Applications of Mathematics

Transcription

1 Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 1: Applications 1 For Approved Pilot Centres ONLY Foundation Tier Thursday 26 May 2016 Morning Time: 1 hour 45 minutes Paper Reference 5AM1F/01 You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided there may be more space than you need. Calculators may be used. If your calculator does not have a button, take the value of to be unless the question instructs otherwise. Information The total mark for this paper is 100 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. P46328A 2016 Pearson Education Ltd. 6/6/6/6/6/3/ Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. *P46328A0132* Turn over

2 GCSE Mathematics 2AM01 Area of trapezium = 1 (a + b)h 2 Formulae: Foundation Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section length h cross section a b length 2 *P46328A0232*

3 Answer ALL questions. 1 Here is Gareth s bank statement for April 2015 Write your answers in the spaces provided. You must write down all stages in your working. Date Deposit ( ) Withdrawal ( ) Balance ( ) Apr Apr Apr Apr Apr (a) Complete the balance column by filling in the two missing amounts. On July 31st, Gareth s account had a balance of 2000 In August the total of the withdrawals was 1280 the total of the deposits was 880 (b) Work out the balance on August 31st (Total for Question 1 is 4 marks) *P46328A0332* 3 Turn over

4 2 Some people were asked if they usually watched films at the cinema, on DVD, on the internet or on television. Here are their answers. internet television internet television DVD internet television internet DVD cinema television DVD DVD internet cinema television internet internet cinema internet (a) Show this information in the tally chart. Tally Frequency cinema DVD internet television 4 *P46328A0432*

5 (b) Draw a suitable chart or diagram to show this information. (3) (Total for Question 2 is 5 marks) *P46328A0532* 5 Turn over

6 3 Graham is collecting money for charity. He makes a column of 10p coins. Each coin is 1.85mm thick. The height of the column is 37cm. (a) Work out the number of coins in the column. Graham also has some pound coins. Each pound coin has a weight of 9.5grams. (b) Work out the total weight of 20 of these coins. Diagram NOT accurately drawn... (3)...grams (Total for Question 3 is 5 marks) 6 *P46328A0632*

7 4 Here is a list of temperatures. (a) Write these temperatures in order. Start with the lowest temperature.... The freezer broke down. By 3pm that day the temperature inside the freezer had gone up by 8 C. (b) (i) Write down the temperature inside the freezer at 3pm. The temperature inside the freezer went up by 4 C every hour after 1pm. (ii) At what time did the temperature inside the freezer reach 0 C?... C... (3) (Total for Question 4 is 4 marks) *P46328A0732* 7 Turn over

8 5 Here is a map of an island used for a computer game. The map is drawn on a centimetre coordinate grid. y O Here are the instructions for the game Start from point A (3,1). From A, move up 4cm parallel to the y-axis to point B. From B, move right 5cm parallel to the x-axis to point C. (a) On the grid, mark with crosses ( ) points A, B and C. Label each point. (b) Write down the coordinates of point C. Treasure is buried at the midpoint of AC. (c) Find the coordinates of the treasure. x (...,...) (...,...) (Total for Question 5 is 5 marks) 8 *P46328A0832*

9 6 (a) Write down the time shown on the clock. Jim s train leaves the station at 5 20 pm. (b) Write 5 20 pm using the 24-hour clock. Each Wednesday Megan has swimming practice before school. It takes Megan a quarter of an hour to get from home to the swimming pool. She spends 45 minutes at the swimming pool. It takes Megan 20 minutes to get from the swimming pool to school. She has to be at school by 8 45 am. (c) What is the latest time she can leave home on Wednesday? (3) (Total for Question 6 is 5 marks) *P46328A0932* 9 Turn over

10 7 Here is some information about some washing machines. Washing machine Energy rating Load (kg) Spin speed (rpm) Price ( ) Boss Excel A ML Speedy A Coolcross Wash A Niele EXA A ML Mini A Zen Slimfit A Paravision Y A ML Nine A (a) Write down the price of the cheapest washing machine. (b) Write down the washing machine that has a load of 7 kg and an energy rating of A+. Mr and Mrs Key want to buy a new washing machine. The energy rating must be A+++. The load must be 8kg. They want to pay the lowest price. The washing machine will be delivered to their house. The delivery charge is (c) (i) Write down the washing machine they should buy. (ii) Work out the total amount they have to pay (Total for Question 7 is 4 marks) 10 *P46328A01032*

11 8 Jean makes a toy. The toy is a box with a shape cut out. Here is an accurate drawing of the shape. (a) What is the mathematical name of this quadrilateral? (b) Measure the size of the angle marked x. (c) Measure the length of the side AB. Jean is going to put tape around all the edges of the quadrilateral. (d) Find the perimeter of the quadrilateral. A x B (Total for Question 8 is 6 marks) *P46328A01132* 11 Turn over

12 9 The pentagon ABCDE represents the front of a house. AB = ED BC = DC Angle BCD = 124 Angle BAE = angle AED = 90 (a) On the diagram, draw the line of symmetry. (b) Work out the size of angle ABC. B A C 124 Diagram NOT accurately drawn D E... (3) 12 *P46328A01232*

13 Michael is going to put solar panels on a part of the roof. This part of the roof is a rectangle, ABCD, 10m by 8m. Michael arranges the solar panels in the shape of a rectangle, 8m by 6m. A D 10m 8m solar panels 6m 8m (c) Work out the area of the rectangle of solar panels. *(d) Is the area of the rectangle of solar panels more than 75% of the area of the rectangle ABCD? You must show all your working. B C Diagram NOT accurately drawn...m 2 (3) (Total for Question 9 is 9 marks) *P46328A01332* 13 Turn over

14 10 Peter has some white rods and some grey rods. Each white rod has a length of x cm. Each grey rod has a length of y cm. Peter puts down 4 white rods to make a row. x cm The total length of the row is T cm. T cm (a) (i) Write down an expression in terms of x for T. T = 40 (ii) Work out the length of a white rod. Peter makes another row of 4 rods. x cm The total length of the row is L cm. L cm y cm (b) (i) Write down an expression in terms of x and y for L. L = 36 (ii) Work out the length of a grey rod. Diagram NOT accurately drawn cm Diagram NOT accurately drawn cm (3) (Total for Question 10 is 5 marks) 14 *P46328A01432*

15 11 Christine works in a care home. Here is the time sheet showing the number of hours she worked each day last week. Mon Tues Wed Thurs Fri Sat Sun Hours Christine is paid 7.40 for each hour she works, Monday to Friday. She is paid 50% extra for each hour she works on Saturday and Sunday. Work out the total amount of money that Christine was paid last week.... (Total for Question 11 is 4 marks) *P46328A01532* 15 Turn over

16 12 Shasta works for a company. Each week the company pays Shasta expenses for all the miles she has driven for work. The company uses this flowchart to work out Shasta s expenses. Start Input N Number of miles driven N Extra miles driven = N No Expenses = extra miles driven 0.25 Output expenses Stop Yes Expenses = N *P46328A01632*

17 In the first week of June, Shasta drove 300 miles for work. (a) Use the flowchart to work out her expenses for the first week of June. In the second week of June, Shasta drove 450 miles for work. (b) Use the flowchart to work out her expenses for the second week of June. The company increases by 5p the amount of expenses paid for each mile driven over 400 miles. This means that one instruction in the flowchart has to be changed. (c) Write down the new instruction that is needed in the flowchart (Total for Question 12 is 4 marks) *P46328A01732* 17 Turn over

18 13 The diagram shows a design for a logo. There are three squares in the design. (a) Shade one part of the diagram above to give a new design with rotational symmetry of order 4 Here is the same design for the logo. (b) Shade some of this diagram to give a logo with rotational symmetry of order 2 18 *P46328A01832*

19 Here is the design with different shading. The dotted lines are lines of symmetry. The three squares of the design are shown below. A B C (c) Write the area of square C as a fraction of the area of square A.... (Total for Question 13 is 4 marks) *P46328A01932* 19 Turn over

20 *14 James teaches at the Grove Primary School. Here are the results of the Year 6 maths exam. James says, Level Number of children Below We expect at least 7 out of every 10 children in Year 6 to get above a level 3 Did at least 7 out of every 10 children get above a level 3? You must show all your working. (Total for Question 14 is 3 marks) 20 *P46328A02032*

21 15 Julie goes to the USA. She changes 750 to US Dollars ($). The exchange rate is 1 = $1.52 (a) Work out how many dollars ($) Julie gets. Karen lives in France. She sees a bag costing 500 euros. An identical bag in England costs 340 The exchange rate is 1 = 1.25 euros. The bag costs less in England than in France. *(b) How much less? $... (3) (Total for Question 15 is 5 marks) *P46328A02132* 21 Turn over

22 16 A shop sells bolts and it sells nuts. It sells the bolts in packets of 12 It sells the nuts in packets of 20 A packet of bolts costs 3.49 A packet of nuts costs 4.19 Keith wants to buy some bolts and some nuts. He wants the number of bolts to be the same as the number of nuts. Work out the least total amount of money he has to pay.... (Total for Question 16 is 4 marks) 22 *P46328A02232*

23 17 The composite bar chart gives information about the percentages of people who go to work by bus or by train or by car in four cities. City D C B A Percentage (a) In city A, what percentage of people go to work by car? (b) In city B, what percentage of people go to work by train? Eric says, More people go to work by car in city D than in city C Eric could be wrong. (c) Explain why Eric could be wrong. Bus Train Car... %... % (Total for Question 17 is 3 marks) *P46328A02332* 23 Turn over

24 18 Eva uses this equation to work out how much tax to pay, y, when the taxable income is x (a) Complete the table. y = 0.2x x x y (b) On the grid, draw the graph of y = 0.2x x from to Tax to pay ( ) y Taxable income ( ) x 24 *P46328A02432*

25 Eva and Adam both pay tax. Adam has 3000 more taxable income than Eva. He has to pay more tax than Eva. (c) How much more?... (Total for Question 18 is 6 marks) *P46328A02532* 25 Turn over

26 19 Tony added mkg of salt to a litre of water. He found the freezing point, T C, of the salt water for different values of m. He then drew this scatter diagram for different values of m. T 5 O m (a) Describe the relationship between the freezing point of salt water and the amount of salt added to the water Tony added some salt to a litre of water. (b) Find an estimate for the amount of salt he added to the water.... kg 26 *P46328A02632*

27 A car uses a mixture of anti-freeze and water to cool the engine. Instructions for the mixture are Mix 3 parts by volume of anti-freeze with 7 parts by volume of water. Trevor has 2 litres of anti-freeze. He wants to make 7 1 litres of the mixture. 2 *(c) Show that Trevor does not have enough anti-freeze to make 7 1 litres of the mixture. 2 (3) (Total for Question 19 is 6 marks) *P46328A02732* 27 Turn over

28 *20 Jonah asked 47 people at a sports centre to tell him the game they liked best from squash badminton tennis 4 of the 20 women said tennis. 6 of the men said tennis. 17 people said badminton. 8 more men than women said squash. How many men said badminton? You must show all your working. (Total for Question 20 is 4 marks) 28 *P46328A02832*

29 21 Jim has x Bill has 4 more than Jim. Alice has twice as much money as Jim. (a) Write down an expression, in terms of x, for the total amount of money Jim, Bill and Alice have. Give your answer in pounds in its simplest form. Jim, Bill and Alice have a total of 60 (b) Work out how much money Alice has. END (3) (Total for Question 21 is 5 marks) TOTAL FOR PAPER IS 100 MARKS *P46328A02932* 29

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