Mathematics Paper 2: reasoning (May 2016) – with hints
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Mathematics
Paper 2 (May 2016): reasoning, with hints
- This test is not timed.
- Hints are available.
- Answers are reviewed after each question.
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completed this test on Friday, 18-Apr-25 16:50:12 UTC
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Question 1 of 25
1. Question
1 (a)Ali puts these five numbers in their correct places on a number line.- 511
- 499
- 502
- 555
- 455
Write the number closest to 500-
(499)
1 mark(s)Correct
Incorrect
Hint
You could do what Ali did and draw a number line, but you can probably spot the number closest to 500 without doing so.
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Question 2 of 25
2. Question
- 511
- 499
- 502
- 555
- 455
Write the number furthest from 500-
(555)
1 mark(s)Correct
Incorrect
Hint
The number furthest away must be either the smallest number or the largest number; all the others will be closer.
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Question 3 of 25
3. Question
2Put these houses in order of price starting with the lowest price.One has been done for you.
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- (E, £91,500)
- B
- (C, £130,500)
- (D, £131,500)
- (A, £135,300)
lowest
1 mark(s)Correct
Incorrect
Hint
Start with the lowest price and work your way along to the highest.
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Question 4 of 25
4. Question
3Write the three missing digits to make this addition correct.-
- A = (1)
- B = (6)
- C = (6)
2 mark(s)Correct
Incorrect
Hint
Start with the units column. What must A be so that A + 4 = 5?
Then look at the tens column. 5 + B = 1 can’t be solved, so there must be a carry digit. That means 5 + B = 11.
When you get to the hundreds column, remember to add the carry digit.
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Question 5 of 25
5. Question
4 (a)This table shows the number of people living in various towns in England.What is the total of the numbers of people living in Formby and in Telford?-
(191,118, 191118)
1 mark(s)Correct
Incorrect
Hint
On a sheet of paper, write down the populations for Formby and Telford and carefully add them up.
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Question 6 of 25
6. Question
4 (b)This table shows the number of people living in various towns in England.What is the difference between the numbers of people living in Bedford and in Dover?-
(48,361, 48361)
2 mark(s)Correct
Incorrect
Hint
To find the difference, write down the larger number and subtract the smaller number.
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Question 7 of 25
7. Question
5Where should the numbers go in the diagram?- 15
- 16
- 17
- 18
- 19
One has been done for you.-
- 15 = F
- 16 = (D)
- 17 = (A)
- 18 = (C)
- 19 = (A)
2 mark(s)Correct
Incorrect
Hint
Take each of the numbers one by one and ask: Is it prime? Is it even? Is it a square number? Then find the right place in the diagram for it. If a number fits into more than one category, you’ll need to place it in an overlapping area.
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Question 8 of 25
8. Question
6This diagram shows a shaded shape inside a border of squares.Tick the diagram that correctly shows the shaded shape and its reflection in the mirror line.1 mark(s)Correct
Incorrect
Hint
A mirror can reflect a shape but it can’t rotate it.
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Question 9 of 25
9. Question
7Write the two missing values to make these equivalent fractions correct.-
- A = (2)
- B = (6)
2 mark(s)Correct
Incorrect
Hint
To find equivalent fractions, multiply both the numerator and denominator by the same whole number.
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Question 10 of 25
10. Question
8Tick two numbers that add together to equal 0.251 mark(s)Correct
Incorrect
Hint
You can rule out 0.5 straightaway because it’s already greater than 0.25, and there aren’t any negative numbers.
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Question 11 of 25
11. Question
96 pencils cost £1.68 3 pencils and 1 rubber cost £1.09 What is the cost of 1 rubber?Show
your
method-
(£0.25, 25p, 25 p, 25pence, 25 pence)
2 mark(s)Correct
Incorrect
Hint
Don’t waste time working out the cost of one pencil. You only need to know the cost of 3 pencils.
Your answer should include the units, pounds or pence, because the answer box does not show it.
Show your method on a separate sheet of paper. If you make a mistake, you could still get one mark if your method is correct.
Here is some suitable squared paper for you to print. -
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Question 12 of 25
12. Question
10Each diagram below is divided into equal sections.Tick every diagram that has three-quarters shaded.2 mark(s)Correct
Incorrect
Hint
For each diagram, find out how many sections make one quarter. Three-quarters shaded means one quarter is unshaded.
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Question 13 of 25
13. Question
11A packet contains 1.5 kg of oats.
Every day Maria uses 50 g of oats to make porridge.How many days does the packet of oats last?Show
your
method-
(30, thirty) days
2 mark(s)Correct
Incorrect
Hint
The number of days until the packet is empty is the same as the number of times you can divide 50g into 1.5kg.
Remember, 1kg = 1,000g.
Show your method on a separate sheet of paper. If you make a mistake, you could still get one mark if your method is correct.Here is some suitable squared paper for you to print.
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Question 14 of 25
14. Question
12n = 22What is 2n + 9?-
(53)
1 mark(s)Correct
Incorrect
Hint
The question tells us that n = 22 so we can replace the letter n in the expression with 22. (We’ll also need a multiplication symbol to stop it looking like 222.)
Then the expression looks like this: 2 x 22 + 9
Can you solve it now?
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Question 15 of 25
15. Question
2q + 4 = 100Work out the value of q.-
q = (48)
1 mark(s)Correct
Incorrect
Hint
We need to get q on its own, but there’s a 4 on the same side. So let’s subtract the 4. The equation will still balance if we remember to subtract 4 from each side. Then we have:
2q = 96
Now it’s pretty easy to get q.
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Question 16 of 25
16. Question
13A stack of 20 identical boxes is 140 cm tall.
Stefan takes three boxes off the top.How tall is the stack now?Show
your
method-
(119) cm
2 mark(s)Correct
Incorrect
Hint
How tall is one box?
Show your method on a separate sheet of paper. If you make a mistake, you could still get one mark if your method is correct.
Here is some suitable squared paper for you to print.
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Question 17 of 25
17. Question
14Write all the common multiples of 3 and 8 that are less than 50-
(24,48, 24, 48, 24 48, 24 48, 48,24, 48, 24, 48 24, 48 24, 24 and 48, 24 & 48, 48 and 24, 48 & 24)
1 mark(s)Correct
Incorrect
Hint
On a piece of paper, write down the eight times table until you reach 50. Which numbers that you have written are also multiples of 3?
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Question 18 of 25
18. Question
15This thermometer shows temperatures in both °C and °F.Work out what 25 °C is in °F.Show
your
method-
(77) °F
2 mark(s)Correct
Incorrect
Hint
25°C is mid-way between 20°C and 30°C. Look at the thermometer to find the Farenheit temperatures that match up with 20°C and 30°C.
What would be mid-way between these?
Show your method on a separate sheet of paper. If you make a mistake, you could still get one mark if your method is correct.
Here is some suitable squared paper for you to print.
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Question 19 of 25
19. Question
16Write the number that is five less than ten million.-
(9,999,995, 9999995)
1 mark(s)Correct
Incorrect
Hint
You can do this as long as you don’t make a careless mistake. Check you have the right number of digits in your answer.
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Question 20 of 25
20. Question
Write the number that is one hundred thousand less than six million.-
(5,900,000, 5900000)
1 mark(s)Correct
Incorrect
Hint
A million is equal to one thousand thousands. How many hundred thousands make one million?
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Question 21 of 25
21. Question
17Calculate the size of angles a and b in this diagram.-
a = (160)°
1 mark(s)Correct
Incorrect
Hint
Where two straight lines intersect, the angles that are opposite each other are equal in size.
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Question 22 of 25
22. Question
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b = (20)°
1 mark(s)Correct
Incorrect
Hint
The interior angles of a quadrilateral add up to 360°.
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Question 23 of 25
23. Question
18Write the missing number.-
70 ÷ (20) = 3.5
1 mark(s)Correct
Incorrect
Hint
What if the question said 7 instead of 70? If you can answer that question, you only need to multiply your answer by 10 to get the final answer.
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Question 24 of 25
24. Question
19Miss Mills is making jam to sell at the school fair.Strawberries cost £7.50 per kg.
Sugar costs 79p per kg.
10 glass jars cost £6.90She uses 12 kg of strawberries and 10 kg of sugar to
make 20 jars full of jam.Calculate the total cost to make 20 jars full of jam.Show
your
method-
£ (111.70)
3 mark(s)Correct
Incorrect
Hint
Take the ingredients one by one – strawberries, sugar and jars – and work out how much she spends on each to make 20 jars of jam.
Show your method on a separate sheet of paper. If you make a mistake, you could still get one mark if your method is correct.Here is some suitable squared paper for you to print.
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Question 25 of 25
25. Question
20Here are two triangles drawn on coordinate axes.
Triangle B is a reflection of triangle A in the x-axis.
Two of the new vertices of triangle B are (10, –10) and (20, –30).What are the coordinates of the third vertex of triangle B?-
( (-10), (-40) )
1 mark(s)Correct
Incorrect
Hint
A vertex just means the corner of a shape.
You first need to know which is the third vertex. First, look at the two pairs of coordinates you’ve been given and match them to the reflected triangle’s vertices. One vertex will be left unmatched. -