#
OCR GCSE Maths 2015 JUNE

â€‹Foundation Tier

MODEL ANSWERS

Model answers and worked solutions for the OCR GCSE Maths (A501/01) 2015 June Unit A Foundation Tier paper.

## Question 1

1. From the numbers 30 to 39, choose

(a) a multiple of 5,

(a) a multiple of 5,

**Solution**

**Answer:**

**[1]**

**30**or

**35**

(b) a square number,

(c) a prime number.

**Solution**

**Answer: [1]**

**31**or

**37**.

## Question 2

2. Choose from these units to complete the following statements.

A small bird weighs 9 ................................... .

The length of a desk is 900 ...................................

When full, a bucket holds 20 ................................... .

The length of a cross-country running race is 6 ................................... .

The length of a desk is 900 ...................................

When full, a bucket holds 20 ................................... .

The length of a cross-country running race is 6 ................................... .

**Solution**

**Answer: [4]**

A small bird weighs 9

**g.**

The length of a desk is 900

**mm**.

When full, a bucket holds 20

**litres**.

The length of a cross-country running race is 6

**km.**

*Diagram: Mobility of Ions in Solid & Liquid/Solution states*

## Question 3

3. Here is a coordinate grid.

(a) Write down the coordinates of point A.

**Solution**

**Answer [1]:**

**(4, 1)**.

**(b)**Plot the point (-3, -4). Label it B.

**(c)**Find the coordinates of the midpoint of AC.

**Solution**

**Answer [2]:**

AC is 3 across and 4 up (starting from point C) therefore its midpoint will be 1.5 across and 2 up (starting from point C) giving us the point

**(2.5, -1)**

## Question 4

4. This bar chart shows the amounts that Paul and Sumita spent on their holidays.

(a) Paul spent £120 on entertainment.

Complete the bar chart to show this information

Complete the bar chart to show this information

(b) How much did Sumita spend on travel?

**SOLution**

**Answer [1]:**

Sumita spent

**£310**on travel.

(c) Whose holiday cost more altogether, and by how much?

**SOLution**

**Answer [3]:**

Paul’s total holiday cost was

£170 + £280 + £90 + £120 = £660

Sumita’s total holiday cost was

£310 + £230 + £40 + £70 = £650

So

**Paul’s holiday cost more by £660- £650 = £10.**

## Question 5

5. (a) Work out.

(i) 8 ÷ 100

(i) 8 ÷ 100

(iii) 4 + 8 × 3

**SOLution**

**Answer [1]:**

From BODMAS we know that multiplication is done

**before**addition so

4+8*3 = 4 + (8*3) = 4 + 24 =

**28**

(b) A number is multiplied by 8.

The answer is positive and less than 8.

Find a possible number and complete the calculation.

The answer is positive and less than 8.

Find a possible number and complete the calculation.

**SOLution**

**Answer [2]:**

- We know the answer is positive and we are multiplying by a positive so our number must be positive.
- It’s less than 8 and we are multiplying by 8 so our answer must be less than one i.e. a fraction.

**1/2**

**8 * 1/2 = 4**

## Question 6

**6.**Dale asked each of 10 students from class 11M how many items they had downloaded the previous day.

Here are their responses.

(a) Find the mode.

**solution**

**Answer [1]:**

The number that occurs the

**most**is the**mode**. In this case it’s**0**.(b) Find the median.

**solution**

**Answer [2]:**

Order the numbers by size.

The one (or mean of the two) in the middle is the

In this case it’s

The one (or mean of the two) in the middle is the

**median**.In this case it’s

**( 7 + 12 ) / 2 =****9.5**(c) Dale also asked each of 10 students from class 11Y how many items they had downloaded the previous day.

The range of their responses was 21 and the mean of their responses was 14.

Calculate the appropriate values for class 11M so that you can complete the following statements.

The range of their responses was 21 and the mean of their responses was 14.

Calculate the appropriate values for class 11M so that you can complete the following statements.

**solution**

**Answer [4]:**

The range for 11M is the biggest number minus the smallest number which is

22 − 0 = 22

The mean for 11M is the numbers added together and divided by the amount of numbers which is

5 + 0 + 4 + 12 + 17 + 22 + 0 + 15 + 7 + 20 = 102

102 ÷ 10 =

**10.2**

**Answer [2]:**

Therefore class 11Y downloaded more items on average because their

**average of 14 is larger than 11M’s average of 10.2.**

Class 11M had a greater spread of items downloaded because their

**spread of 22 is bigger than 11Y’s spread of 21.**

## Question 7

7. This map shows some places in Norfolk.

(a) What is the compass direction of Guist from Bawdeswell?

**solution**

**Answer [1]:**

**NW**

(b) A bird flies direct from Bawdeswell to Longham.

(i) Draw a line on the map for this journey and measure it. Calculate the actual distance the bird flies.

(i) Draw a line on the map for this journey and measure it. Calculate the actual distance the bird flies.

(ii) Find the bearing of Longham from Bawdeswell.

**SOLUTION**

**Answer [1]:**

Using a protractor the bearing of Longham

**from**Bawdeswell is

**between 246 and 251.**

(c) Reepham is 24 km from Norwich.

About how many miles is 24 km? Ring the correct answer.

About how many miles is 24 km? Ring the correct answer.

**SOLUTION**

**Answer [1]:**

We know that 8km is 5 miles.

24𝑘𝑚 = 3 × 8𝑘𝑚 = 3 × 5 𝑚𝑖𝑙𝑒𝑠 = 𝟏𝟓 𝒎𝒊𝒍𝒆𝒔

## Question 8

8. A shop has these prices for bird food.

(a) Pavel wants to buy

• 3 kg of nuts

• 24 suet spheres.

Show that buying these is not enough to get the special offer.

• 3 kg of nuts

• 24 suet spheres.

Show that buying these is not enough to get the special offer.

**SOLUTION**

**Answer [3]:**

Pavel buys 3kg of nuts at £5.30 per kg so he spends

3 × £5.30 = £15.90

on nuts. He also buys 24 suet spheres which come in bags of 6 for £1.90. So he bought

24 ÷ 6 = 4 𝑏𝑎𝑔𝑠.

4 × £1.90 = £7.60

And so in total he spends

£15.90 + £7.60 = £23.50

Which is £6.50 less than £30 so he does not qualify for the offer.

(b) Show that if Pavel also buys 1 kg of seeds and one more bag, from the three types of bird food available,

it is possible for him to get the special offer.

Find how much he will spend when he does this.

it is possible for him to get the special offer.

Find how much he will spend when he does this.

**SOLUTION**

**Answer [4]:**

1kg is 1000g and seeds come in 500g bags for £2.25. Pavel buys 1kg of seeds, which is two bags, for

2 × £2.25 = £4.50

And he also buys another bag of bird food (£5.30, £2.25, or £1.90).

He spends, in total

£23.50 + £4.50 + £5.30 (𝑂𝑅 £2.25 𝑂𝑅 £1.90)

= £37.45 (𝑂𝑅 £33.30 𝑂𝑅 £30.25)

All the possible answers qualify for the discount so he gets -£10 on his total giving the answer(s):

**£𝟐𝟕. 𝟒𝟓 𝑜𝑟 £𝟐𝟑. 𝟑𝟎 𝑜𝑟 £𝟐𝟎. 𝟐𝟓**

## Question 9

9. (a) Simplify as much as possible.

4a + 5a

4a + 5a

**SOLUTION**

**Answer [1]:**

4a + 5a

Factorise out the a to get

(4 + 5) a =

4a + 5a

Factorise out the a to get

(4 + 5) a =

**9a**

(b) Write an expression for the total cost in pence of two doughnuts at d pence each and three teacakes at t pence each.

**SOLUTION**

**Answer [1]:**

Total Cost =

Total Cost =

**2d + 3t**

(c) Solve these equations.

(i) y – 7 = 4

(i) y – 7 = 4

**SOLUTION**

**Answer [1]:**

y - 7 = 4

Add 7 to both sides to cancel the -7 on the left

y - 7 = 4

y - 7 + 7 = 4 + 7

**y = 11**

(ii) 2(3x – 1) = 10x – 5

## Question 10

10. Samira and Joanne share their living costs in the ratio 3 : 2.

(a) The rent for their flat for a month is £700.

Work out how much of this rent they each pay.

(a) The rent for their flat for a month is £700.

Work out how much of this rent they each pay.

**SOLUTION**

**Answer [3]:**

The ratio Samira : Joanne is 3 : 2. We need to split their rent £700 into 5 parts then Samira pays 3 parts and Joanne pays 2 parts.

£700 ÷ 5 = £140

Therefore

**𝑆𝑎𝑚𝑖𝑟𝑎 𝑝𝑎𝑦𝑠 = 3 × £140 = £420**

𝐽𝑜𝑎𝑛𝑛𝑒 𝑝𝑎𝑦𝑠 = 2 × £140 = £280

𝐽𝑜𝑎𝑛𝑛𝑒 𝑝𝑎𝑦𝑠 = 2 × £140 = £280

(b) For one gas bill, Joanne pays £84 for her share.

How much was the whole gas bill?

How much was the whole gas bill?

## Question 11

11. In this question, use a ruler and a pair of compasses.

Do not rub out your construction lines.

This scale drawing shows Colin’s garden.

Do not rub out your construction lines.

This scale drawing shows Colin’s garden.

Colin wants to put a bird feeder in his garden. He wants it to be

• up to 3 m from the tree T

• up to 2 m from the bush B

• nearer to the water tap W than to the seat S.

Construct the region where Colin can put the bird feeder. Label the region R.

• up to 3 m from the tree T

• up to 2 m from the bush B

• nearer to the water tap W than to the seat S.

Construct the region where Colin can put the bird feeder. Label the region R.