Maths Berg. Grade 8 Mathematics Paper 1 November 2015 Marks Available: 140 Time Available: 2 ¼ hours

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1 Maths Berg Grade 8 Mathematics Paper 1 November 2015 Marks Available: 140 Time Available: 2 ¼ hours

Your tribe will vote you off at the next tribal council if you dare to do any of the following: Use a calculator Work

2 One hundred and eighty grade 8s abandoned on a wild, but beautiful mountain, surrounded by a magnificent lake, where everything is mathematical. Pure bliss! 2 ¼ hours, 180 people, 1 mountain, many winners! Who will be voted out tonight? Your tribe will vote you off at the next tribal council if you dare to do any of the following: Use a calculator Work untidily Show only your answer Work in pencil Give up Grab a torch and light it from the fire of knowledge. It will stay lit as long as you wish.

3 Task 1 Before you leave for MathsBerg you need to show that you have the basic algebraic skills needed to survive on the mountain. Simplify the following: a) a + a + a (1) b) b b b (1) c) c c c (1) d) d d (1) e) 3e 4 + 2e + 5 (2) f) 5fg 2gf + 3fh 8gf + f²g (2) g) h) (5 8) (5) k k (1) i) 4 5m 4 2m (3) j) 7 p q 2 n p q n (3) k) 27r 6t 18 3 (3) 6 54x y l) 4 3 6x y 3 (3) z 3 4 m) 3z 5 z 2 z (3) 2 3z

4 Task 2 Come on in, guys! Immunity is up for grabs. You will swim out to a platform in the lake. There you will solve a bunch of equations. You will swim back, remembering your solutions. You will then climb a tower and find puzzle pieces which will spell out a word that should be well-known to you. Survivors ready..... go! Solve these equations: a) 7a 3 = 32 (2) b) 5b + 12 = 3b + 54 (3) c) 8(2x + 3) = 5 (3) d) 2(y 1) + 4y = 178 4y (4) e) 5(2z + 3) 4(z 7) = 7 6(z + 3) (2z 40) (4) When you choose puzzle pieces, ignore minus signs. If your answer was a fraction take both puzzle pieces one for the numerator and one for the denominator. Only attempt this check once everything else on the exam is finished.

Task 3 The following formula is used to assess a Survivor s chance of making it far enough to be on the jury the higher the value of J, the higher their chance.

(3) b) Find the value of J if 1 a, 3 1 b 1 and c = 4. (3) 2 c) Find the value of J if a = 3, b = 10 and c = 1 (3) Task 4 Your tribe receives treemail in mathematical expressions.

5 Task 3 The following formula is used to assess a Survivor s chance of making it far enough to be on the jury the higher the value of J, the higher their chance. J = 5a + b 2 3(c 4) where a stands for their looks, b stands for their strength and c stands for their arrogance. a) Find the value of J if a = 4, b = 8 and c = 10. (3) b) Find the value of J if 1 a, 3 1 b 1 and c = 4. (3) 2 c) Find the value of J if a = 3, b = 10 and c = 1 (3) Task 4 Your tribe receives tre in mathematical expressions. It advises you that the answers to each clue below may be useful in later challenges. Work out what each clue is: 3 5 a) The number of seasons of Survivor aired in South Africa b) The number of viewers of the first season (in normal notation) c) The percentage (that this fraction represents) of people in the world who know about Survivor 3, d) The revenue of the first season in millions of dollars 5,32 + 0,89 0,5 0,4 (11)

Task 5 For this team challenge you will need to fill in a table of substitutions, selecting the correct answers from the puzzle pieces that are given.

6 Task 5 For this team challenge you will need to fill in a table of substitutions, selecting the correct answers from the puzzle pieces that are given. Some puzzle pieces will not be used. Fill in only your answers on the separate answer sheet that has been given and staple it to the front of your lined paper. (8) m n m n 5n² 3 m n

Task 6 Your next challenge involves catapulting three balls onto an open piece of grass that has been marked off in a grid as shown below: 27 31 121 4 977 13 46

What is the largest total that you can score from the sum of the three balls?

7 Task 6 Your next challenge involves catapulting three balls onto an open piece of grass that has been marked off in a grid as shown below: a) Each ball that lands on a prime number will be added to your score. If it falls on a composite number, it will not count. What is the largest total that you can score from the sum of the three balls? (3) b) The group of 180 Survivors was originally split into two tribes; one of 80 and one of 100. i) Write 80 and 100 as products of their prime factors. (4) ii) Find the highest common factor of 100 and 80. (2) iii) Find the lowest common multiple of 100 and 80. (2)

8 Task 7 For a reward of Cokes and doughnuts (as many as you can eat and drink), Survivors have to put together a puzzle that has various stages as shown below. Stage 1 Stage 2 Stage 3 a) Complete the copy of the table that is given on your answer sheet: Stage (s) Number of squares with a logo (x) Number of blank squares (y) Answer these questions on your lined paper: s (13) b) Find a formula connecting x and y. (2) c) How many blank squares are used in the stage that has 102 squares with logos? (2)

9 Task 8 A second puzzle has the following as its first three stages. Only squares with logos are used. Stage 1 Stage 2 Stage 3 Complete the copy of the following table that is given on the answer sheet: (5) Stage p Number of squares

10 Task 9 1. The ages of the winners of the first 24 seasons of Survivor are given below: The sum of the ages of those winners under 30 is 295 The sum of those winners over 30 is 449. a) What is the mean age of the winners of these seasons? (3) b) What is the range of these ages? (2) 2. A back to back stem and leaf diagram for a season of Survivor is shown. The left hand side shows the weights of 32 Survivors when they started and the right hand side shows their weights when they left the game. One person was medically evacuated and so is not on the second list. Weight before starting Weight when leaving the game 5 7 means 57 kg a) What was the median starting weight? (2) b) What was the median ending weight? (2) c) What was the mode of the starting weights? (1) d) What was the mode of the ending weights? (1)

11 Task 10 A group of 120 people is asked which of four reality shows they prefer. Their responses are shown in the one pie chart below. The gender composition of the group is shown in the second pie chart. Preferred Reality TV Show Gender of Watchers Masterchef, 5 American Idol, 15 Amazing Race, 30 Female 40% Survivor, 70 Male 60% a) Show what size angle would be used to draw the portion of the pie chart for those people who preferred Survivor. (3) b) What percentage of viewers preferred Amazing Race? (2) c) How many females were in the group surveyed? (2) d) Choose the best answer for the following question: (1) How many females of this group preferred Amazing Race? A) 18 B) 12 C) 48 D) 30 E) Can t be determined

Task 11 a) The winner of Survivor earns $1 000 000. She invests this for 4 years at a 15% p.a. simple interest rate. How much will she have after 4 years?

12 Task 11 a) The winner of Survivor earns $ She invests this for 4 years at a 15% p.a. simple interest rate. How much will she have after 4 years? (3) b) The winner of the viewer s prize of $ decides to split it between three charities in the ratio of 2 : 5 : 3. How much will each charity receive? (4) c) You see that e-bay is offering one of the winner s buffs for R You want to buy it, but cannot afford the full amount. You enter into a hire purchase agreement with the following conditions: You will pay a 20% deposit. You will then pay interest on the remainder at a rate of 25% p.a. You will pay it all off over a period of 2 years. What will your monthly instalments be? (5) Task 12 Do not attempt this task until all other work has been completed. A hidden immunity idol is up for grabs amongst the following questions. If you simplify or solve each question, you will find one of them will yield a value that will see you safely through the year ahead. (3) a) 13 (5 2 4) 5 7, a 9 a ( 2a 4) 5a 7 2a 2a 20 8a 4a a 4! b) x 2x 1 3 x x 24x 2x 8 x 2x x 2 c) Hopefully I ve got something for you head back to camp and enjoy your afternoon!

13 Answers Staple this answer sheet to the front of your lined paper. Name: Teacher: BG BO ED HU Task 5: m n m n 5n² 3 m n Task 7: Stage (s) Number of squares with a logo (x) 1 7 Number of blank squares (y) s Task 8: Stage p Number of squares

14 The more that students can get used to being presented with challenges, the more they get used to that, the more willing they will be to push past it and persevere and the more they will end up learning. - Anthea Roberts

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