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

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

Edexcel GCSE 9 - 1 Specimen Paper 3 Higher (Calculator) Solutions

For questions 1 - 8, refer to questions 21 - 28 of the Foundation Paper 3

Edexcel GCSE 9 - 1 Specimen Paper 3 (Calculator) Solutions for Questions 9 - 24

- 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. - 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 - 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 - 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.

- 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. - Factorise x
^{2}+ 3x – 4 - 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. - Ian invested an amount of money at 3% per annum compound interest.

At the end of 2 years the value of the investment was £2652.25

(a) Work out the amount of money Ian invested.

Noah has an amount of money to invest for five years.

Saver Account: 4% per annum, compound interest.

Investment Account: 21% interest paid at the end of 5 years.

Noah wants to get the most interest possible.

(b) Which account is best?

You must show how you got your answer. - The diagram shows two vertical posts, AB and CD, on horizontal ground.

AB = 1.7 m

CD : AB = 1.5 : 1

The angle of elevation of C from A is 52°

Calculate the length of BD.

Give your answer correct to 3 significant figures. - On the grid, shade the region that satisfies all these inequalities.

x + y < 4; y > x – 1; y < 3x

Label the region R. - Write x
^{2}+ 2x – 8 in the form (x + m)^{2}+ n

where m and n are integers.

12 The diagram shows a cuboid ABCDEFGH.

AB = 7 cm, AF = 5 cm and FC = 15 cm.

Calculate the volume of the cuboid.

Give your answer correct to 3 significant figures.

13. There are 14 boys and 12 girls in a class.

Work out the total number of ways that 1 boy and 1 girl can be chosen from the class.

14. Write as a single fraction in its simplest form.

You must show your working.

15. A virus on a computer is causing errors.

An antivirus program is run to remove these errors.

An estimate for the number of errors at the end of t hours is 10^{6} × 2^{−t}

(a) Work out an estimate for the number of errors on the computer at the end of 8 hours.

(b) Explain whether the number of errors on this computer ever reaches zero.

16. The graph of y = f(x) is transformed to give the graph of y = −f(x + 3)

The point A on the graph of y = f(x) is mapped to the point P on the graph of y = −f(x + 3)

The coordinates of point A are (9, 1)

Find the coordinates of point P.

17. The diagram shows a solid cone.

The diameter of the base of the cone is 24x cm.

The height of the cone is 16x cm.

The curved surface area of the cone is 2160π cm^{2}.

The volume of the cone is Vπ cm^{3}, where V is an integer.

Find the value of V.

18. Thelma spins a biased coin twice.

The probability that it will come down heads both times is 0.09

Calculate the probability that it will come down tails both times.

19 (a) Write 0.000423 in standard form.

(b) Write 4.5 × 10^{4} as an ordinary number.

20. Mark has made a clay model.

He will now make a clay statue that is mathematically similar to the clay model.

The model has a base area of 6cm^{2}

The statue will have a base area of 253.5cm^{2}

Mark used 2kg of clay to make the model.

Clay is sold in 10kg bags.

Mark has to buy all the clay he needs to make the statue.

How many bags of clay will Mark need to buy?

21. (a) Show that the equation 3x^{2} – x^{3} + 3 = 0 can be rearranged to give x = 3 + 3/x^{2}

(b) Using

x_{n + 1} = 3 + 3/x^{2}_{n}

x_{0} = 3.2, find the values of x_{1}, x_{2} and x_{3}

(c) Explain what the values of x_{1}, x_{2} and x_{3} represent.

22. Here are the first five terms of an arithmetic sequence.

7, 13, 19, 25, 31

Prove that the difference between the squares of any two terms of the sequence is always a multiple of 24

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