1.
(a)
Matt buys 12 boxes of orange juice at 43 pence each.
(i)
Calculate the total cost.
............................................................................................................................
............................................................................................................................
Answer £ ...........................................................
(2)
(ii)
He pays with a £10 note.
How much change will he receive?
............................................................................................................................
............................................................................................................................
Answer £ ...........................................................
(1)
(b)
Aisha buys c apples at 16 pence each.
(i)
Write down an expression for the total cost in terms of c.
Answer ........................................................... pence
(1)
(ii)
She now buys d pears at 20 pence each.
Write down an expression for the total cost of the apples and pears.
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Answer .......................................................... pence
(2)
(Total 6 marks)
2.
(a)
At a cafe a cup of coffee costs 75p.
Write down an expression for the cost, in pence, of x cups of coffee.
.....................................................................................................................................
Answer ..............................................................pence
(1)
(b)
(i)
The cafe sells twice as many cups of tea as it does cups of coffee.
Write down an expression for the number of cups of tea sold when x cups of coffee
are sold.
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Answer .......................................................................
(1)
The Robert Smyth School
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(ii)
Each cup of tea costs 50p.
Write down an expression for the cost, in pence, of the cups of tea sold.
...........................................................................................................................
Answer ..............................................................pence
(1)
(c)
The cafe also sells cakes and buns.
(i)
Write down an expression for the cost, in pence, of y cakes at 40p each and 3 buns
at 60p each.
...........................................................................................................................
Answer ..............................................................pence
(2)
(ii)
The total cost of the y cakes and 3 buns is £4.60
Find the number of cakes sold.
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Answer .......................................................................
(3)
(Total 8 marks)
3.
Grace is x years old.
Harry is 3 years older than Grace.
(a)
Write down an expression for Harry’s age.
Answer ………………………………………
(1)
(b)
Jack is twice as old as Harry.
Write down an expression for Jack’s age.
Answer ………………………………………
(1)
(Total 2 marks)
The Robert Smyth School
2
4.
Sticks are used to make a sequence of patterns.
The first three patterns are shown.
Pattern 1
(a)
Pattern 2
Pattern 3
Pattern 4
Draw pattern 4 in the space provided.
(1)
(b)
Complete the table showing the number of matches in each pattern.
Pattern number
1
2
3
Number of sticks
8
11
14
4
5
(1)
(c)
What pattern do you notice in the number of sticks?
.....................................................................................................................................
.....................................................................................................................................
Answer ....................................................
(1)
(Total 3 marks)
5.
Sam makes a sequence of patterns with sticks.
Here are his first three patterns.
(a)
Pattern 1
Draw Pattern 4.
Pattern 2
Pattern 3
(1)
The Robert Smyth School
3
(b)
Complete the table.
Pattern number
1
2
Number of sticks
3
5
3
4
(2)
(c)
How many sticks will Sam use for Pattern 5?
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Answer ...............................................
(1)
(d)
There are 33 sticks in Pattern 16.
How many sticks are there in Pattern 17?
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Answer ...............................................
(1)
(Total 5 marks)
6.
Patterns are made of sticks.
Pattern 1
(a)
Pattern 2
Pattern 3
Pattern 4
Complete the table for Pattern 4.
Pattern
number
1
2
3
Number of
sticks
5
7
9
4
(1)
(b)
Sketch Pattern 5.
(1)
The Robert Smyth School
4
(c)
Which pattern will have 25 sticks?
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.....................................................................................................................................
Answer ..................................................................
(2)
(d)
Here is the rule for working out the number of sticks.
Multiply pattern number by 2 and add 3
How many sticks will be in Pattern 100?
.....................................................................................................................................
Answer ..................................................................
(1)
(Total 5 marks)
7.
Patterns are made from shaded and unshaded squares.
Pattern 1
(a)
Pattern 2
Pattern 3
Pattern 4
Pattern 5
Draw Pattern 6.
(1)
(b)
How many shaded squares will there be in Pattern 20?
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Answer .........................................................................
(1)
(c)
How many unshaded squares will there be in Pattern 20?
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.....................................................................................................................................
Answer .........................................................................
(1)
(d)
Which pattern will have 30 squares altogether?
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.....................................................................................................................................
Answer .........................................................................
(1)
(Total 4 marks)
The Robert Smyth School
5
8.
(a)
Find the value of 3x + 4y
(i)
when x = 2 and y = 5
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...........................................................................................................................
Answer ........................................................................
(2)
(ii)
when x = 6 and y = –3
...........................................................................................................................
...........................................................................................................................
Answer ........................................................................
(2)
(b)
Find the value of a3 + b2 when a = 2 and b = 5
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.....................................................................................................................................
Answer ........................................................................
(2)
(Total 6 marks)
9.
(a)
Use the formula a = 5b + 2c to work out a when b = 3 and c = –4
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.....................................................................................................................................
Answer .........................................................................
(2)
(b)
Use the formula a = 5b + 2c to work out c when a = 16 and b = 2
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Answer .........................................................................
(3)
(Total 5 marks)
10.
Use the formula v = u + 10t to work out u when v = –4 and t = 7
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Answer u =…………………………………………………
(Total 3 marks)
The Robert Smyth School
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1.
(a)
(b)
(i)
12 × 43 or 12 × 0.43
Or 516 screen
M1
(£) 5.16
A1
(ii)
(£) 4.84
10 – “their (a)(i)” where (a)(i) < 10
B1 ft
(i)
16c or £0.16c
Accept c × 16 but not c16
B1
(ii)
20d or £0.20d
Accept d × 20 but not d20
(penalise only once)
M1
16c + 20d or £0.16c + £0.20d
Accept c × 16 + d × 20
c16 + d20 scores B0 M1 A1
A1
[6]
2.
(a)
75x, 75 × x, P = 75x
oe B0 for x75 mark answer on
answer line throughout this question
B1
(b)
(i)
B1
2x
oe B0 for x2
(c)
(ii)
2x50 or 100x
oe B0 for x100 only penalise once
for x in front of number in (a) and (b)
B1
(i)
40y or y40 or y × 40 or 3 × 60
oe
B1
40y + 3 × 60 or y40 + 3 × 60
oe 40y + 180
B1
40y + 3 × 60 = 460
oe y + 4.5 = 11.5
M1
(ii)
40y = 460 – 180
y = 11.5 – 4.5
7
DM1
A1
[8]
3.
(a)
x+3
B1
Accept H = x + 3 not H = G + 3
(b)
2(x + 3)
Bl ft
2 (their (a)) provided their (a) has 2
terms
[2]
The Robert Smyth School
7
4.
(a)
Correct drawing
B1
(b)
17 and 20
B1
Must have both
(c)
Goes up in 3’s
Any sensible description
B1
[3]
5.
(a)
correct pattern
can add triangle on left or right
B1
(b)
7,9
(c)
11
B1
(d)
35
B1
B1,B1
[5]
6.
(a)
11
B1
(b)
(c)
(d)
B1
Valid method eg (25 – 3) ÷ 2
Accept build up method
M1
11
A1
203
B1
[5]
7.
(a)
B1
Condone slightly different sizes
Shading must be seen
Shapes must match up (± 2 mm)
(b)
2
B1
(c)
20
B1
(d)
(Pattern) 28
B1
[4]
The Robert Smyth School
8
8.
(a)
(i)
(ii)
6 + 20
M1
26
A1
18 and – 12 seen
M1
6
A1
Note: 18x – 12y scores M0 A0
(b)
8 or 25
M1
33
A1
[6]
9.
(a)
(b)
5 × 3 (+) 2 × –4 or 15 (+) -8
23 implies M1 A0
M1
7
A1
16 = 10 +2c
M1
(c =) a  5b
2
6 = 2c
M1
(c =) 16  10
2
10 + 2 × 3 (= 16) scores M2
3
A1
[5]
10.
–4 = u + (10 × 7)
M1
v – 10t = u
–4 –70 = u
u = –74
M1
A1
[3]
The Robert Smyth School
9