Q1.
Each shape stands for a number.
 
Work out the value of each shape.
 
1 mark
 
1 mark
Q2.
n = 22
What is 2n + 9?
 
1 mark
2q + 4 = 100
Work out the value of q.
 
1 mark
Q3.
Maria bakes cakes and sells them in bags.
 
She uses this formula to work out how much to charge 
for one bag of cakes.
 
Cost = number of cakes × 20p + 15p for the bag	
How much will a bag of 12 cakes cost?
 
1 mark
Olivia buys a bag of cakes for £5.15
Use the formula to calculate how many cakes are in the bag.

2 marks

Q4.
g stands for a number on a grey card.
w stands for a number on a white card.
Join all pairs of numbers that match this rule:
 
2g + w = 10	
One is done for you.

2 marks
Q5.
Here is an equation.
m − 2n = 10
When n = 20 what is the value of m?
 
m = ____________
1 mark
When m = 20 what is the value of n?
 
  n = ____________
1 mark

Q6.
m stands for a whole number greater than 10 and less than 20
n stands for a whole number greater than 2 and less than 10
What is the smallest number that m × n could be?
 
1 mark
What is the largest number that m – n could be?
 
1 mark
Q7.
(a)     There are n counters in Alfie’s bag.

Alfie puts 3 more counters in the bag.
Write an expression for the number of counters that are in the bag now. 
 
1 mark
(b)     Megan has two boxes.
There are m counters in each box.

She puts all her counters together in a pile, then removes 5 of them.
Write an expression for the number of counters that are in the pile now. 
 
Q8.
Here are an equilateral triangle and a regular pentagon.
Not actual size
 
Each side of the triangle is 10 cm
Each side of the pentagon is d cm
The perimeter of the pentagon is 4 centimetres more than the perimeter of the triangle.
What number does d represent?
 
2 marks
Q9.
Write the missing numbers so that 2a + 5b = 30
One is done for you.
2a + 5b = 30       when      a = 0       and        b = ___6___
2a + 5b = 30       when      a = 5       and        b = _______
1 mark
2a + 5b = 30      when      a = 15     and        b = _______
1 mark

Q10.
Here is an equation.
k = 100 − 4n
(a)     Find the value of k when n = 60
 
1 mark
(b)     Find the value of n when k = 99
 
1 mark
Q11.
Alfie has some photographs printed.
The cost is £2.50 for postage and
12 pence for each print.	 	

Alfie uses this formula for the total cost (C) in pence.
C = 250 + 12n
n stands for the number of photographs.
The total cost for Alfie is £6.70
How many photographs does he have printed?

2 marks
Q12.
A shop sells fruit.
Chen buys 2 apples and 3 bananas.
He pays £2.35	 	
 
Megan buys 2 apples and 1 banana.
She pays £1.25	 	
 
How much does one banana cost?

Q13.
Here is a rule for the time it takes to cook a chicken.
 
Cooking time = 20 minutes plus an extra
                                   40 minutes for each kilogram	
How many minutes will it take to cook a 3 kg chicken?
 
What is the mass of a chicken that takes 100 minutes to cook? 
Q14.
The numbers in this sequence increase by 30 each time.
20      50      80      110  ...
The sequence continues in the same way.
Which number in the sequence will be closest to 300?

Q15.
In this diagram, the shaded rectangles are all of equal width (w).
 
Calculate the width (w) of one shaded rectangle.
 
2 marks
Q16.
Here is a pattern of number pairs.
 
a	b	
1	9	
2	19	
3	29	
4	39	
Complete the rule for the number pattern.
 
1 mark

Mark schemes
Q1.
(a)      = 32
1
(b)      = 18
If the answers to  and  are incorrect, award ONE mark if
 +  = 50 unless  = 25
1
[2]
Q2.
(a)     53
1
(b)     48
1
[2]
Q3.
(a)     £2.55
1
(b)     Award TWO marks for the correct answer of 25
If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g:
•        £5.15 − 15p = £5
£5 ÷ 20p
OR
•        £5.15 − 15p = £5
5 × 5
Answer need not be obtained for the award of ONE mark.
Commentary: The 2014 national curriculum specifies that pupils should use simple formulae (6A2).
Up to 2
[3]
Q4.
Draws the three correct lines and no incorrect lines, ie:

!    Lines do not touch the shapes
Accept provided the intention is clear
2
or
Draws two correct lines and no incorrect lines
OR
Draws the three correct lines and one incorrect line
1
[2]
Q5.
(a)     50
1
(b)     5
1
[2]
Q6.
(a)     33
Accept 3 × 11
1
(b)     16
Accept 19 – 3
U1
[2]
Q7.
(a)     n + 3 or 3 + n
!     Algebra
!     Alternative letter used, eg, for part (a),
accept m used instead of n, if the expression
is otherwise correct:
•   m + 3
1
(b)     2m – 5
!     Condone unsimplified or unconventional algebra,
eg, for part (b):
•   m + m − 5
•   m2 − 5
1
[2]
 
Q8.
6.8
Accept equivalent fractions and decimals, eg:
•   
•    
2
or
Shows or implies a complete, correct method, eg:
•        5d = 3 × 10 + 4
5d = 34
  d = 34 ÷ 5
•        3 × 10 = 40 (error)
40 + 4 = 44
44 ÷ 5 = 8.4 (error)
•        30 + 4 = 34
34 ÷ 5
Do not accept incorrect methods, eg:
where the perimeter of the pentagon is treated as
being 4cm less than the perimeter of the triangle:
•   30 – 4 = 26
    26 ÷ 5 = 5.2
1
[2]
 
Q9.
(a)     4
!   Algebra
1
(b)     0
1
[2]
Q10.
(a)     −140
1
(b)     0.25 or 
Accept equivalent fractions or decimals
Do not accept embedded solutions
1
[2]
Q11.
35
2
or
Shows or implies a complete correct method, eg:
•        (670 – 250) ÷ 12
•        670 = 250 + 12n
12n = 670 - 250
12n = 430 (error)
n = 430 ÷ 12 = 25.8 (error)
!    Inconsistent units
Within an otherwise correct method, condone
eg, for 1 mark accept
(£6.70 – 250) ÷ 12
!    Condone correct embedded solutions
Award 1 mark, for a response which shows 35 as the embedded solution to their working
1
[2]
Q12.
Award TWO marks for the correct answer of 55p OR £0.55
If the answer is incorrect, award ONE mark for evidence of appropriate working, eg
■       £2.35 – £1.25 =  £1.10
£1.10 ÷ 2 = wrong answer
Accept for ONE mark £55 OR £55p OR 0.55p as evidence of appropriate working.
Working must be carried through to reach an answer for the award of ONE mark.
Up to 2
U1
[2]
Q13.
(a)     140
The answer is a time interval
1
(b)     2
1
[2]
Q14.
Award TWO marks for the correct answer of 290
If the answer is incorrect, award ONE mark for evidence of appropriate working, eg:
■        110   140   170   200   230   260   290    
Not spotting closest number.
OR
■        110   140   170   190   220   250   280   
One step size incorrect (170 to 190).
OR
■        300 + 20 = 320
320 - 30 = wrong answer
Working must be carried through to reach an answer for the award of ONE mark.
Up to 2
U1
[2]
Q15.
Award TWO marks for the correct answer of 7
If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g.
•    18 + 9 + 2 widths = 34 + 1 width
     27 + 2 widths = 34 + 1 width
     27 + 1 width = 34
     34 − 27
OR
•    34 − (18 + 9)
Answer need not be obtained for the award of ONE mark.
Award ONE mark for a method which uses algebraic representation correctly, e.g.
•    34 + w = 18 + w + 9 + w
     34 + w = 27 + w + w
Up to 2m
[2]
Q16.
Both numbers correct as shown:
 
[1]