Questions and Worked Solutions for Edexcel GCSE 9 - 1 Mathematics Specimen Paper 3 (Calculator).

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Edexcel GCSE 9 - 1 Mathematics Specimen Past Paper 3 (Pdf)

Edexcel GCSE 9 - 1 Specimen Paper 3 Foundation (Calculator) Solutions for Questions 1 - 28

1. Write the number 5689 correct to the nearest thousand.

2. Work out (30 + 12)/(5 + 3)

3. Work out the reciprocal of 0.125

4. Here is a list of numbers.

1, 2, 5, 6, 12

From the list, write down

(i) a multiple of 4

(ii) a prime number

5. There are 1.5 litres of water in a bottle.

There are 250 millilitres of water in another bottle.

Work out the total amount of water in the two bottles.

6. Here is a trapezium.

This diagram is accurately drawn.

(a) Measure the length of the line PQ.

(b) Measure the size of the angle marked x.

7. (a) Solve f + 2f + f = 20

(b) Solve 18 – m = 6

(c) Simplify d

8. Jayne writes down the following

3.4 × 5.3 = 180.2

Without doing the exact calculation, explain why Jayne’s answer cannot be correct.

9. The two numbers, A and B, are shown on a scale.

The difference between A and B is 48

Work out the value of A and the value of B.

10. Complete this table of values.

(a) Find the missing number.

(b) Work out 4

12. Here are two numbers.

29, 37

Nadia says both of these numbers can be written as the sum of two square numbers.

Is Nadia correct?

You must show how you get your answer.

13. Here are the first three terms of a sequence.

32, 26, 20

Find the first two terms in the sequence that are less than zero.

14. Here is a triangle ABC.

(a) Mark, with the letter y, the angle CBA.

Here is a cuboid.

Some of the vertices are labelled.

(b) Shade in the face CDEG.

(c) How many edges has a cuboid?

15. There are 5 grams of fibre in every 100 grams of bread.

A loaf of bread has a weight of 400 g.

There are 10 slices of bread in a loaf.

Each slice of bread has the same weight.

Work out the weight of fibre in one slice of bread.

16. Give an example to show that when a piece is cut off a rectangle the perimeter of the new shape

(i) is less than the perimeter of the rectangle,

(ii) is the same as the perimeter of the rectangle,

(iii) is greater than the perimeter of the rectangle.

17. ABC is an isosceles triangle.

When angle A = 70°, there are 3 possible sizes of angle B.

(a) What are they?

When angle A = 120°, there is only one possible size of angle B.

(b) Explain why.

18. In a breakfast cereal, 40% of the weight is fruit.

The rest of the cereal is oats.

(a) Write down the ratio of the weight of fruit to the weight of oats.

Give your answer in the form 1 : n.

A different breakfast cereal is made using only fruit and bran.

The ratio of the weight of fruit to the weight of bran is 1 : 3

(b) What fraction of the weight of this cereal is bran?

19. Boxes of chocolates cost £3.69 each.

A shop has an offer.

Boxes of chocolates

3 for the price of 2

Ali has £50

He is going to get as many boxes of chocolates as possible.

How many boxes of chocolates can Ali get?

20. ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {multiples of 2}

A ∩ B = {2, 6}

A ∪ B = {1, 2, 3, 4, 6, 8, 9, 10}

Draw a Venn diagram for this information.

21. The scatter diagram shows information about 10 students.

For each student, it shows the number of hours spent revising and the mark the student achieved in a Spanish test.

One of the points is an outlier.

(a) Write down the coordinates of the outlier.

For all the other points

(b) (i) draw the line of best fit,

(ii) describe the correlation.

A different student revised for 9 hours.

(c) Estimate the mark this student got

The Spanish test was marked out of 100

Lucia says,

“I can see from the graph that had I revised for 18 hours I would have got full marks.”

(d) Comment on what Lucia says.

22. The length, L cm, of a line is measured as 13 cm correct to the nearest centimetre.

Complete the following statement to show the range of possible values of L

23. Line L is drawn on the grid below.

Find an equation for the straight line L.

Give your answer in the form y = mx + c

24. Jenny works in a shop that sells belts.

The table shows information about the waist sizes of 50 customers who bought belts from the shop in May.

(a) Calculate an estimate for the mean waist size.

Belts are made in sizes Small, Medium, Large and Extra Large.

Jenny needs to order more belts in June.

The modal size of belts sold is Small.

Jenny is going to order 3/4 of the belts in size Small.

The manager of the shop tells Jenny she should not order so many Small belts.

(b) Who is correct, Jenny or the manager?

You must give a reason for your answer.

25. The diagram shows part of a wall in the shape of a trapezium.

Karen is going to cover this part of the wall with tiles.

Each rectangular tile is 15 cm by 7.5 cm

Tiles are sold in packs.

There are 9 tiles in each pack.

Karen divides the area of the wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.

(a) Use Karen’s method to work out an estimate for the number of packs of tiles she needs to buy.

Karen is advised to buy 10% more tiles than she estimated.

Buying 10% more tiles will affect the number of the tiles Karen needs to buy.

She assumes she will need to buy 10% more packs of tiles.

(b) Is Karen’s assumption correct?

You must show your working.

26. Factorise x

27. Here are the equations of four straight lines.

Line A: y = 2x + 4

Line B: 2y = x + 4

Line C: 2x + 2y = 4

Line D: 2x – y = 4

Two of these lines are parallel.

Write down the two parallel lines.

28. The densities of two different liquids A and B are in the ratio 19 : 22

The mass of 1 cm

5 cm

Work out the density of liquid C.

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