Applications of Mathematics

Transcription

1 Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Applications of Mathematics Unit 2: Applications 2 For Approved Pilot Centres ONLY Foundation Tier Thursday 9 June 2016 Morning Time: 1 hour 45 minutes Paper Reference 5AM2F/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. P46330A 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. *P46330A0128* 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 *P46330A0228*

3 Answer ALL questions. 1 A bus to the cinema leaves at (a) Write as a 12-hour clock time. A film starts at The film lasts 106 minutes. (b) What time does the film end? Write your answers in the spaces provided. You must write down all stages in your working.... (1)... (Total for Question 1 is 3 marks) *P46330A0328* 3 Turn over

4 2 Peter has a fair 8-sided spinner. Peter will spin the spinner once (a) On the probability scale below, mark with a cross ( ) the probability that the spinner will land on 5 (b) On the probability scale below, mark with a cross ( ) the probability that the spinner will land on 6 (c) On the probability scale below, mark with a cross ( ) the probability that the spinner will land on (1) (1) (1) 4 *P46330A0428*

5 Lucy has a different fair 8-sided spinner. The spinner is equally likely to land on 2 as on 3 The spinner is more likely to land on 4 than on 1 The total of all eight numbers on the spinner is 24 There are five numbers missing from the spinner. (d) Write the missing numbers on the spinner. 3 Naveed is going to buy new doors for his house. He buys 13 doors. Each door has 2 hinges. Each hinge needs 8 screws. Naveed has to buy all the screws he needs for the hinges. There are 20 screws in each packet of screws. 3 3 How many packets of screws does Naveed need to buy? 1 (3) (Total for Question 2 is 6 marks) hinge... (Total for Question 3 is 3 marks) *P46330A0528* 5 Turn over

6 4 Usain ran 100 m in 9.63 seconds. (a) Write down the value of the 3 in the number million people watched an Olympic final on TV. (b) Write 19.4 million in figures. An athlete won (c) Write down the value of the 2 in the number Two athletics teams, Harriers and Jaguars, ran a relay race. There were 4 runners in each team. Each runner ran 100 metres. The table shows the time, in seconds, each runner took to run 100 metres. Runner 1 Runner 2 Runner 3 Runner 4 Harriers Jaguars Both teams started at the same time. *(d) Which team finished the relay race first? You must show clearly how you get your answer.... (1)... (1)... (1) (3) (Total for Question 4 is 6 marks) 6 *P46330A0628*

7 5 Here is a scale drawing of an elephant s footprint. length The shoulder height of the elephant is approximately six times the length of its footprint. (a) Find an estimate for the shoulder height of the elephant. Here is the elephant s footprint drawn on a grid of centimetre squares. On the grid every centimetre square represents 100 cm 2. (b) Find an estimate for the area of the elephant s footprint. Scale: 1 cm represents 10 cm... cm represents 100 cm 2... cm 2 (3) (Total for Question 5 is 5 marks) *P46330A0728* 7 Turn over

8 6 Dan uses his bank card at an ATM. Dan needs to enter his PIN. His PIN is a 4-digit number. Dan knows that the first digit is 3 the second digit is 5 the third digit is 2 or 4 or 6 the fourth digit is 2 or 4 or 6 Write down all the possibilities for Dan s PIN. One has been done for you. 3522, (Total for Question 6 is 2 marks) 8 *P46330A0828*

9 7 Food Mart has a special offer. Food Mart Soup 89p per tin Special offer 5 tins for 3.00 James buys 5 tins of soup for 3.00 It is cheaper than buying 5 tins of soup at 89p per tin. (a) How much cheaper? Tim s Store also has a special offer. Tim s Store Soup 89p per tin Special offer 4 tins for 2.00 Kirsty is going to buy 10 tins of soup. She wants to buy the soup as cheaply as possible. *(b) Should Kirsty buy the soup from Food Mart or from Tim s Store? You must show all your working.... (3) (Total for Question 7 is 5 marks) *P46330A0928* 9 Turn over

10 8 Hannah and John go to a theme park. In the theme park they see this sign. (a) Is the sign closer to the roller coaster or to the log flume? You must show how you get your answer. This sign is on the roller coaster. Roller coaster 1 4 km Roller Coaster You must be at least 1.4 m tall to ride on the roller coaster Hannah is 125 cm tall. She is not tall enough to ride on the roller coaster. Log flume 0.3 km (b) How much taller does Hannah need to be to ride on the roller coaster? *P46330A01028*

11 John is 4 feet 8 inches tall. 12 inches = 1 foot 1 inch = 2.54 cm *(c) Is John tall enough to ride on the roller coaster? You must show how you get your answer. (3) (Total for Question 8 is 7 marks) *P46330A01128* 11 Turn over

12 9 In this question, each diagram represents part of a bridge. (a) On this diagram, mark with arrows (>>) a pair of parallel lines. The diagram below is a trapezium. x 38 (b) Find the size of the angle marked x. Diagram NOT accurately drawn (1) *P46330A01228*

13 C A ABC, CDE, AFD and BFE are straight lines. Angle ABF = 115 Angle DFE = 40 *(c) Find the size of the angle marked y. Give reasons for your answer. y B 115 F 40 D E Diagram NOT accurately drawn (3) (Total for Question 9 is 6 marks) *P46330A01328* 13 Turn over

14 10 Here is some information about the cost of sending a parcel. Parcel delivered by 10 am Parcel delivered by 12 noon Ben is going to send a parcel. The parcel has a weight of 15 kg. It is cheaper to have the parcel delivered by 12 noon. (a) How much cheaper? Amy sends a parcel. She pays to have the parcel delivered by 12 noon. Amy pays (b) Work out the weight of Amy s parcel. Cost plus 0.35 for each kg more than 10 kg plus 0.30 for each kg more than 10 kg... (3)... kg (3) (Total for Question 10 is 6 marks) 14 *P46330A01428*

15 11 Tom makes a model. Part of the model is a cube. Two of the shapes below are nets of a cube. (a) Write down the letter of each of these two shapes. A B D The other part of the model is a square-based pyramid. (b) In the space below, draw a sketch of a net for this pyramid. E C... and... (Total for Question 11 is 4 marks) *P46330A01528* 15 Turn over

16 12 You can use this graph to change between litres and gallons. Gallons Nadia buys 40 litres of petrol. (a) Change 40 litres to gallons. There are 7 gallons of oil in a tank. (b) Change 7 gallons to litres Litres... gallons (1)... litres (1) 16 *P46330A01628*

17 Carol has a water barrel. There are 150 litres of water in the barrel. A full watering can holds 2 gallons of water. (c) How many times can Carol completely fill the watering can with water from the barrel? You must show your working.... (3) (Total for Question 12 is 5 marks) *P46330A01728* 17 Turn over

18 13 Sue made patterns with square tiles. Here are two of her patterns drawn on a grid of centimetre squares. Pattern A Pattern B is an enlargement of Pattern A. (a) Work out the scale factor of the enlargement. Here is part of another pattern Sue made. Pattern C The complete Pattern C is an enlargement of Pattern A. (b) Work out the perimeter of the complete Pattern C. Pattern B... (1)... cm (3) (Total for Question 13 is 4 marks) 18 *P46330A01828*

19 14 You can use this rule to work out the total cost of hiring a car from Hire Cars. Andy hired a car from Hire Cars for 9 days. The cost per day was 21 (a) Work out the total cost. Total cost = cost per day number of days hired You can use this formula to work out the total cost of hiring a car from Cheap Carz. T = 15n + 23 T is the total cost in pounds. n is the number of days the car is hired. Ana hired a car from Cheap Carz for 7 days. (b) Work out the total cost (Total for Question 14 is 4 marks) *P46330A01928* 19 Turn over

20 15 Sarah and Tina cycled from their home to school along the same roads. The distance from their home to school is 7 km. The travel graph for Sarah s journey to school is shown below. Distance from home in km Time On the way to school, Sarah stopped at her friend s house. (a) What time did Sarah get to her friend s house? (b) How far was Sarah from school at 07 35? Tina left home 15 minutes after Sarah. She cycled to school at a steady speed. She did not stop on the way to school. Tina took 30 minutes to cycle to school. (c) On the grid, show the travel graph for Tina s journey to school. (d) How many minutes did it take Tina to reach Sarah?... (1)... km (1)... minutes 20 *P46330A02028*

21 (e) Work out Tina s average speed on her way to school. Give your answer in km/h. 16 Chloe is going to roll a fair 6-sided dice 150 times. (a) Work out an estimate for the number of times the dice will land on 4 Harry has a biased 6-sided dice. He rolls the dice 200 times. The table gives information about his results. Score David is going to roll this biased dice 60 times. Frequency (b) Work out an estimate for the number of times the score will be 4... km/h (Total for Question 15 is 8 marks) (3) (Total for Question 16 is 5 marks) *P46330A02128* 21 Turn over

22 17 box 12 cm 18 cm 7 cm A box of sugar is 12 cm by 7 cm by 18 cm. A carton is 60 cm by 70 cm by 54 cm. carton 60 cm The carton is completely filled with boxes of sugar. Work out the number of boxes of sugar in the carton. 54 cm 70 cm Diagram NOT accurately drawn... (Total for Question 17 is 3 marks) 22 *P46330A02228*

23 * 18 Here is a list of ingredients for making 16 cereal bars. Sally wants to make 40 cereal bars. She has 500 g of caster sugar 454 g of honey 300 g of peanut butter 270 g of toasted oatmeal Cereal Bars Ingredients to make 16 cereal bars 100 g caster sugar 175 g honey 130 g peanut butter 90 g toasted oatmeal Does Sally have enough of each ingredient to make 40 cereal bars? You must show all your working. (Total for Question 18 is 4 marks) *P46330A02328* 23 Turn over

24 19 Students take an exam at the end of a catering course. All students who fail the exam first time take the exam a second time. The probability that a student will pass the exam first time is 0.85 The probability that a student who fails first time will pass second time is 0.6 (a) Complete the decision tree diagram First time Pass Fail A student on the catering course is chosen at random. (b) Work out the probability that this student will fail the exam both times Second time Pass Fail... (Total for Question 19 is 4 marks) 24 *P46330A02428*

25 20 Ali sells salad cream in three different sizes of bottle g g 600 g small medium large A small bottle costs 1.29 and contains 285 g of salad cream. A medium bottle costs 2.25 and contains 460 g of salad cream. A large bottle contains 600 g of salad cream. Ali wants the large bottles of salad cream to be the best value for money. Work out the greatest possible cost of a large bottle of salad cream.... (Total for Question 20 is 4 marks) *P46330A02528* 25 Turn over

26 21 The stopping distance, y feet, of a car in dry weather is given by the formula y where x is the speed of the car, in mph. 2 x = + x 20 2 x (a) Complete the table of values for y = + x 20 x y (b) On the grid, draw the graph of y y x = + x for values of x from 0 to O x 26 *P46330A02628*

27 The stopping distance of a car in wet weather at 35 mph is double the stopping distance in dry weather at 35 mph. A car is travelling in wet weather at 35 mph. (c) Find the stopping distance of the car.... feet (Total for Question 21 is 6 marks) TOTAL FOR PAPER IS 100 MARKS *P46330A02728* 27

28 BLANK PAGE 28 *P46330A02828*