# This Is a Hard Version with Some Challenging Questions! If You Can Do All of This . .

**2015 Calculator Predicted Paper**

**This is a hard version with some challenging questions! If you can do all of this . . .**

Grade C

1.Sophie says ‘For any whole number, n, the value of 6n – 1 is always a prime number’.

Sophie is wrong. Give an example to show that Sophie is wrong.

(Total 2 marks)

2.Write 140 as the product of its prime factors.

......

(Total 2 marks)

3.Here are the first 4 terms of an arithmetic sequence

371115

Find an expression, in terms of n, for the nth term of the sequence.

…………………………

(Total 2 marks)

4.David and Clare are studying a number pattern.

The first three numbers in the pattern are 1, 2 and 6.

David says the next two numbers are 13 and 23.

Clare says the next two numbers are 15 and 31.

(i)Explain why David could be right.

...... ………………………………………………………………………………

...... ………………………………………………………………………………

(1)

(ii)Explain why Clare could be right.

...... ………………………………………………………………………………

...... ………………………………………………………………………………

(1)

(Total 2 marks)

5.–2 < x 1

x is an integer.

Write down all the possible values of x.

......

......

(Total 2 marks)

6.Mrs. Jones shared £375 between her two children in the ratio 1 : 6

She gave the bigger share to Matthew.

Work out how much money she gave to Matthew.

£ ………………

(Total 2 marks)

7.(a)Solve7p + 2 = 5p + 8

p = ......

(2)

(b)Solve7r + 2 = 5(r – 4)

r = ......

(2)

(Total 4 marks)

8.Find the highest common factor (HCF) of 72 and 120.

......

(Total 2 marks)

9.(a)Complete the table of values for y = 2x + 3

x / –2 / –1 / 0 / 1 / 2y / 1 / 3

(2)

(b)On the grid, draw the graph of y=2x + 3

(2)

(c)Use your graph to find

(i)the value of y when x = –1.3

y = ......

(ii)the value of x when y = 5.4

x = ......

(2)

(Total 6 marks)

10.Asif, Barbara and Curtly share some money.

Asif receives of the money.

Barbara receives of the money.

What fraction of the money does Curtly receive?

…………………

(Total 3 marks)

11.Bob uses gas to heat his house.

This rule gives the cost of gas.

The cost of one unit of gas is 24 pence.

Last year Bob used 564 units of gas to heat his house.

(a)Work out the cost of 564 units of gas.

£……………………

(2)

Sarah uses electricity to heat her house.

This rule gives the cost of electricity.

The cost of one unit of electricity is 6 pence.

The fixed charge is £7.24

Last year Sarah used 2130 units of electricity to heat her house.

Sarah says that last year she paid less to heat her house than Bob paid to heat his house.

(b)Is Sarah correct?

You must show how you reached your decision.

(3)

(Total 5 marks)

Grade B

12.The equationx3 15x = 31

has a solution between 4 and 5.

Use a trial and improvement method to find this solution.

Give your answer correct to one decimal place.

You must show ALL your working.

x = …………….

(Total 4 marks)

13.(a)Complete the table for y = x2 – 3x + 1

x / –2 / –1 / 0 / 1 / 2 / 3 / 4y / 11 / 1 / –1 / 1 / 5

(2)

(b)On the grid, draw the graph of y = x2 – 3x + 1

(2)

(c)Use your graph to find an estimate for the minimum value of y.

y = ……………………

(1)

(d)Use a graphical method to find estimates of the solutions to the equation

x2 – 3x + 1 = 2x – 4

x = …………………… orx = ……………………(3)

14.

Calculate the volume of the triangular prism.

......

(Total4marks)

15.

The diagram shows a right-angled triangle ABC.

AC = 12.6 m.

Angle CAB = 41°

Angle ABC = 90°

Find the length of the side AB. Give your answer correct to 3 significant figures.

……………… m

(Total 3 marks)

16.

ABCD is a quadrilateral. Work out the size of the largest angle in the quadrilateral.

……………..°

(Total 4 marks)

17.Peter cuts a square out of a rectangular piece of metal.

All measurements are in centimetres. The shaded shape in the diagram shows the metal remaining.

The area of the shaded shape is 20 cm2.

(a)Show that x2 + 7x – 12 = 0

(4)

(b)(i)Solve the equation x2 + 7x – 12 = 0

Give your answers correct to 4 significant figures.

……………………………..

(3)

(ii)Hence, find the perimeter of the square.

Give your answer correct to 3 significant figures.

…………………….. cm

(1)

(Total 8 marks)

18.Solve the simultaneous equations

2x + 3y = 6

3x − 2y = 22

x = ……………………

y = ……………………

(Total 4 marks)

Grade A

19.Write down the reciprocal of 4

......

(Total 1 mark)

20.Use your calculator to work out the value of

(a)Write down all the figures on your calculator display.

…………………………………….

(2)

(b)Give your answer to an appropriate degree of accuracy.

…………………….

(1)

(Total 3 marks)

21.The times, in seconds, taken by 11 teachers to solve a puzzle are listed in order

412131718202224253034

(a)Find

(i)the lower quartile,

………………………seconds

(ii)the interquartile range.

…………………………seconds

(2)

b)Draw a box plot for this data.

(3)

(Total 5 marks)

22.Kevin regularly travels from Manchester to Oxford.

He travels on two different trains.

His first train is from Manchester to Birmingham and his second train is from Birmingham to Oxford.

On the first train, the probability that a seat has a table is .

On the second train, the probability that a seat has a table is .

Kevin is travelling from Manchester to Oxford tomorrow.

(a)Complete the probability tree diagram to show the outcomes of Kevin’s seating on the two trains.

Label clearly the branches of the probability tree diagram.

The probability tree diagram has been started in the space below.

(3)

(b)Calculate the probability that Kevin will have a seat with a table on both the first train and the second train.

……………………

(2)

(c)Calculate the probability that Kevin will have a seat with a table on at least one of the two trains.

…………………….

(3)

(Total 8 marks)

23.Fred did a survey on the areas of pictures in a newspaper.

The table gives information about the areas.

0< A 10 / 38

10 < A 25 / 36

25 < A 40 / 30

40 < A 60 / 46

(a)Work out an estimate for the mean area of a picture.

...... cm2

(4)

(b)Draw a histogram for the information given in the table.

(3)

(Total 7 marks)

Grade A*

24.Solve the simultaneous equations

x2 + y2 = 29

y – x = 3

………………………………………………………

(Total 7 marks)

25.

AB is parallel to DC.

The lines AC and BD intersect at E.

AB = 8 cmEC = 5 cmDC = 6 cm

(a)Explain why triangle ABE and triangle CDE are similar.

………………………………………………………………………………………………..

………………………………………………………………………………………………..

(2)

(b)Calculate the length of AC.

…………………….. cm

(3)

(Total 5 marks)

26.Diagram 1 is a sketch of part of the graph of y = sin x°.

(a)Write down the coordinates of

(i)P,

( …… , ……)

(ii)Q.

( …… , ……)

(2)

Diagram 2 is a sketch of part of the graph of y = 3 cos 2x°.

(b)Write down the coordinates of

(i)R,

( …… , ……)

(ii)S

( …… , ……)

(2)

(Total 4 marks)

27.

CDEF is a quadrilateral with = a, = b and = a – b.

(a)Express in terms of a and b.

……………………..

(1)

(b)Prove that FE is parallel to CD.

………………………………………………………………………………………………...

…………………………………………………………………………………………………

(2)

M is the midpoint of DE.

(c)Express in terms of a and b.

…………………….

(1)

*X is the point on FM such that FX : XM* = 4 : 1.

(d)Prove that C, X and E lie on the same straight line.

(3)

(Total 7 marks)

Neston High School1