GCSE Mathematics Higher Paper 1 Non-calculator

Transcription

1 GCSE Mathematics Higher Paper 1 Non-calculator 1 hour 30 mins (77 marks) Name: Class: Page 1 of 15

2 1. ABCD, EFGH, BFI and CGI are straight lines. ABCD and EFGH are parallel. FI=GI. Angle FIG=48. Find angle BCG, giving reasons for your answer. [4 marks] C D B A H F G E 48 I Page 2 of 15

3 2. Kela is going to buy 8 new mugs. She has found the mugs she wants for sale in the stores Mugs R Us and Muggins. The price list of each store is given. At which store could Kela buy the mugs for the lowest price, and by how much? You must show all of your working. Mugs R Us [6 marks] Set of 6 for Individual mugs 2.99 Sale now on: Muggins Set of 4 for /4 off all prices Page 3 of 15

4 3. Evaluate: a) [3 marks] b) Point A has coordinates (2,7). Point M is the midpoint of line AB and has coordinates (3,1). What are the coordinates of point B? Page 4 of 15

5 5. The map shows the positions of the wi-fi router and the power points in Adisa s office. In order for his computer to function, his desk needs to be within 2m of a power point and within 4m of the router. Shade the area in which he could put his desk. [4 marks] router power point power point Scale 1m: 2cm 6. a) Expand: 4x(2x+3) b) Factorise fully: 9x 2 y - 15xy Page 5 of 15

6 c) Expand and simplify: 3(2x+4y) - 2(4y-2x) 7. George is going to Florida. On the day that he changes his money, the exchange rate is 1=$1.27. a) Draw a conversion graph for to $, for values from 0 to Dollars ($) Pounds ( ) b) George buys a pair of flip flops for $11 while he is in Florida. Use your graph to give an approximate value of the cost of the flip flops in British pounds. Page 6 of 15

7 c) A currency conversion graph shows an example of (circle 1 answer): Inverse proportion A reciprocal relationship Direct proportion A quadratic relationship 8. Evaluate giving your answer as a fully simplified mixed number retired people were asked how long they spent using the Internet on a typical day. The results are shown below: Time t (minutes) Frequency 0 t < < t < t < t a) Draw a cumulative frequency diagram to show this information. [3 marks] Page 7 of 15

8 60 50 Cumulative Frequency Time (minutes) b) Another survey shows that 95% of a group of 60 students spend more than 200 minutes per day using the Internet. Compare the group of teenagers to the group of retired people in terms of Internet usage. Your answer should contain a comparative figure and a summarising comment. 10. a) Write in standard form. b) Write as an ordinary number. Page 8 of 15

9 11. a) i) Explain why this is a geometric sequence: 1, 10, 100, 1000 ii) What is the common ratio in this sequence? b) What are the next two terms in this geometric sequence? 5, 5 2, 10,...,... c) Jadyn is training to run a marathon. On day one of his training programme, he runs 2 miles. On day two, he runs 2.5 miles. Each day after that, he runs 0.5 miles further than he ran the day before. Circle the type of sequence formed by the daily distances run. Fibonacci Geometric Arithmetic Quadratic 12. Mo runs 1000m in 4 minutes. Usain runs 1.8km in 7 minutes 30 seconds. Who has the greater average speed, Usain or Mo? [3 marks] Page 9 of 15

10 13. James and Emma share 2520 in the ratio x:7. James gets Find x. [3 marks] 14. The Venn diagram shows the number of members in the sets A, B, C and ε. ε A B C Find: a) n(a) Page 10 of 15

11 b) n(a B) c) n((a C) A') 15. The equation of a circle is x 2 + y 2 = 4. a) Sketch the circle on this set of axes Page 11 of 15

12 b) Points A and B lie on the circle and have x coordinates of 1. A is above the x axis and B is below it. Find the y coordinates of A and B. Give your answers in surd form. c) Find the equation of the tangent to the circle at A, giving your answer in surd form. [5 marks] 16. Candace makes a cake. The top of it is circular, with a circumference of 40cm. She uses green icing in the centre of the circle and a 5cm ring of white icing on the outside, as shown. If the icing is 2mm thick, what volume of white icing did she use? Give your answer in terms of π, in cm 3. [7 marks] Page 12 of 15

13 green 5cm 40cm = 4 a What is the value of a? [4 marks] Page 13 of 15

14 18. The diagram shows the side view of a slide at a park. The slide is 6m long, as shown. The angle that the slide makes with the horizontal ground is 30 and the angle that the steps make with the horizontal ground is 45. What is the length of the steps, l, as shown on the diagram? Give your answer as a simplified surd. [5 marks] 6m l steps slide 30 o Page 14 of 15

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