1.
A straight line has equation y = 4x – 5.
(a)
Find the value of x when y = 1.
x = ………………………….
(2)
(b)
Write down the equation of the straight line that is parallel to y = 4x – 5 and passes
through the point (0, 3).
………………………………
(2)
(c)
Rearrange the equation y = 4x – 5 to find x in terms of y.
x = ………………………….
(2)
(Total 6 marks)
IV
2.
The table shows some rows of a number pattern.
Row 1
1
=
1 2
2
Row 2
1+2
=
23
2
Row 3
1+2+3
=
3 4
2
Row 4
1+2+3+4
Row 8
(a)
In the table, complete row 4 of the number pattern.
(1)
(b)
In the table, complete row 8 of the number pattern.
(1)
(c)
Work out the sum of the first 100 whole numbers.
.....................................
(1)
(d)
Write down an expression, in terms of n, for the sum of the first n whole numbers.
.................................
(2)
(Total 5 marks)
IV
3.
Jennifer made x cakes.
She put 4 sweets on top of each cake.
(a)
Write down an expression, in terms of x, for the number of sweets she used.
……………………………..
(1)
Paul made 3 more cakes than Jennifer.
(b)
Write down an expression, in terms of x, for the number of cakes Paul made.
…………………………..
(1)
Paul also put 4 sweets on each of his cakes.
(c)
Write down an expression, in terms of x, for the number of sweets Paul used.
……………………………..
(1)
(Total 3 marks)
IV
4.
(a)
Solve 7x + 18 = 74
x = ………………………
(2)
(b)
Solve 4(2y – 5) = 32
y = ………………………
(2)
(c)
Solve 5p + 7 = 3(4 – p)
p = ………………………
(3)
(Total 7 marks)
IV
5.
(a)
Simplify
4x + 7y + 2x – 3y
…………………………
(2)
(b)
Simplify
2pq + pq
…………………………
(1)
(c)
Factorise 3t – 12
…………………………
(1)
(d)
Expand and simplify 3(2x – 1) – 2(2x – 3)
…………………………
(2)
(Total 6 marks)
IV
6.
y
12
11
10
9
8
7
6
5
4
3
A
2
1
–5
–4
–3
–2
–1
O
x
1
2
3
4
5
6
7
8
9
–1
–2
–3
–4
–5
–6
Shape A has a line of symmetry.
(a)
Write down the equation of this line of symmetry.
…………………………
(1)
(b)
Reflect shape A in the x-axis to give shape B.
Draw and label shape B.
(c)
Enlarge shape A by scale factor 2, centre O, to give shape C.
Draw and label shape C.
(1)
(3)
(Total 5 marks)
IV
7.
(i)
Solve the inequality
5x – 7 < 2x – 1
………………………
(ii)
On the number line, represent the solution set to part (i).
–5
–4
–3
–2
–1
0
1
2
3
4
5
(Total 3 marks)
8.
(a)
Complete the table for y = x2 – 3x + 1
x
–2
y
11
–1
0
1
1
–1
2
3
4
1
5
(2)
(b)
On the grid below, draw the graph of y = x2 – 3x + 1
(2)
IV
y
12
11
10
9
8
7
6
5
4
3
2
1
–2
–1
O
1
3
2
x
4
–1
–2
–3
–4
–5
(c)
Use your graph to find an estimate for the minimum value of y.
y = ……………………
(1)
(Total 5 marks)
IV
9.
Martin cleaned his swimming pool.
He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.50 for the first day,
then £18.25 for each extra day.
Martin’s total cost of hiring the machine was £163.25
(a)
For how many days did Martin hire the machine?
.................. days
(3)
Martin had to buy some cleaning materials.
The cost of the cleaning materials was £64.00 plus VAT at 17
(b)
1
%.
2
Work out the total cost of the cleaning materials.
£ .......................
(2)
Martin filled the pool with 54 000 gallons of water.
He paid £2.38 for each 1000 gallons of water.
(c)
Work out the total amount he paid for 54 000 gallons of water.
£ .......................
(2)
(Total 7 marks)
IV
10.
(a)
Solve
20y – 16 = 18y – 9
y = ....................
(3)
(b)
Solve
40 – x
=4+x
3
x = ....................
(3)
(Total 6 marks)
11.
Eggs are sold in boxes.
A small box holds 6 eggs.
A large box holds 12 eggs.
Hina buys x small boxes of eggs.
Hina also buys 4 less of the large boxes of eggs than the small boxes.
(a)
Find, in terms of x, the total number of eggs in the large boxes that Hina buys.
..........................
(1)
(b)
Find, in terms of x, the total number of eggs that Hina buys.
Give your answer in its simplest form.
..........................
(2)
(Total 3 marks)
IV
12.
(a)
Solve x + 2x = 12
x = .............................
(1)
(b)
Solve 2y – 1 = 13
y = .............................
(2)
(Total 3 marks)
13.
P, Q and R are three stations on a railway line.
P
R
Q
26 miles
4 miles
PQ = 26 miles.
QR = 4 miles.
A passenger train leaves P at 12 00. It arrives at Q at 12 30.
Information about the journey from P to Q is shown on the travel graph opposite.
The passenger train stops at Q for 10 minutes.
It then returns to P at the same speed as on the journey from P to Q.
(a)
On the grid, complete the travel graph for this train.
(2)
A goods train leaves R at 12 00.
It arrives at P at 13 00.
(b)
On the grid, draw the travel graph for the goods train.
(1)
IV
(c)
Write down the distance from P where the goods train passes the passenger train.
............................ miles
(1)
Distance
(miles)
from P
R
Q
P
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
12 00
12 30
13 00
13 30
14 00
Time of Day
(Total 4 marks)
14.
Jo buys 8 cups and 8 mugs.
A cup costs £x.
A mug costs £(x + 2)
(a)
Write down an expression, in terms of x, for the total cost, in pounds, of 8 cups and
8 mugs.
£..............................
(2)
IV
The total cost of 8 cups and 8 mugs is £72
(b)
(i)
Express this information as an equation in terms of x.
....................................
(1)
(ii)
Solve your equation to find the cost of a cup and the cost of a mug.
Cost of a cup £ ..............................
Cost of a mug £ ..............................
(4)
(Total 7 marks)
IV
15.
y=
r  t sin x
r  t sin x
r = 8.8
t = 7.2
x = 40
Calculate the value of y. Give your answer correct to 3 significant figures.
y = ............................
(Total 3 marks)
16.
(a)
Solve
4(x + 3) = 6
x = ………………….
(3)
IV
(b)
Make t the subject of the formula v = u + 5t
t = ………………….
(2)
(Total 5 marks)
17.
(a)
Simplify
a3  a4
…………………….
(1)
(b)
Simplify
3x2y  5xy 3
…………………….
(2)
(c)
Simplify
( x  1) 2
x 1
…………………….
(1)
(d)
Factorise x2 – 9
…………………….
(1)
(Total 5 marks)
IV
18.
y = 5x  2
Draw the graph of
on the grid below.
y
10
8
6
4
2
–2
–1
O
x
1
2
–2
–4
–6
–8
–10
(Total 3 marks)
19.
Simplify fully
(i)
m 4  m5
……………………………..
(ii)
p6  p2
………………………………
(iii)
q2  q6
q3
(iv)
5 x y  2 xy
………………………………
IV
3
8
………………………………
4k  8
k 8
2
(v)
……………………………..
(Total 6 marks)
20.
A straight line has equation y  4 x  5 .
(a)
Write down the equation of the straight line that is parallel to y  4 x  5 and passes
through the point (0, 3).
………………………..
(2)
(b)
Rearrange the equation
y  4 x  5 to find x in terms of y.
x = ……………………..
(2)
(Total 4 marks)
21.
(a)
Simplify
8x + 5y – 3x + y
……………………………
(2)
IV
(b)
Solve
2x – 5 = 4
x = ……………………………
(2)
(c)
Factorise
3m + 15
……………………………
(1)
(Total 5 marks)
22.
Make c the subject of the formula
a = 3c – 4
c = ……………………………
(Total 2 marks)
IV
23.
James left home at 10 00 am.
He walked to the swimming pool.
On the way to the swimming pool he stopped to talk to a friend.
Here is the distance-time graph for his complete journey.
Distance in km 5
from
James’ home
4
3
2
1
0
10 00
(a)
11 00
12 00
Time
For how many minutes did James stop and talk to his friend?
…………………………… minutes
(1)
(b)
What is the distance from James’ home to the swimming pool?
…………………………… km
(1)
(Total 2 marks)
24.
Solve the inequality 3x + 2 > –7
............................
(Total 2 marks)
IV
25.
A straight line has equation
y=
1
x+1
2
The point P lies on the straight line.
P has a y-coordinate of 5.
(a)
Find the x-coordinate of P.
............................
(2)
(b)
Write down the equation of a different straight line that is parallel to y =
1
x+1
2
............................
(1)
(c)
Rearrange y = ax + c to make x the subject.
x = ......................
(2)
(Total 5 marks)
26.
Factorise
9x + 12
…………………..
(Totak 1mark)
27.
(a)
Factorise
x2 + x
……………..
(1)
IV
(b)
Factorise
y2  2y  35
…………………………….
(2)
(Total 3 marks)
28.
B
D
2x º
P
(x + 15)º
A
C
Q
Diagram NOT accurately drawn
PACQ is a straight line.
AB and CD are parallel.
Angle PAB = (2x)°.
Angle QCD = (x + 15)°.
Work out the value of x.
x = ………………
(Total 3 marks)
29.
(a)
Complete the table of values for
x
3
y
11
2
1
5
y = 3x  2
0
1
2
3
7
(2)
IV
(b)
y = 3x  2
On the grid below, draw the graph of
y
12
10
8
6
4
2
–3
–2
–1
O
1
2
3 x
–2
–4
–6
–8
–10
–12
(2)
(Total 4 marks)
30.
Factorise
x2  10x
……..…………………..
(Total 1 mark)
31.
(a)
Solve 3x – 2 = 22
x = ....................
(2)
IV
(b)
Solve 20y – 16 = 18y – 9
y = ....................
(3)
(Total 5 marks)
32.
Eggs are sold in boxes.
A small box holds 6 eggs.
A large box holds 12 eggs.
Hina buys x small boxes of eggs.
Hina also buys 4 less of the large boxes of eggs than the small boxes.
(a)
Find, in terms of x, the total number of eggs in the large boxes that Hina buys.
..........................
(1)
(b)
Find, in terms of x, the total number of eggs that Hina buys.
Give your answer in its simplest form.
..........................
(2)
(Total 3 marks)
33.
A straight line has equation
y = 2(3 – 4x)
Find the gradient of the straight line.
..........................
(Total 2 marks)
IV
34.
P = 3a + 5b
a = 5.8
b = –3.4
Work out the value of P.
P = ..........................
(Total 2 marks)
35.
C = 2p – 5q
p = –3
q=4
Work out the value of C.
C = ..........................
(Total 2 marks)
36.
(a)
Expand and simplify
(3x + 2)(4x + 1)
............................................
(2)
(b)
Factorise completely
3x2 + 6xy
............................
(2)
(Total 4 marks)
37.
(a)
Expand
y(y + 5)
..........................
(1)
IV
(b)
Factorise
10x – 6
..........................
(1)
(Total 2 marks)
38.
Solve
5(x + 8) =
7x  4
2
x = ............................
(Total 4 marks)
IV
39.
Alex has a mobile phone.
Each month he pays
13.4p for each minute he uses his mobile phone
and
a fixed charge of £18.75
In January Alex uses his mobile phone for 405 minutes.
Work out the total amount Alex pays.
£ ...............................
(Total 3 marks)
40.
Make p the subject of the formula
m = 3n + 2p
p = ...............................
(Total 2 marks)
41.
Solve 5x + 3 > 19
............................
(Total 2 marks)
IV
42.
A man left home at 12 noon to go for a cycle ride.
The travel graph represents part of the man’s journey.
At 12.45pm the man stopped for a rest.
(a)
For how many minutes did he rest?
…………… minutes
(1)
The man stopped for another rest at 2pm.
He rested for one hour.
Then he cycled home at a steady speed. It took him 2 hours.
(b)
Complete the travel graph.
(2)
(Total 3 marks)
IV