1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven. [1] (ii) Write down, in words, the number 6014. [1] (b) Using

1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven.

[1]

(ii) Write down, in words, the number 6014.

[1]

[1]

(b) Using the following list of numbers

22 81 24 35 78 59 3 61 69 write down

(i) two numbers that have a sum of 100,

(ii) the number that must be added to 36 to make 95,

(iii) a multiple of 7,

(iv) the square of 9.

[1]

[1]

[1]

(c) Write down all the factors of 55.[2]

(d) How many torches at £3.85 each can be bought with £20?[2]

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[1]


[1]

[1]


22 81 24 35 78 59 3 61 69 write down





[1]

[1]

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24,507

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Six thousand and fourteen

22 and 78

95 – 36 = 59

35

81

1, 5, 11, 55

20 3.85

≈ 20 4

Don’t miss out 0 in tens

Numbers must be

from the list

Not 9 × 2 = 18FO

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= 5 20 4


[1]


[1]

[1]


22 81 24 35 78 59 3 61 69 write down





[1]

[1]

[1]



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AO1 – AO1 – Recall and use knowledge of properties of numbers

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[1]


[1]

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22 81 24 35 78 59 3 61 69 write down





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[1]

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2. Which metric unit is best used to measure

the volume of water in a bucket,

[3]

the area of the floor of a classroom,

the distance from Llandudno to Swansea,

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m 2

km

Use metric units, not Imperial units e.g. use kilometres and litres not

miles and gallons

Area must be a square unit

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[3]



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AO1 – AO1 – Recall and use knowledge of metric units

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3. (a) Complete the following shape so that it is symmetrical about the line AB.

[2]

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[2]

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AO1AO1 – Recall and use knowledge of line symmetry

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3 (b) Draw all the lines of symmetry on each of the following diagrams.

[3]

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[3]

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AO1AO1 – Recall and use knowledge of line symmetry

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ASSESSMENT

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4. A bag contains a large number of cards. Drawn on each card there is either a circle, a triangle, a parallelogram or a hexagon.

[6]

Circle (C) Triangle (T) Parallelogram (P) Hexagon (H)

Thirty two pupils were asked to select a card at random, note down the shape and replace the card in the bag.Here are the results.

(a) Using the centimetre squared grid, draw a bar chart of the data given.

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[6]




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RevealPart b

11

32

5

7

9

Shape Tally Frequency

C

T

H

P

Total

Circle (C

)

Triangle (T

)

Parallelogram

(P)

Hexagon (H

)

0

1

2

3

4

5

6

7

8

9

10

11

12

Fre

qu

enc

y

Check that you’ve got all (4 × 8) = 32

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[6]




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AO3AO3 – Generating a strategy to collate the data e.g. tally chart

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ASSESSMENT

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4 (b) One of the pupils is selected at random and asked to show their card. What is the probability that the card has a triangle drawn on it?

[2]

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732

7 because there are 7 triangles

32 because there are 32 cards in total

Answer has to be written as a fraction, decimal or percentage.

NOT ‘7 out of 32’, ‘7 in 32’ or ‘7 : 32’

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[2]

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AO1AO1 – Recall and use knowledge of the probability of equally likely

events

ASSESSMENT

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ASSESSMENT

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[2]

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5. The chart shows the times five friends spent at a gym.

(a) Who was the first person to arrive at the gym?

[1](b) For how long was Jake at the gym?

(c) State the times when at least 3 of the friends were in the gym together.

[2]

[2]

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[2]

[2]

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Lisa

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4:30pm to 6:15pm so 1 hour and 45 minutes

4:30pm to 5:15pm and 5:30pm to 6:15pm

As 4 squares represent 1 hour, 1 square represents 15 minutes

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[2]

[2]

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AO1 – AO1 – Recall and use knowledge of diagrams and scales

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ASSESSMENT

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[2]

[2]

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6. (a) Write down the next term in each of the following sequences.

[2]

(i) 2, 10, 18, 26,

(b) Susan thinks of a number.She multiplies her number by 5 and subtracts 6.Her answer is 34.What was her number?

(ii) 100, 84, 68, 52,

[2]

(c) Simplify 6g + 2g + g. [1]

(d) Find the value of 3c + 4d, when c = 4 and d = 2.

[2]

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[2]

(i) 2, 10, 18, 26,


(ii) 100, 84, 68, 52,

[2]



[2]

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34

RevealPart e

36

+ 8 + 8 + 8 + 8

– 16 – 16 – 16 – 16

9g

(3 × 4) + (4 × 2)

Her number was 8

g is the same as 1g

(Not 34 + 42 or 12c + 8d)

3c means 3 c

Input × 5 – 6 Output

8 ÷ 5 + 6 34

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= 12 + 8 = 20


[2]

(i) 2, 10, 18, 26,


(ii) 100, 84, 68, 52,

[2]



[2]

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((a), (c) and (d) – AO1 – a), (c) and (d) – AO1 – Recall and use knowledge of basic algebra

((bb) – AO2 – ) – AO2 – Select and apply a method to find an unknown

((a), (c) and (d) – AO1 – a), (c) and (d) – AO1 – Recall and use knowledge of basic algebra

((bb) – AO2 – ) – AO2 – Select and apply a method to find an unknown

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ASSESSMENT

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[2]

(i) 2, 10, 18, 26,


(ii) 100, 84, 68, 52,

[2]



[2]

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6 (e) There is a relation between the x-coordinate and the y-coordinate of each of the following points.

(1, 4) (2, 5) (3, 6) (4, 7) . . . . . . . . . (x, y)

Write down the formula connecting x and y.

[2]

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(1, 4) (2, 5) (3, 6) (4, 7) . . . . . . . . . (x, y)


[2]

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For each point, the y-coordinate is 3 more than the x-coordinate.

RevealParts a-d

+ 3 + 3 + 3 + 3

So, the formula is

y = x + 3

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(1, 4) (2, 5) (3, 6) (4, 7) . . . . . . . . . (x, y)


[2]

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AO2AO2 – Select and apply a method to find the relationship between x

and y

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ASSESSMENT

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(1, 4) (2, 5) (3, 6) (4, 7) . . . . . . . . . (x, y)


[2]

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7. (a) A unit used in the Imperial system for measuring the area of a field is the acre. The unit used in the metric system is the hectare. The table shows the number of acres and the number of hectares in each of three areas.

[2]

[2]

Use the data in the table to draw a conversion graph between acres and hectares.

(b) Find an estimate for the number of hectares in 200 acres.

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[2]

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Reveal

2 acres 0.8 hectares

0.8

× 100

200 acres 80 hectares

As 200 acres is not on the graph, pick a smaller number that is a factor of 200. e.g. 2

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(a)(a) AO1 – AO1 – recall and use knowledge of conversion graphs

(b)(b) AO2 –AO2 – select an appropriate method to convert a value that is not on either axis

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ASSESSMENT

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8. Petra and Steve are organising a packed lunch and a bottle of water for each pupil going on a school trip.Petra puts the packed lunches into boxes with each box holding 20 lunches.Steve puts the bottles of water into crates with each crate holding 18 bottles.When they have finished Petra has filled 45 boxes and Steve has filled 52 crates.Showing all your calculations, explain whether or not Steve has enough water to give one bottle with each lunch?

[6]

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52 × 18

Reveal

45 × 20 = (45 × 2) × 10

5 2

1

8

05

02

40

169

3 6936 bottles

= 90 × 10

= 900 lunches

Steve has 936 bottles and there are 900 lunches, so yes, he does have enough.

The number of water bottles is

The number of packed lunches is 45 × 20

There are other methods you could use for long

multiplication.

You must show your working!

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0


[6]

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AO3 – AO3 – Interpret and analyse the problem and develop a strategy to

solve it

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ASSESSMENT

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[6]

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9. A red box contains four discs numbered 3, 6, 9 and 12 respectively. A green box contains four discs numbered 4, 7, 10 and 13 respectively. In a game, a player takes one disc at random from each of the two boxes. The score for the game is the smaller of the two numbers on the discs.

(a) Complete the following table to show all the possible scores.

[6]

(b) A player wins if the score is less than 6.It costs 50p to play the game once.The prize for winning the game is £1.If 80 people play the game once, find the expected profit.

[2]

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[6]


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6

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9 12

6 9 10

Probability of winning = 716

Expected number of winners = 716

× 80 = 702

35=10

2

Cost to play = 50p × 80 = 0.5 × 80 = £40

Expected pay out for winning = £1 × 35 = £35

Expected profit = 40 – 35 = £5

Less than 6 does not include 6

Alternatively, if 16 play the game, we expect 7 to win. If 160 play, we

expect 70 to win. So, if 80 play, we expect 35 to win.

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[6]


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(a)(a) AO1 AO1 – Recall and use knowledge of sample space diagrams

(b)(b) AO2AO2 – Selecting and applying methods to find the expected profit

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ASSESSMENT

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[6]


[2]

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10. Helen cycles home from a village that is 30 miles from her home. The travel graph below represents her journey.

[1]

(a) How far did Helen cycle in the first hour?

(b) For how many minutes did Helen stop on her journey?

[1]

(c) Without calculating any speeds, explain how you can decide whether Helen was cycling faster before stopping or after she had stopped.

[1](d) At what time did she arrive home?

[1]

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[1]

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30 – 17 = 13 miles

Reveal

17

11:09 to 11:45 36 minutes

The line before she stops is steeper. So, she was cycling fasterbefore she stopped.

13:30 + 6(mins) = 13:36

1 hour (60 minutes) = 20 little squares. So, 1 little square = 3 minutes

(Or, line is 12 squares long. 12 × 3 = 36 minutes.)

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(a), (d) AO1 (a), (d) AO1 – Recall and use knowledge of distance-time graphs(b), (c) AO2 (b), (c) AO2 – Select and apply methods using scale and gradient

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ASSESSMENT

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[1]

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11. Sarah and Paige live in Nottingham and are planning a trip to Liverpool. They need to be in Liverpool by 2:00 pm. They can travel by train, bus or in Sarah’s car.

Showing all your reasoning, how do you recommend they travel from Nottingham to Liverpool? Give one advantage and one disadvantage for your choice of transport.

[8]Part of rail timetable

Part of the national bus timetable informationTravelling by car:Distance from Nottingham to Liverpool is 105 miles.Expected average speed of car on this journey is 35 m.p.h.Cost of running Sarah’s car is 30p per mile.

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By Train

Reveal

The fastest train to get there before 2 p.m.:

10:52 to 13:27 2hrs 35min

Cost = £39.50 + £39.50 = £79.00

By Bus

The fastest bus to get there before 2 p.m.:

7:15 to 11:55 4hrs 40min

Cost = £32.00

By Car

Time = 105 ÷ 35 = 3hrs

Cost = £0.30 ×105 = £31.50

£31.50 × 2 = £63.00

Speed = DistanceTime

Time = DistanceSpeed

I recommend the bus because it’s a lot cheaper, but it takes longer.

One possible solution is to work out the cost and quickest time for each mode of transport.

Note!!

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Double the £31.50 to include the return journey

This could be a different answer





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AO2 – AO2 – selecting and applying mathematical methods to justify a

selected mode of transport.

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ASSESSMENT

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12. (a) Solve

[1]

(i) 6x = 3

(ii) 7x – 10 = 11.

(b) Simplify 2a – 7b – 5a – 6b.[2]

[2]

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12. (a) Solve

[1]

(i) 6x = 3

(ii) 7x – 10 = 11.

(b) Simplify 2a – 7b – 5a – 6b.[2]

[2]

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AR x = 3 × 6

x = 18

Reveal

7x = 11 + 10

x = 21 7

Check:

(7×3) – 10

= 21 – 10

= 11

= 2a = – 3a – 13b

Check:

18 ÷ 6 = 3

x = 3

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– 7b – 5a

7x = 21

– 6b

12. (a) Solve

[1]

(i) 6x = 3

(ii) 7x – 10 = 11.

(b) Simplify 2a – 7b – 5a – 6b.[2]

[2]

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AO1 – AO1 – Recall and use knowledge of solving linear equations and

collecting like terms

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ASSESSMENT

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12. (a) Solve

[1]

(i) 6x = 3

(ii) 7x – 10 = 11.

(b) Simplify 2a – 7b – 5a – 6b.[2]

[2]

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13. (a) Draw an enlargement of the shape shown below using a scale factor of 2.

Use the point A as the centre of the enlargement. [3]

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This is the correct size but drawn in the wrong place. This is the correct size but drawn in the wrong place.

Make sure you use the centre of enlargement, AMake sure you use the centre of enlargement, A



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AO1AO1 – Recall and use knowledge of enlargement

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ASSESSMENT

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13 (b) Rotate the shape shown below through 90° anticlockwise about the point (2, 1). [2]

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Remember the three key facts:

Angle: 90°

Centre: (2, 1)

Direction: anticlockwise

Remember the three key facts:

Angle: 90°

Centre: (2, 1)

Direction: anticlockwise


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AO1AO1 – Recall and use knowledge of rotation

ASSESSMENT

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ASSESSMENT

OBJECTIVE

Part a

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14. (a) Showing all your working, find an estimate for:

[2]

[2]

4.1503 × 20.3

(b) The value of is approximately 3.14. Estimate the circumference of a circle with radius 20 cm.

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[2]

[2]

4.1503 × 20.3


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Reveal

Circumference = × diameter

= 2500

= 3.14 × 40

= 3.14 × 4 × 10

= 12.56 × 10

= 125.6 cm

Remember to use diameter.

i.e. 2 × 20 = 40

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10000 4

=

500 × 204

Round all numbers to 1 significant figure


[2]

[2]

4.1503 × 20.3


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AO1 – AO1 – Recall and use knowledge of estimation and significant figures.

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[2]

[2]

4.1503 × 20.3


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15. The houses on one side of a long street have odd numbers and the houses on the other side of the street have even numbers.

[1]

(a) Fill in the numbers on these houses.

(b) The numbers on five houses next to each other on one side of the street total 65.What are the numbers on these five houses?

[3]

(c) The product of the numbers on two houses which are directly opposite each other is 90. What are the numbers on these two houses?

[1]

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[3]


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65 ÷ 5 = 13

Reveal

(number) × (number + 1) = 90

+1 +2 +2 +2 +2

97 99 101 105

98 100 102 106104

9 11 13 15 17

By investigation : 9 and 10

This must be the middle house number. So, the solution is:

The numbers will be consecutive i.e.Product means “multiply”

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[1]



[3]


[1]

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AO2 – AO2 – Select and apply appropriate numerical methods

ASSESSMENT

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ASSESSMENT

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[1]



[3]


[1]

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16. The diagram represents an aerial view of a building.A dog, D, on a lead is tied to a side of the building at X.Draw the boundary of the region in which the dog can roam. [3]

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4.9cm

3cm

1.9cm

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The lead is shortened by the corner, so the answer is not a circle.

The lead is shortened by the corner, so the answer is not a circle.


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AO2 – AO2 – Select and apply appropriate rules of loci

ASSESSMENT

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ASSESSMENT

OBJECTIVE

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17. You will be assessed on the quality of your written communication in part (b) of this question.

Mrs. Roberts is travelling to Hong Kong on business.(a) There is a time difference between the UK and Hong Kong. When the time is 6 a.m. in the UK the time is 2 p.m. on the same day in Hong Kong.

(i) When it is 10 a.m. in the UK what time is it in Hong Kong?

[1]

(ii) Mr. Roberts stays in the UK and has given his wife his time schedule, shown below.

Mrs. Roberts will be in meetings most of the day in Hong Kong from 8 a.m. until 11 a.m., then from 12 noon to 6 p.m.She plans to telephone her husband at a convenient time during the day.During which time period should Mrs. Roberts telephone her husband?Give your answer in UK and Hong Kong times.

[2]

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[1]



[2]

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6am (UK) is 2pm (HK) (+8hrs) so 10am (UK) is 6pm (HK)

Between

8:30pm – 10:00pm HK time [Mrs Roberts has finished work]

12:30pm – 2:00pm UK time [Mr Roberts is having lunch]

So they are both free to talk

RevealPart b

HK2:002:303:307:308:30

10:000:002:005:006:00

pm

meeting

am

Hong Kong is 8 hours ahead of UK




[1]



[2]

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(a)(a) (i) AO2(i) AO2 – Select and apply appropriate numerical technique to calculate time difference.(ii) AO3(ii) AO3 – Interpret times and select appropriately.

ASSESSMENT

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ASSESSMENT

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[1]



[2]

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17 (b) Mrs. Roberts is going to be in Hong Kong for 4 nights. She finds two suitable hotels on the internet.

[5]

Which hotel should Mrs. Roberts choose? You must show your working and give a reason for your answer.

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[5]


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Hotel Gelton

£80 × 4 = £320 B&B

RevealPart a

Hotel Bear

£107 × 3 = £321 B&B + dinner

Choose Hotel Bear as you also get dinner for 4 nightsfor an extra £1, so this is better value for money.

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Remember to include a valid reason for your choice

Remember to include a valid reason for your choice


[5]


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AO3AO3 – Interpret, analyse and compare both options presented and justify their choice of hotel.

ASSESSMENT

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ASSESSMENT

OBJECTIVE

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[5]


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1. Ashley visits a computer store.(a) She sees the following display.

[4]

(i) Ashley buys a box of re-writable discs, 2 packets of photo paper, 3 printer cartridges and 6 packets of printer paper.

Complete the following table to show her bill for these items.

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[4]



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2 packets of photo paper

RevealPart (ii)

2 × £6.39 12.78

3 printer cartridges 3 × £16.78 50.34

6 packets of printer paper 6 × £3.47 20.82

7.46 + 12.78 + 50.34 + 20.82 91.40

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Don’t forget to include this in the

total.

Don’t forget to include this in the

total.

Remember to write

down the ‘0’ 91.40

Remember to write

down the ‘0’ 91.40

Remember you can use your

calculator.


[4]



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AO1AO1 – Recall and use knowledge of money using a calculator

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[4]



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[2]

[1]

1a (ii) The store gives a discount of 5% of the total cost of these items.What discount does Ashley receive?

(b) (i) What percentage of the following shape is shaded?

(ii) What percentage of the shape is NOT shaded?

[1]

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[2]

[1]




[1]

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RevealPart (i)

5100

× 91.4 = £4.57 or 0.05 × 91.4 = £4.57

12

3

4

4 shaded out of 104

10= 40%40

100=

100% – 40% = 60%

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Use a calculator!

[2]

[1]




[1]

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AO1AO1 – Recall and use knowledge of percentages

ASSESSMENT

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ASSESSMENT

OBJECTIVE

Part (i)

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[2]

[1]




[1]

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[1]

2. (a) (i) What is the mass of Mia’s pet hamster?

The mass of Mia’s pet hamster is g.

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[1]



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340

RevealPart (ii)

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2 Each section is

10g

Each section is

10g

[1]



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AO1AO1 – Recall and use knowledge of metric units of mass and reading

scales

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part (ii)

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[1]



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[1]

[1]

2a (ii) She puts her hamster on a different scale.Draw the pointer to show the hamster’s mass.

(b) Mia goes out in her car.What speed is she doing, correct to the nearest 10 miles per hour?

m.p.h.

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[1]

[1]



m.p.h.

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60

Arrow is nearer to

60 than 50

Arrow is nearer to

60 than 50

RevealPart (i)

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Each section is 20g

Each section is 20g

50 60

[1]

[1]



m.p.h.

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AO1AO1 – Recall and use knowledge of reading scales and rounding to

nearest 10

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part (i)

AO1AO1 – Recall and use knowledge of metric units of mass and

interpreting scales

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[1]

[1]



m.p.h.

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[3]

3. (a)

The above shape, drawn on a square grid, represents a large garden.Estimate the area of the garden if every square represents an area of 5 m2.

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[3]

3. (a)


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Counting gives 77 squares

RevealPart b

Area = 77 × 5

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Count whole squares and squares more than half full

= 385 m2

[3]

3. (a)


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AO1AO1 – Recall and use knowledge of estimation of the area of an

irregular shape drawn on a square grid

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part b

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[3]

3. (a)


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[2]

[3]

(b) Write down the special name of the straight line shown in each diagram below.

(c) Write down the name of each of the shapes shown below.

A B

C

A

B

C

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[2]

[3]



A B

C

A

B

C

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Chord

RevealPart a

Diameter

Trapezium

Pentagon

Cylinder

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[2]

[3]



A B

C

A

B

C

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AO1AO1 – Recall and use knowledge of vocabulary of circles, polygons

and solid figures

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part a

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[2]

[3]



A B

C

A

B

C

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(b) Find the Number of days, when the Total Cost is £61 and the Hire charge is £7.

4. The formula to find the Total Cost, in pounds, of hiring a carpet cleaner is

Total Cost = Number of days × £6.75 + Hire charge.

(a) Find the Total Cost when the Number of days is 3 and the Hire charge is £10.

[2]

[2]

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[2]

[2]

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6.75 × 3

Reveal

20.25 20.25+10.00

30.25

Add on the hire chargeAdd on the hire charge

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20.25

Total cost = £30.25

Number of days × £6.75 = Total cost – Hire charge

= 61 – 7

Number of days = 54 ÷ 6.75

= 8

= 54





[2]

[2]

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AO1 – AO1 – Recall and use knowledge of rearranging simple formulae

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

AO1 – AO1 – Recall and use knowledge of substitution of positive integers

into simple formulae

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[2]

[2]

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[2]

[1]

5.

(a) Write down the coordinates of the points A and B.

Coordinates of A are:

( , )

Coordinates of B are:

( , )

(b) C is the mid-point of AB.Mark the point C on the graph. [1]

(c) The perpendicular to the line AB from the point D meets AB at the point E.Mark the point E on the graph paper above.

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[2]

[1]

5.



( , )


( , )



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– 3 4

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– 3 – 2

C

E

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Perpendicular means ‘at right angles to…’

The x-coordinate is always first.

[2]

[1]

5.



( , )


( , )



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AO1 – AO1 – Recall and useknowledge of Cartesian

coordinates in 4 quadrants and vocabulary of geometrical terms

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[2]

[1]

5.



( , )


( , )



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[1]

6. (a) The diagram shows a number of cubes of side 1 cm forming a solid shape.

Find the volume of the shape and state the units of your answer.

Volume of the shape =

(b) (i) Measure the size of ABC.

[2]

ABC = º

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Show/hide protractorShow/hide protractor

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[1]





[2]

ABC = º

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Number of cubes = 7 × 2

Reveal

12

34

56 7

2 layers

14 cm3

53º53º

53

Part b

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Make sure the correct reading is used: the angle is acute, so it is less

than 90°

[1]





[2]

ABC = º

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AO1AO1 – Recall and use knowledge of volume of composite solids by counting cubes and accurate use

of a protractor

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part b

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[1]





[2]

ABC = º

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[1]

6 (ii) On the diagram below, draw XYZ, which is 124°.

X Y

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[1]


X Y

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Make sure the correct reading is used: the angle is greater than 90°, so it is obtuse.

[1]


X Y

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AO1AO1 – Recall and use knowledge of accurately using a protractor

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part a

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[1]


X Y

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[3]

7. Siân, Ryan and Dafydd are neighbours and have houses on a new housing estate.

Siân makes a rectangular front lawn measuring 9m by 4m.

9m

4m

(a) Ryan makes a square lawn, which has the same perimeter as Siân’s lawn. Find the length of a side of Ryan’s lawn.

(b) Dafydd also makes a square lawn, but his lawn has the same area as Siân’s lawn. Find the length of a side of Dafydd’s lawn.

[3]

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[3]



9m

4m



[3]

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Perimeter of Siân’s lawn

Length of Ryan’s lawn

Area of Siân’s lawn

Length of Dafydd’s square lawn

= 4 + 9 + 4 + 9 = 26 cm

= 26 ÷ 4 = 6.5 cm

= 36 cm2= 4 × 9

= √36 = 6 cm

[3]



9m

4m



[3]

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AO2 – AO2 – Select and apply mathematical methods of perimeter and area to find the lengths of the

lawns

ASSESSMENT

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ASSESSMENT

OBJECTIVE

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[3]



9m

4m



[3]

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[4]

8.

The above picture shows two houses each with a front door.

Write down an estimate for the actual height of a door.

Using this estimate for the height of a door, estimate the actual distance between the two houses shown by the arrowed line.

You must show all your working.

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Show/hide ruler (vertical)

Show/hide ruler (horizontal)

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[4]

8.





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2m

Reveal

Door measures 2cm

Therefore 2cm ≡ 2m Scale 1cm ≡ 1m

Measured distance between two houses = 9cm

Actual distance between two houses = 9m

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[4]

8.





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AO2 – AO2 – Select and apply mathematical methods of

estimation and scale to find the actual distance between the two

houses

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[4]

8.





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9. (a) (i) The mass of a donkey is x kg. During the year the donkey’s mass increases by 8 kg.What is the mass of the donkey at the end of the year?

(ii) A pencil costs 32 pence.What is the cost of g pencils?

[1]

[1](b) Describe in words the rule for continuing each of the following sequences.

(i) 48, 42, 36, 30, ….

[1]

Rule:

(ii) 2, 8, 32, 128, …

[1]

Rule:

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[1]


(i) 48, 42, 36, 30, ….

[1]

Rule:

(ii) 2, 8, 32, 128, …

[1]

Rule:

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(x + 8) kg

RevealPart (c)

32g pence

Take away 6 from previous number

Multiply previous number by 4

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To increase is to ADD

32 × g

= 32g



[1]


(i) 48, 42, 36, 30, ….

[1]

Rule:

(ii) 2, 8, 32, 128, …

[1]

Rule:

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AO1AO1 – Recall and use knowledge of describing the rule for the next

term of a sequence

ASSESSMENT

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ASSESSMENT

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Part (c)

AO1AO1 – Recall and use knowledge of formation of simple algebraic

expressions,

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ASSESSMENT

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[1]


(i) 48, 42, 36, 30, ….

[1]

Rule:

(ii) 2, 8, 32, 128, …

[1]

Rule:

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Part (c)

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9 (c) Solve each of the following equations.

(i) 6x = 48

[1]

(ii) y + 6 = 19

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Part (a) & (b)

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(i) 6x = 48

[1]

(ii) y + 6 = 19

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RevealPart (a) & (b)

x = 486

x = 8

y = 19 – 6

y = 13

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(i) 6x = 48

[1]

(ii) y + 6 = 19

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ASSESSMENT

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Part (a) & (b)

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(i) 6x = 48

[1]

(ii) y + 6 = 19

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[6]

10.A group of 3 adults and a number of children travel in a minibus to visit Arthur’s Castle.

It costs a total of £58 to park the minibus and pay for the tickets for everyone to visit the castle.

How many were there in the group altogether?

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[6]




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Total cost of tickets = 58 – 5 = £53

Reveal

Cost for 3 adults = 3 × 7 = £21

Cost for children = 53 – 21 = £32

Number of children = 32 ÷ 4 = 8 children

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Total on trip = 8 + 3 = 11 people

Take away cost of minibus

Don’t forget to add on the 3 adults

[6]




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AO2 – AO2 – Select and apply mathematical methods by using the

numerical information to find the number of people in the group

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ASSESSMENT

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[6]




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[5]

11. Fran needs at least £800 in euros (€) to go on a visit to France.

When he goes to the bank he finds that the lowest euro note the bank will give him is the 5 euro note.

The exchange rate is £1 = €1.14.

What is the least number of euros that Fran buys to ensure he has at least £800 worth and how much did he pay for them?

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[5]





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Euros = 800 × 1.14 = 912 euro

Reveal

Round UP to the nearest 5 …. = 915 euro

He needs 915 euro

Cost in pounds = 915 ÷ 1.14

= £802.63

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Must round up as 910 euro would not be enough

Reasonable answer: you are expecting it to cost more than £800 as you are getting more than 912 euro

[5]





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AO2 – AO2 – Select and apply mathematical methods involving foreign currencies and exchange

rates

ASSESSMENT

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ASSESSMENT

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[5]





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[2]

12. Year 11 and 12 pupils in a comprehensive school were asked:

“In the election for a pupil governor, for whom would you vote?”

The two pie charts below were drawn by a pupil to illustrate the results for Year 11 and

Year 12 separately.

Year 11 Year 12

(a) Estimate the fraction of Year 11 pupils who would vote for Jitesh. [1]

(b) Can you tell from the pie charts whether fewer Year 11 pupils than Year 12 pupils would vote for Tom?Put a circle around your choice.

Yes / NoExplain the reasoning for your answer.

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[2]




Year 12 separately.

Year 11 Year 12




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You do not know the number of pupils surveyed in each year.

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[2]




Year 12 separately.

Year 11 Year 12




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AO1 – AO1 – Recall and use knowledge of pie charts

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ASSESSMENT

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[2]




Year 12 separately.

Year 11 Year 12




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[1]

13. (a) Reflect the triangle A in the y-axis.G

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Count squares at right angles to mirror line

[1]


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AO1AO1 – Recall and knowledge of reflection in 4 quadrants

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ASSESSMENT

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Part (b)

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[1]


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[1]

13 (b) In the diagram below, describe the translation that maps A to B.G

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3 to the left and 4 up

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[1]


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AO1AO1 – Recall and use knowledge of translation in 4 quadrants

ASSESSMENT

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ASSESSMENT

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Part (a)

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[1]


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14. a) The diagram on the next page, drawn to the scale of 1 cm represents 10 km, shows a coastline with harbours at A and B. Find the actual distance, in kilometres,

between the two harbours.

[3]

[6]

b) At 1:00 p.m. a ship sets off from A and another ship sets off from B. Each ship travels in a straight line. The ship from A maintains an average speed of 40 km/hour whilst the ship from B keeps to an average speed of 30 km/hour.The ships meet at 4:00 p.m.Giving full details of your working and reasoning, find the position where the two ships meet.Write down the bearing of this point from B.

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Open map in order to try find a solution Open map in order to try find a solution

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Open map in order to try find a solution Open map in order to try find a solution



[3]

[6]


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RevealOpen map to show the rest of the solutionOpen map to show the rest of the solution

AB = 15.5 cm

Actual distance = 15.5 × 10= 155 km

Time taken is from 1.00pm to 4.00pm = 3 hrs

Ship A travels 40 × 3 = 120 km

Ship B travels 30 × 3 = 90 km

120 = 12 cm10

90 = 9 cm10

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Remember to give full details

Find distances travelled in 3hrs

(Distance = speed × time)

Scale 1cm ≡ 10km



[3]

[6]


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AO3AO3 – Interpret and analyse the problem and generate a strategy to

find the bearing using speed, distance, time of where the two

ships meet

ASSESSMENT

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ASSESSMENT

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AO1AO1 – Recall and use knowledge of scale

ASSESSMENT

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ASSESSMENT

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[3]

[6]


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14.

Show/hide protractor

Show/hide ruler Rotate ruler 3cm 6cm 9cm 12cm

Show/hide arc

Back to questionBack to questionF

OU

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Pap

er 2

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14.Back to questionBack to question

12cm (120km)

9cm (90km)

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2Cannot be here as cannot travel over land

Bearing is 303º

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14.

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14.

[2]

15. The owner of a takeaway coffee shop uses two types of paper cups.

Hi-rim cup Base-stay cup

Diagrams are not drawn to scale.

They can be stacked like this...


(a) How high is a stack of 25 Hi-rim cups?

(b) A stack of Base-stay cups is 18.6 cm high.How many Base-stay cups are in the stack?

[2]

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[2]








[2]

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Height of cup 1 = 14 cm

Remove cup 1: 18.6 – 9 = 9.6

RevealPart (c)

Height of cups 2 to 25 = 24 × 0.5 = 12 cm

Total height = 14 + 12 = 26 cm

Number of cups 9.6 ÷ 1.2 = 88 cups + 1 cup = 9 cups

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Remember there are 24 cups above the bottom cupTherefore 24 × 0.5 NOT 25 × 0.5

Add height of bottom cup

[2]








[2]

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AO2AO2 – Select and apply mathematical methods using the

visual information of how the cups are stacked

ASSESSMENT

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ASSESSMENT

OBJECTIVE

Part (c)

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[2]








[2]

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Part (c)

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[3]

15 (c) A stack of Hi-rim cups is the same height as a stack of Base-stay cups.

There are 21 Base-stay cups in the stack.

How many cups are there in the stack of Hi-rim cups?

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Part (a) & (b)

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[3]




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Height of Base-stay 20 × 1.2 + 9 = 33 cm

RevealPart (a) & (b)

To find number of Hi-rim 33 – 14 = 19

19 ÷ 0.5 = 38 cups

38 + 1 = 39 cups

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Don’t forget the bottom cup

[3]




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AO3AO3 – Interpret and analyse the problem and generate a strategy to

find the number of cups

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

Part (a) & (b)

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[3]




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Part (a) & (b)

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[3]

16. (a) Find the value of 3.72 + √21.16

[1]

(b) In a shop, the marked price of a television is £542.

The shop offers a discount of 28% of the marked price.

Find the discounted price of the television.

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[3]


[1]




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18.29

Reveal

28 × 542 = £151.76100

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Discounted price = 542 – 151.76

Use your calculator!

As you have a calculator, you could do…:

28% = 0.28

1 – 0.28 = 0.72

0.72 x 542 = £390.24= £390.24

[3]


[1]




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AO1 – AO1 – Recall and use knowledge of percentage reduction

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

AO1 – AO1 – Recall and use knowledge of squares and square roots using

a calculator

ASSESSMENT

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ASSESSMENT

OBJECTIVE

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[3]


[1]




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[2]

17. The table below shows the probabilities of selecting one ball at random from a bag of coloured balls.

(a) Are there any balls of another colour in the bag? Give a reason for your answer.

(b) What is the probability of selecting either a yellow or a purple ball?

[2]

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[2]




[2]

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0.25 + 0.14 + 0.06 + 0.15 + 0.40 = 1

Reveal

P(yellow or purple)

There are no balls of any other colour because the probabilities add up to 1.

= 0.06 + 0.40

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= 0.46

The ball can’t be yellow and purple at the same time, so the ruleP(A or B) = P(A) + P(B) works.= P(yellow) + P(purple)

[2]




[2]

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AO3 – AO3 – Generating a strategy involving the law of total probability

to solve the problem

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

AO2 – AO2 – Select and apply the probability law for mutually

exclusive events

ASSESSMENT

OBJECTIVE

ASSESSMENT

OBJECTIVE

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[2]




[2]

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[3]

18. Solve the equation 6x – 7 = 4(x + 3).

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Reveal

6x – 7 = 4x + 126x – 4x = 12 + 7 2x = 19

x = 192

x = 9.5

Expand brackets

Collect terms

[3]


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AO1 - AO1 - Recall and use knowledge of expanding brackets and solving

linear equations with x on both sides

ASSESSMENT

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ASSESSMENT

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[3]


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[7]

19. You will be assessed on the quality of your written communication in this question.

A number is written on each of five cards.

The cards are arranged in ascending order.

It is known that the mean of the five numbers is 9.6, the range is 12, the median is 10, the greatest number is 16 and the fourth number is twice the second number.

Explaining your reasoning, find the five numbers written on the cards.

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[7]






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6 10 12 16

The median is 10. Therefore, the number on the middle card is 10.

The range is 12. Therefore, the smallest number is 16 – 12 = 4

Now, mean × number of cards = total

total of 5 cards – total of 3 cards = 48 – (4 + 10 + 16)

The fourth number is twice the second, and the two add up to 18.

The fourth number is 12, the second is 6.

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The largest number is 16.

So, 9.6 × 5 = 48

= 18

[7]






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AO3 – AO3 – Interpret and analyse the problem to generate a strategy

using knowledge of mean, median and range

ASSESSMENT

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ASSESSMENT

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[7]






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[3]

20. Jaspal invests £2500 for 2 years at 7% per annum compound interest.

What is the value of his investment after 2 years?

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1st year:

Reveal

7% of £2500 = 7 × 2500 = £175100

Add this on: 2500 + 175 = £2675

So, Jaspal has £2675 in his account after 1 year.

2nd year:

7% of £2675 = 7 × 2675 = £187.25100

Add this on: 2675 + 187.25 = £2862.25

So, Jaspal has £2862.25 in his account after 2 years.

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[3]



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AO1 - AO1 - Recall and use knowledge of compound interest

ASSESSMENT

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ASSESSMENT

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[3]



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Documents

1. (a) (i) Write down, in figures, the number twenty four thousand, five hundred and seven. [1] (ii) Write down, in words, the number 6014. [1] (b) Using