South Peninsula High School Mathematics Department November 2017 Grade 9 Mathematics Duration: 1 Hour 30 Mins Paper 1 Moderator/s: JAB, ISN, DUG, FOG, MEM EDA November 2017 Marks: 75 Examiner: M Prins Instructions: 1. Write your name and grade (e.g. 9E) as well as the name of your SUBJECT TEACHER at the top of your answer script. 2. This paper consists of 7 Questions. Answer ALL the questions. 3. Calculators may NOT be used. 4. Number your questions correctly according to the numbering system used in this question paper. 5. It is in your own interest to write LEGIBLY and to present your work neatly. 6. No TIPPEX (Correction fluid) to be used. Question 1: 1.1 Simplify the following: 1.1.1 6a 2 a 7 b 2a 2x 8 1.1.2 x2 1.2 (3) 2 3 b 3 (3) Expand and simplify: 1.2.1 4 x 14 x 1 (2) 1.2.2 5 x 22x 1 (3) 1.2.3 5 x 32 (3) [14] 1 South Peninsula High School Copyright 2017 © South Peninsula High School Mathematics Department November 2017 Question 2 Factorise the following 2.1 xy 2xy 2 6 x 3 y 3 (2) 2.2 4m 2 x 5 5 x (4) 2.3 x 2 7 x 10 (2) 2.4 x 4 16x 2 (2) 2.5 a 4 8a 2b 2 16b 4 (3) [13] Question 3 Solve for 𝑥 3.1 8x 5 2x 5 (3) 3.2 x 6 x 4 1 2 6 (4) 3.3 x 2 6 x 5 (4) 3.4 4 x 128 (3) [14] Question 4 4.1 Consider the following sequence: 4; 11; 18; 25; … 4.1.1 Write down the next two terms in the pattern. (2) 4.1.2 Determine an expression for the general term Tn (2) 2 South Peninsula High School Copyright 2017 © South Peninsula High School Mathematics Department November 2017 th 4.1.3 Determine the 11 term? 4.2 (2) Consider the following sequence: 0; 1; 1; 2; 3; 5; … Write down the values to the 8th term. (2) [8] Question 5 5.1 Kristy drives at 120 km/h from Johannesburg to Cape Town which is about 1398 km apart. How long did it take her to reach Cape Town? 5.2 (3) When working at the same rate, 6 builders take 80 days to complete a house. How many builders must be employed to build the same house in just 16 days? 5.3 (4) Jesse invests R2000 which she got as a gift from her grandmother for her 18th birthday. The bank gives her an interest rate of 10% p.a. and she withdraws it on her 21st Birthday. Calculate the total amount she will withdraw? 5.4 (3) Calculate how much interest you will owe a bank after 2 years if you borrow R9 000 from the bank at 20% per annum compound interest. (3) [13] 3 South Peninsula High School Copyright 2017 © South Peninsula High School Mathematics Department November 2017 Question 6 6.1 The graphs of line AF, PF and AP are shown in the accompanying sketch y A P(x;y) 4 3 2 1 x -7 -6 -5 -4 -3 -2 0 -1 1 2 3 4 5 6 7 -1 -2 F -3 -4 6.1 6.2 6.3 Write down the: 6.1.1 co-ordinates of point P(x;y) (1) 6.1.2 equation of line AP (1) Determine the equation of: 6.2.1 line AF (2) 6.2.2 line PF (2) Write down the gradient of a line parallel to y 5 x 10 . 2 (1) [7] 4 South Peninsula High School Copyright 2017 © South Peninsula High School Mathematics Department November 2017 Question 7 Joshua sells ice-cream from home. They come in two flavours, plain and chocolate. The toppings may either be sprinkles or a flake. 7.1 Complete the tree diagram on the diagram sheet provided to show the possible ice-cream options. 7.2 (3) What is the probability of randomly choosing a plain ice-cream with a flake topping? 7.3 (1) What is the probability of randomly choosing any ice-cream with a sprinkle topping? (2) [6] 5 South Peninsula High School Copyright 2017 © South Peninsula High School Mathematics Department November 2017 DIAGRAM SHEET Name:…………………………….. Grade:……….. 7.1 …… …… …… …… …… …… …… …… …… …… 6 South Peninsula High School Copyright 2017 ©