Year 10 Team Mathematics Competition 2013

Transcription

1 Year 10 Team Mathematics Competition 013 Instructions and Answer Booklet for Team Supervisors Please ensure that students do not have access to this booklet during the competition, and take care to hold it so that the answers cannot be seen Page 1 Year 10 Team Mathematics Competition 013

2 Thank you for supporting this competition and supervising a team in the competition. Your role is very important and the competition wouldn t be able to run without your help. Throughout the competition you will be asked by the presenter/organiser to hand out, collect in and mark questions for the rounds. After marking the answers, please hand the completed sheet(s) promptly to the presenter/organiser to collate the marks. If in any doubt about the marking please check with the presenter/organiser. Round 1 Comparisons (0 marks) 1 minutes Team Supervisors to quickly mark Round 1 whilst Round is running. Round Quick Year Round (10 marks) 6 minutes Team Supervisors to quickly mark Round whilst Round 3 is running. Round 3 Problem Solving (40 marks) 30 minutes Team Supervisors to mark Round 3 whilst Round 4 is running. Break for minutes Round 4 Studied Round (0 marks) 1 minutes Teams have been advised to prepare for this round in advance. Team Supervisors to mark Round 4 whilst Round 5 is running. Round 5 Multi-Choice Round (30 marks) 18 minutes Marked by the Team Supervisor before the start of the Carousel Round 6 Carousel (50 marks) 0 minutes This round will be carefully explained to the teams by the presenter / organiser however the instructions are also included here. This round requires the team to be supervised at all times as they will be asking for answers to be checked quickly throughout. Marked by the Team Supervisor at the end. Please record a final mark out of 50 (don't forget marks need dividing by ). Please ensure all marked sheets have now been handed to the presenter / organiser While the marks are being collated by the organiser, please return to your own school s team and hand out feedback forms for your students to complete. Feedback forms can be found in the Team Supervisor s pack. There is also feedback form for teachers. Please hand these feedback forms to the presenter / organiser before you leave. The Team Pack also contains participation certificates that can now be completed and handed to your school team members. Page Year 10 Team Mathematics Competition 013

3 Instructions for the Carousel round The students sit around the four sides of a table. Students work individually and do not communicate with each other. There are five sets of ten questions. On each sheet the answer to one question is used in the next question. Each student is given a sheet to work on and the fifth sheet is placed face down in the centre of the table. Students start work on their own sheet. At any time they can swap their sheet for the sheet in the middle of the table. At any point a student can ask the Team Supervisor to mark their answers, after which it will be returned to them. Supervisors give marks for each correct answer until they come to an incorrect answer. Put a circle around 1 mark on the incorrect question and return. Any time an answer is successfully corrected it will receive only 1 mark. No question beyond an incorrect answer is ever marked (since it is going to be wrong anyway!). At five minute intervals a whistle will be blown. The question sheets are then rotated clockwise one place around the table (hence the name Carousel). After 0 minutes the round ends. The Team Supervisor then marks any remaining answers, totals up the marks and gives a final mark out of 50 (don't forget to divide by ). Page 3 Year 10 Team Mathematics Competition 013

4 FMSP Year 10 Team Mathematics Heat 013 marks each Round 1 Comparisons (0 marks) 1. A < B [A: x B: ]. A = B [A: 60 o B: 60 o ] 3. A < B [A: B: ] 4. A < B [A: 4.8 B: 5] 5. A < B [A: 5.43 B: 5.48] 6. A > B [A: 600km/hr B: 583km/hr] 7. A < B [A: 1.9cm B: cm] 8. A = B [A: 4.0 B: 4.0] 9. A > B [A: 97.9 o B: 90 o ] 10. A > B [A: 5.5 o B: 4.5 o ] TOTAL 0 Marks Page 4 Year 10 Team Mathematics Competition 013

5 1. FMSP Year 10 Team Mathematics Heat 013 Round Quick Year Round (10 marks) The year 013 has four different digits. When was the last previous year to have four different digits.. 30 can be written as x 3 x 5 (a product of prime numbers) Express 013 as a product of prime numbers. 3. Find the number of factors in ( marks) 3 x 11 x 61 ( marks, any 1 error only 1 mark) can be written as a 10 b b a a a Find suitable integer values of a and b. 8 factors ( marks) a = (1 mark), b = 3 (1 mark) 5. q 013 can be written as p Find the values or p, q, r and s. rs, where p, q, r and s are all prime numbers. p =, q = 11, r = 7, s = 5 or p =, q = 11, r = 5, s = 7 (All correct marks, any 1 error only 1 mark) Page 5 Year 10 Team Mathematics Competition 013

6 FMSP Year 10 Team Mathematics Heat 013 Round 3 Problem Solving (40 marks) Problem A. ARE YOU CONCENTRATING? In bottle X there is an apple juice drink made from 40% pure apple juice (the remainder is water). In bottle Y there is an apple juice drink made from 5% pure apple juice. Bottle X Bottle Y A certain amount of drink is removed from bottle X and then replaced with apple juice drink from bottle Y. Bottle X now contains an apple juice drink made from 35% pure apple juice. 1 What fraction of bottle X was removed? 3 (4 marks) TOTAL 4 marks Page 6 Year 10 Team Mathematics Competition 013

7 Problem B. THE SHADED SQUARE (a) Given that b = a, what fraction of the square is shaded? (b) Given that b = 3a, what fraction of the square is shaded? 5 9 ( 3 marks) 9 16 ( 3 marks) (c) Given that b = ka, what fraction of the square is shaded (in terms of k)? k 3k ( k 1) ( marks for numerator) ( marks for denominator) Accept any equivalent expressions TOTAL 10 marks Page 7 Year 10 Team Mathematics Competition 013

8 Problem C. CALCUDOKU Each vertical and horizontal line must contain the digits 1 to 6. The numbers in the heavily outlined set of squares (called a cage) must produce the number in the top corner. For example: 4+ means the numbers must add up to 4 8x means the numbers must multiply to give 8 Tips: 5- means the difference in the numbers 1 and 6 could be either way round. Numbers can be repeated in a set of squares, as long as they are not repeated in the same row or column. MARKS: 1 mark for all numbers in a cage correct 1 mark for correct numbers in a cage, but in wrong positions. TOTAL 1 marks x x x Page 8 Year 10 Team Mathematics Competition 013

9 Problem D. London 01 Men s 110m Hurdle Final In the mens 110m Hurdles Final: Brathwaite finished between Clarke and Ortega. Richardson was next to Parchment. Fourie was immediately after Ortega. Richardson was immediately after Merritt. Clarke was next to Parchment. Robles did not finish. In what order did they finish? Position 1st nd 3rd 4th 5th 6th 7th 8th Name Merritt Richardson Parchment Clarke Brathwaite Ortega Fourie Robles TOTAL 6 marks for a correct table. Subtract 1 mark for each error. Minimum score zero. Page 9 Year 10 Team Mathematics Competition 013

10 Problem E. OLYMPIC RINGS The Olympic Rings are a familiar symbol. (a) How many lines of symmetry does this symbol have? 1 (1 mark) The five rings are coloured blue, black, red, orange and green. (b) In how many different ways can the five coloured rings be arranged? 60 ( marks) It s decided to only colour the rings with two colours, red and blue. (c) Complete the table below to work the number of different ways the rings can be coloured with only two colours. Colours Number of ways 5 blue 1 (1 mark) 4 blue/1 red 3 (1 mark) 3 blue/ red 5 (1 mark) blue/3 red 5 1 blue/4 red 3 5 red 1 TOTAL 18 (1 mark) 1 mark for the second part of the table being a reflection of the first (ft). TOTAL 8 marks Page 10 Year 10 Team Mathematics Competition 013

11 FMSP Year 10 Team Mathematics Heat 013 Round 4 Absolute Value Function (0 marks) mark each. Solve the equation 5 x 9 x = 7 and x = - 1 mark each 3. Sketch the graph of: (i) y x (ii) y x mark for the shape 1 mark for the shape 1 mark - marking on the vertex 1 mark - marking -4 on the vertex 1 mark - gradients looking like -1/1 1 mark - gradients looking like -1/1 Solve the equation x 4 x x = -1 (1 mark) Page 11 Year 10 Team Mathematics Competition 013

12 4. Sketch the graph of: (i) y x 1 x 1 mark for the shape 1 mark for the gradients looking like -, 0 and 3 Write down the coordinates of the vertices. (-1,3) and (,3) 1 mark each 5. Solve the equation x 1 x 1 x = 0 and x = -/3 1 mark each 6. Solve the inequality x 1 x 1 x 0 3 marks TOTAL = 0 Marks Page 1 Year 10 Team Mathematics Competition 013

13 FMSP Year 10 Team Mathematics Heat 013 Round 5 Multi-Choice Round (30 marks) Circle the correct answer. 1. B: 9 (5 marks). D: 4 cm (5 marks) 3. C: 1km (5 marks) 4. D: 31kg (5 marks) 5. C: 75cm (5 marks) 6. A: 5 (5 marks) TOTAL = 30 Marks Page 13 Year 10 Team Mathematics Competition 013

14 FMSP Year 10 Team Mathematics Heat 013 Round 6 CAROUSEL (5x0/ = 50 marks) SHEET A. SHEET B. Answer Answer 1 Q = 13 1 Q = R = 65 % R = S = 91 3 S = 5 4 T = 4 4 T = 7 5 U = 10 cm 5 U = 5 inches 6 V = 1440 o 6 V = 15 inches 7 W = 9 cm 7 W = X = 9 8 X = 1 9 Y = 3645 cm 3 9 Y = 48 cm 10 Z = Z = 88 π SHEET C. SHEET D. SHEET E. Answer Answer Answer 1 Q = 11 Q = 7 Q = R = R = 9 16 R =144% 3 S = 6 cm S = 75% S = 5 4 T = 4 T = 105 T = -3 5 U = 6.4 km U = 31pounds U = 6.6 o F 6 V = 64000cm V = 19 o V = 1330 l 7 W = 40 amps W = 1g W = 4 8 X = 80 o X = 15 Bits X = Y = 6 Y = 5 Y = Z = 3 Z = 1 3 Z = 13 Page 14 Year 10 Team Mathematics Competition 013