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PPE+1 March 2016

Higher Tier Edexcel Style PAPER 2H Calculator allowed

Time 1 hour 45 minutes Marks Available 100

Commissioned by The PiXL Club Ltd.

Name

Class

Question Mark Maximum mark

1 3 2 4 3 2 4 3 5 4 6 5 7 5 8 4 9 4 10 4 11 4 12 7 13 7 14 4 15 4 16 3 17 5 18 3 19 3 20 3 21 3 22 7 23 4 24 5 Total 100

2

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Question 1 The two-way table gives some information about how 100 children travelled to school one day.

Walk Car Other

Girl 13 23 16 Boy 24 10 14

One of the children is picked at random.

(a) Write down the probability that this child is a girl who walked to school.

..................................... (1)

(b) Write down the probability that this child was driven to school.

..................................... (2)

(Total 3 marks)

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Question 2 The equation

x3 + 2x = 90 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)

5

Question 3 Use your calculator to work out the value of .

√ . . Write down all the figures on your calculator display.

....................................................................................

(Total 2 marks)

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Question 4 Lucy is driving home from a concert.

Lucy drives 5 miles from the concert venue to the A road 100 miles on an A road 10 miles from the A road to her home Lucy takes 10 minutes to drive from the concert venue to the A road drives at an average speed of 40 mph on the A road takes 30 minutes to drive from the A road to her home Lucy stops for a 30 minute rest on her drive home. Lucy leaves the concert at 6:00pm. What time does Lucy get home? You must show all your working.

.......................................... (Total 3 marks)

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*Question 5 Sweet Treats sell boxes of mixed sweets in three different sizes of box. Small Medium Large A small packet has 25 sweets and costs £3.75 A medium packet has 60 sweets and costs £8.70 A large packet has 80 sweets and costs £12.40 Work out which size of box gives the best value for money. You must show all your working.

(Total 4 marks)

Sweet Treats 25 sweets £3.75

Sweet Treats 60 sweets £8.70

Sweet Treats 80 sweets £12.40

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Question 6 (a) Expand and simplify 2 + 3 + 8

.......................................... (2)

(b) Solve 3 + 7 =

= ......................................... (3)

(Total 5 marks)

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Question 7 Will gets paid £490 for some summer work. Will shares his money with his brother Jim, in the ratio 5: 2 Will then gives 8% of his money to his mum. How much does Will have left?

…………………………. (Total 5 marks)

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*Question 8 In the UK, petrol costs £1.02 per litre.

In USA, petrol costs $1.86 per gallon. 1 US gallon = 3.79 litres £1 = 1.42 dollars Is petrol cheaper in the UK or in the USA?

(Total 4 marks)

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Question 9 PQR is a triangle. Shade the region inside the triangle which is both greater than 8 centimetres from the point P and closer to the line QR than the line QP.

(Total 4 marks)

Q

R P

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*Question 10 Toni is organising a wedding reception for her friend.

People at the reception will sit at circular tables.

Each table has a diameter of 167 cm. Each person needs 60 cm around the circumference of the table. There are 15 of these tables in the conference room. A total of 100 people will be at the wedding reception Are there enough tables at the reception?

(Total 4 marks)

Diagram NOT Accurately drawn

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Question 11 On the grid, draw the graph of y = − 1 for values of x from –2 to 3

(Total 4 marks)

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Question 12 The diagram shows the positions of three boats A, B and C.

C is 120 km due north of boat B. A is 90 km due east of boat B. (a) Calculate the distance AC.

.............................................. km (3)

(b) Calculate the bearing of C from A. Give your answer correct to the nearest degree.

.............................................. ° (4)

(Total 7 marks)

Diagram NOT Accurately drawn

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Question13 Kevin asked 60 people how many text messages they each sent on Friday. The tables shows his results.

Number of texts sent Frequency 0 to 4 7 5 to 9 5 10 to 14 18 15 to 19 14 20 to 24 16

(a) Write down the modal class.

……..………….

(1) (b) Work out an estimate for the mean number of texts sent on Friday.

………………. (4)

(c) What percentage of these people sent less than 10 texts?

………….%

(2) (Total 7 marks)

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Question 14 (a) Write 23 600 in standard form.

................................................................

(1) (b) Write 3.76 × 10−4 as an ordinary number.

................................................................ (1)

(c) Work out the value of 54 500 ÷ (1.25 × 10−4)

Give your answer in standard form.

................................................................ (2)

(Total 4 marks)

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Question 15

A, B, C and D are points on the circumference of a circle, centre O. AC is a diameter of the circle. AC and BD intersect at E. Angle CAD = 30° Angle BEC = 80° Work out the size of angle BAC. You must show all your working.

(Total 4 marks)

Diagram NOT Accurately drawn

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Question 16 Find an equation of the line parallel to the line = 10 − 2 and passes through the point (3, 1)

(Total 3 marks)

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Question 17

The box plot gives information about the distribution of the weights of bags on a plane.

(a) Jonathan says the lightest bag weighs 9 kg. He is wrong. Explain why. ....................................................................................................................................................................... .......................................................................................................................................................................

(1) (b) Write down the median weight.

.............................. kg (1)

(c) Work out the interquartile range of the weights.

.............................. kg (1)

There are 220 bags on the plane. (d) Work out the number of bags with a weight of 22 kg or less.

.............................. (2)

(Total 5 marks)

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*Question 18 22. Prove that 2 + 1 − 2 − 1 is a multiple of 4, for all positive integer values of n.

(Total 3 marks)

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Question 19

Enlarge the shaded shape by scale factor 2

1 with centre (–1, –2).

(Total 3 marks)

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Question 20 M is inversely proportional to Q.

When Q = 4, M = 18. Find the value of M when Q = 6

..........................................

(Total 3 marks)

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Question 21 Simplify fully

− 13 + 402 − 11 + 5

................................................ (Total 3 marks)

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Question 22 A rectangular lawn has a length of 4x metres and a width of 3x metres.

The lawn has a path of width 1 metre on three of its sides. The total area of the lawn and the path is 102 m2 (a) Show that 12x2 + 10x – 100 = 0

(2) (b) Calculate the area of the lawn. Show clear algebraic working.

................................ m2 (5)

(Total 7 marks)

Diagram NOT Accurately drawn

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Question 23

The histogram shows some information about the ages of passengers travelling on a flight to Los Angeles.

Work out the proportion of passengers on the flight aged between 20 and 60.

.......................................... (Total 4 marks)

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Question 24 The diagram shows a sector of a circle with centre O.

The radius of the circle is 7 cm. ARB is an arc of the circle. AB is a chord of the circle. Angle AOB = 150°

Calculate the area of the shaded segment. Give your answer correct to 3 significant figures.

............................. cm2 (Total 5 marks)

TOTAL FOR PAPER: 100 marks

Diagram NOT Accurately drawn