................... km/h
[3]
[Total: 6]
30
Change 300 m / min to km / h.
................................................... km / h
[2]
[Total: 2]
16
31
A coach travels at an average speed of 54 km/h.
Find how long, in hours and minutes, this coach takes to travel 126 km.
.............................. h .............................. min [3]
[Total: 3]
32
A plane leaves Shanghai at 20 05 local time on 13th November.
The plane stops for 2 hours 30 minutes in Sydney.
The plane lands in Auckland at 17 25 local time on 14th November.
The local time in Auckland is 5 hours ahead of the local time in Shanghai.
(a) Work out how long the plane is flying, in hours and minutes.
.................... h .................... min [3]
(b) Write your answer to part (a) in hours, correct to 3 decimal places.
................................................... h
[1]
................................................... km
[1]
(c) The flight distance from Shanghai to Sydney is 7882 km.
The flight distance from Sydney to Auckland is 2156 km.
Find the total distance the plane flies.
17
(d) Calculate the average speed of the plane when it is flying.
................................................... km/h
[2]
[Total: 7]
33
The diagram shows the route of a boat race.
The route is in the shape of a regular octagon, ABCDEFGH.
(a) Each side of the octagon is 1.35 km.
The average speed of a boat is 45 km/h.
Work out the time it will take this boat to complete the race.
Give your answer in minutes.
................................................... min
[3]
18
(b) Hetty wants to draw a scale drawing of the route.
She chooses a scale of 1:500 000.
Has Hetty chosen a suitable scale?
Show all your working and explain your decision.
.............................. because ....................................................................................................... [2]
[Total: 5]
34
Here is part of a bus timetable.
Abbots
06 50
08 25
09 20
Callet
07 12
08 47
09 42
North Moor
07 30
09 05
10 00
South Moor
07 37
09 12
10 07
Centre Point
08 00
09 35
10 30
The distance from Abbots to Centre Point is 29.4 km.
Each bus takes the same time for the journey.
Calculate the average speed of a bus for this journey.
Give your answer in kilometres per hour.
................................................... km/h
[2]
[Total: 2]
19
35
There is a straight road between town A and town B of length 130 km.
Maxi travels from town A to town B.
Pippa travels from town B to town A.
Both travel at a constant speed of 40 km/h.
Maxi leaves 30 minutes before Pippa.
Work out how far from town A they will be when they pass each other.
...................................km [4]
[Total: 4]
36
A train travels 36 km at an average speed of 75 km/h.
Work out the journey time.
Give your answer in minutes.
................................................... min
[2]
[Total: 2]
37
Pierre travels by plane from Paris to Singapore.
The plane leaves Paris at 16 35 on Thursday and arrives in Singapore 13 hours and 45 minutes later.
The local time in Singapore is 6 hours ahead of the local time in Paris.
20
(a) Work out the day and time in Singapore when the plane arrives.
Day ......................................... Time .............................. [3]
(b) The distance from Paris to Singapore is 10 736 kilometres.
Work out the average speed of the plane.
................................................... km/h
[2]
[Total: 5]
38
Diego flies from Madrid to Buenos Aires.
The distance between Madrid and Buenos Aires is 10 050 km.
Diego’s flight takes 12 hours 30 minutes.
Calculate the average speed, in km/h, for the flight.
................................................... km/h
[1]
[Total: 1]
21
39
A train of length 105 m takes 11 seconds to pass completely through a station of length 225 m.
Calculate the speed of the train in km/h.
................................................... km/h
[3]
[Total: 3]
40
A train journey takes 5 hours 54 minutes.
The average speed of the train for this journey is 80 km/h.
Calculate the distance travelled.
................................................... km
[2]
[Total: 2]