##### Mathematics Paper 2: reasoning (May 2016) – with hints

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# Mathematics

## Paper 2 (May 2016): reasoning, with hints

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completed this test on Wednesday, 26-Jun-19 05:42:09 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)CorrectIncorrect##### 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.

- Question 2 of 25
##### 2. Question

- 511
- 499
- 502
- 555
- 455

Write the number**furthest**from 500- (555)

1 mark(s)CorrectIncorrect##### Hint

The number furthest away must be either the smallest number or the largest number; all the others will be closer.

- Question 3 of 25
##### 3. Question

2Put these houses in order of price starting with the lowest price.One has been done for you.

- (E, £91,500)
**B**- (C, £130,500)
- (D, £131,500)
- (A, £135,300)

lowest

1 mark(s)CorrectIncorrect##### Hint

Start with the lowest price and work your way along to the highest.

- 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)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### Hint

On a sheet of paper, write down the populations for Formby and Telford and carefully add them up.

- 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)CorrectIncorrect##### Hint

To find the difference, write down the larger number and subtract the smaller number.

- 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)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### Hint

A mirror can reflect a shape but it can’t rotate it.

- Question 9 of 25
##### 9. Question

7Write the two missing values to make these equivalent fractions correct.**A = (2)****B = (6)**

2 mark(s)CorrectIncorrect##### Hint

To find

**equivalent fractions**, multiply both the numerator and denominator by the same whole number. - Question 10 of 25
##### 10. Question

8Tick two numbers that add together to equal 0.251 mark(s)CorrectIncorrect##### Hint

You can rule out 0.5 straightaway because it’s already greater than 0.25, and there aren’t any negative numbers.

- 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)CorrectIncorrect##### 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. - 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)CorrectIncorrect##### Hint

For each diagram, find out how many sections make one quarter. Three-quarters shaded means one quarter is unshaded.

- 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)CorrectIncorrect##### 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.

- Question 14 of 25
##### 14. Question

12n = 22What is 2n + 9?- (53)

1 mark(s)CorrectIncorrect##### Hint

The question tells us that

= 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.)**n**Then the expression looks like this: 2 x 22 + 9

Can you solve it now?

- Question 15 of 25
##### 15. Question

2q + 4 = 100Work out the value of q.- q = (48)

1 mark(s)CorrectIncorrect##### Hint

We need to get

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:**q**2

= 96**q**Now it’s pretty easy to get

.**q** - 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)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### 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?

- 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)CorrectIncorrect##### 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.

- Question 19 of 25
##### 19. Question

16Write the number that is five less than**ten million**.- (9,999,995, 9999995)

1 mark(s)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### Hint

A million is equal to one thousand thousands. How many hundred thousands make one million?

- Question 21 of 25
##### 21. Question

17Calculate the size of angles a and b in this diagram.- a = (160)°

1 mark(s)CorrectIncorrect##### Hint

Where two straight lines intersect, the angles that are opposite each other are equal in size.

- Question 22 of 25
##### 22. Question

- b = (20)°

1 mark(s)CorrectIncorrect##### Hint

The interior angles of a quadrilateral add up to 360°.

- Question 23 of 25
##### 23. Question

18Write the missing number.- 70 ÷ (20) = 3.5

1 mark(s)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### 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.

- 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)CorrectIncorrect##### 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.