CARDINAL NEWMAN CATHOLIC SCHOOL Mathematics Non Calculator Paper Higher Tier PRACTICE Year 9 Assessment 2

Transcription

1 CARDINAL NEWMAN CATHOLIC SCHOOL Mathematics Non Calculator Paper Higher Tier PRACTICE Year 9 Assessment 2 Name : Subject Teacher : Examination Instructions Use black ink or ball point pen. Use pencil and coloured pencils only for drawing Fill in the boxes at the top of this page. You may not use a calculator for this paper Answer ALL the questions. Write your answers in the spaces provided in this question paper, including rough work. In all calculations, show clearly how you work out your answer. Examination Information This examination will last 80 mins. Mark allocations are shown in brackets. This paper is out of 66 marks. You may ask for more answer paper, graph paper and tracing paper. Check your answers if you have time at the end. Tutor Group: 9 Tutor: For Examiners Use Question Number Total Marks Percentage Grade QCA Points Target Mark Awarded

2 Self-Assessment and Reflection Question Mark Awarded Topic (Maths Watch CD Title & Clip Number) Number (RAG rating) 1 Coordinates (CLIP 8) 2 Arithmetic with 4 operations and integers (CLIP 17-21) 3 Using Formulae (CLIP 95) 4 Substitution and Expanding Brackets (CLIP 93) 5 Y=mx+c (CLIP 96) 6 Sequences and Patterns (CLIP 37) 7 Drawing Straight Line Graphs (CLIP 96) 8 Arithmetic with 4 operations and fractions (CLIP 70-74) 9 Finding Fractions and Percentages (CLIP 72) 10 Problem Solving in Fractions (CLIP 86-89) 11 Equivalence (CLIP 85) 12 Interpreting Pie Charts (CLIP 128) 13 Box Plots (CLIP 187) 14 Angles in a Polygon (CLIP 123) 15 Angles in Parallel Lines (Clip 120) 16 Place Value in using thirds and equivalence (CLIP 177)

3 Q1. A map is drawn on a centimetre grid. 1 cm represents 3 km. (a) Write down the coordinates of South Point. Answer (...,... ) (b) Write down the coordinates of West Bay. Answer (...,... ) (c) Work out the actual distance between South Point and West Bay. Answer... km (2) (Total 4 marks) 3

4 Q2. The table shows UK postal rates. Weight First Class Second Class Letter 0 100g g Large Letter g g g g g g Packet g g g 4.25 Each additional 250 g or part thereof Please note items heavier than 1000 g cannot be sent Second Class (a) What is the cost of sending a 225 g large letter using First Class? Answer... (b) What is the weight of the heaviest item that can be sent Second Class? Answer... (c) A packet weighs 1.3 kg. How much does it cost to send it using First Class? 4

5 Answer... g (3) (Total 5 marks) Q3. Here are instructions for cooking a turkey. Cook for 15 minutes at 220 C Reduce the oven temperature to 160 C and cook for 40 minutes per kilogram. Kirsty is going to cook a 7 kilogram turkey. She wants to take it out of the oven at pm. At what time must she start to cook it? Answer... (Total 4 marks) Q4. (a) Simplify 8a b + 4a 2b Answer... (2) 5

6 (b) Multiply out x(x + 7) Answer... (Total 3 marks) Q5. An activity centre hires out road bikes and mountain bikes. The graph shows the cost, C ( ) of hiring a road bike for a number of days, d. (a) Circle the correct formula connecting the cost, C and the number of days, d for hiring a road bike. C = 2d + 5 C = 5d + 10 C = 10d + 5 6

7 (b) The cost of hiring a mountain bike is given by the formula C = 5d + 15 Rowan would like to hire a mountain bike. He thinks that a mountain bike will always cost more to hire than a road bike. Is this true? Yes No Explain your answer. (3) (Total 4 marks) Q6. Here is a sequence of numbers (a) Write down the next term in the sequence. Answer... (b) Write down the rule for continuing the sequence. Answer... (Total 2 marks) 7

8 Q7. (a) On the grid below draw the graph of y = 2x 3 for values of x from 1 to 4. (3) (b) The line y = 4.5 crosses the line y = 2x 3 at P. Use the graph to work out the coordinates of P. Answer (...,... ) (2) (Total 5 marks) 8

9 Q8. Tom is 60. His daughter Fiona is of his age. His grandson James is of his age. How many years older than James is Fiona? Answer... (Total 4 marks) Q9. Here is an advert for a summer holiday. 9

10 (a) Martha books a 14-night holiday in May. She books for herself, husband Billy and daughter Mary (aged 11). She books the holiday online. Explain clearly why the total cost will be 990. (4) (b) Salima books a 7-night holiday in April for two adults. The travel agent adds a percentage surcharge to the cost of the holiday for booking fees. Salima s final bill is What was the percentage surcharge? 10

11 Answer... % (3) (Total 7 marks) Q10. For each part circle the fraction whose value is closest to 1. (a) (b) (Total 2 marks) Q11. The pie charts show the age distribution in two villages A and B. The population of the villages is proportional to the area of the pie charts. There are 660 people over 65 in village A. Village A Village B 11

12 Drawn to scale How many people are over 65 in village B? Show clearly any measurements or assumptions that you make. Show your method clearly Answer... (Total 5 marks) Q12. Brian and George played 40 games of golf. The cumulative frequency diagram shows information about Brian s scores. The box plot shows information about George s scores. 12

13 (a) Showing your method clearly, find (i) Brian s median score Answer... (ii) Brian s inter-quartile range Answer... (2) (b) Use the cumulative frequency diagram and the box plot to answer the following. 13

14 (i) Which player is the more consistent in his scoring? Give a reason for your choice (ii) The winner of a game of golf is the player who has the lowest score. Who do you think is the better player? Give a reason for your choice (Total 5 marks) Q13. (a) Explain why the exterior angle of a regular pentagon, marked p on the diagram, is 72. (b) Two identical regular pentagons are joined as shown. 14

15 Not drawn accurately Work out the size of angle x. Answer...degrees (2) (Total 3 marks) Q14. In the diagram AB and CD are parallel. Not drawn accurately (a) Write down the value of x. Answer... degrees 15

16 (b) Work out the value of y. Answer... degrees (2) (Total 3 marks) Q15. Here are some circles each containing two numbers. The numbers are in a pattern. The numbers in the top of each circle are multiples of four. The numbers in the bottom of each circle are multiples of five. (a) Here are two more circles in the pattern. Write in the missing numbers. (2) (b) Here is another circle in the pattern. Write the two numbers in the circle so that their total is closest to

17 (2) (Total 4 marks) 17

18 . (a) (2, 3) (b) (2, 8) (c) [4] M2. (a) ( ) 0.70 (p) oe Accept 70 p (b) 1000 g 1 kg (c) 1300 seen or used eg, sight of dep ( ) 5 SC1 for ( )1.38 [5] 18

19 M or or 280 (their) or 4 h 55 m (their) or 4 h 40 m oe 12:45 (their) 4 h 55 m 12:45 (their) 4 h 40 m 15 m 07:50 oe SC3 08:05 [4] M4. (a) 12a 3b For one correct term seen, 12a or 3b B2 (b) x 2 + 7x [3] M5. (a) C = 10d + 5 (b) Correct substitution of a value for d in formula 20, 25, 30 Identifies equal pay at d = 2 No and cheaper at d > 2 dep 19

20 oe Alternate method Plots at least two correct coordinates on graph for mountain bike (0, 15) (1, 20) (2, 25) (3, 30) Correct line at least as far as intersection at (2, 25) No and cheaper at d > 2 dep [4] M6. (a) 16 (b) Add 3 oe Allow n + 3 [2] M7. (a) Two points calculated or plotted For each point or ( 1, 5) Line through (0, 3) (0, 3) Line gradient 2 (1, 1) (2, 1) (3, 3) (4, 5) Straight line drawn B2 20

21 (b) Attempt to read off at y = 4.5 or 2x = 7.5 or 4.5 as y coordinate 3.75 ft Their graph ± 1 mm ( square) ft [5] M or oe Fiona = 36 James = [4] M9. (a) (= 1100) Total % of 1100 = = oe (b)

22 Their [7] 0. (a) Circles Any indication (b) Circles Any indication [2] 1. Radius A = 1.5cm Radius B = 2.5 cm These must be clearly stated or implied (eg 2.25π, 6.25π) at some stage in solution. 22

23 1980 (population A) 6.25(π) 2.25(π) NB Scale factor such as 0.6, 1.66, NB Check pie charts for these. for attempt to compare areas. eg 25:9, population in B Allow implies Alt. Radius A = 1.5cm Radius B = 2.5cm These must be clearly stated or implied (eg 2.25π, 6.25π) at some stage in solution. 23

24 NB Scale factor such as 0.6, 1.66, NB Check pie charts for these. implies Compares a population to an area for village A eg 660 (=)

25 π 1980:2.25π Finds a value for person per area or area per person people per cm cm 2 per person Calculates area of quadrant in B and either multiplies or divides by appropriate value 1375 [5] 2. (a) (i) 100 (ii) Reading from graph = 13 (b) (i) George, lower interquartile range Accept smaller range/smaller spread oe (ii) Brian, lower median oe (B0 Brian 70, George 85) [5] 25

26 3. (a) 5 (equal) exterior angles must total 360 and = 72 or 5 72 = = 72 is not enough there must be some reference to exterior angles (b) 2 72 or 360 (2 108) oe (x =) 144 [3] 4. (a) 41 (b) their 41 oe [3] 5. (a) (b) 26

27 for any equivalent fraction with sum 900 eg, 27

28 or sum 1100 eg, B2 [4] 28