Mathematics Grade 9 Gauteng November 2014 Question Paper

Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION GRADE 9 NOVEMBER COMMON EXAMINATION 2014 SUBJECT : MATHEMATICS TASK : COMMON EXAMINATION TIME : 2 HOURS MARKS : 120 This assessment task consists of 13 pages

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 INSTRUCTIONS 1. This Question Paper has two sections, Section A and Section B. 2. SECTION A has ten multiple questions. Answer this section on the answer sheet provided. Four possible answers are given. Circle the letter (A - D) of next to the correct answer. 3. SECTION B has 6 Questions. Answer ALL Questions. 4. A non-programmable calculator may be used unless otherwise stated. 5. Show ALL your work. (SECTION B) 6. Answer sheets for Questions 1; 6.1; 9.1, and 9.2.1 are provided. (See the Annexure A, B and C). These sheets must be handed in with your answer book. Page 2 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 SECTION A This section has 10 multiple choice questions. Four possible answers are given. Circle the letter (A - D) next to the correct answer. Answer this section on the answer sheet provided. QUESTION 1 1.1 Three sisters shared R500 and divided it into R250. R150 and R100. In which the ratio is divided? A. 3: 2: 1 B. 5: 3: 2 C. 5:4:3 1 (2) D. 2 :3 :1 1.2 Which one of the following is NOT a prime number? A. 23 B. 11 C. 2 D. 1 (2) 1.3 Arrange the following numbers in ascending order: -135; 45; -139; 77; 0; -220 A. 77; 45; 0; -135; -139; -220 B. -135; -139; -220; 0; 77; 45 C. -220; -139; -135; 0; 45; 77 D. 0; 45; 77; -135; -139; -220 (2) 1.4 The LCM of 8; 12 and 20 is: A. 120 B. 80 C. 2 D. 4 (2) 1.5 The value of the constant term in 2𝑥³ - 5𝑥² + 3𝑥 – 9 is: A. -2 B. 9 C. -9 D. 5 (2) Page 3 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 1.6 20 learners wrote a math test and their results in percentage were as follows: 30; 22; 45; 44; 29; 59; 46; 61; 29; 56; 62; 35; 53; 35; 51; 26; 68; 86; 72; 64 The range is: A. 64 B. 108 C. 57 D. 34 (2) 1.7 The factors of 𝑝4 − 1 are: A. (𝑝2 − 1)(𝑝2 − 1) B. (𝑝 − 1)(𝑝 + 1) C. (𝑝 − 1)(𝑝 + 1)(𝑝2 − 1) D. (𝑝 − 1)(𝑝 + 1)(𝑝2 + 1) (2) 1 −1 1.8 Simplify: 4−2 + ( ) 4 1 A. 4 16 B. 8 1 C. 2 4 D. 1 (2) 𝑥 𝑥 1.9 Solve for x: − 5=3 4 60 A 9 B. 20 C. 60 60 D. 20 (2) 1.10 Simplify: √𝑥 3 A 𝑥 𝑥3 B 2 (2) Page 4 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 C Undefined number D 𝑥 √𝑥 [20] SECTION B QUESTION 2 2.1 Simplify the following: 5𝑚2 𝑛𝑝 × 𝑚𝑛2 𝑝2 − 3𝑚3 𝑛3 𝑝3 × (4𝑚𝑛𝑝)0 (4) 2.2 Calculate the following without a calculator: 2.2.1  1 2  2   0,5 2  2 (3) 0,08 (3) 2.2.2  64 0,64 2.3 If 6 gardeners can mow the grass of a soccer field in 2 hours, how many gardeners can mow the same soccer field in 3 hours? (2) 2.4 r i= A = P (1 + i.n) A = P (1 + i ) n 100 Miss Lee needs to draw up a budget of her monthly expenses. She earns R8 900 per month. Her bills in one month are: Rent: R2 100, Electricity R300, Car payments R 1 450, Insurance R370, Petrol R600 Clothing account repayment R655 and Groceries R1 350. 2.4.1 What are her total expenses for one month? (1) 2.4.2 How much money does she have left after paying all her expenses? (1) 2.4.3 She borrows money from the bank to fix her car. Calculate the simple interest on a R5 000 loan for 3 years at 8Type equation here.,5% interest. (3) 2.4.4 Her grandparents gives her R15 000 for her 21st birthday. Calculate the compound interest earned over 2years at 12% p.a. interest. (4) [21] Page 5 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 QUESTION 3 3.1 Simplify the following expression 3.1.1 Add:−4𝑥 + 6 + 11𝑥 − 5 (2) 3.1.2 Multiply: 3(𝑥 − 1) − 4(𝑥 − 2) (3) 3.1.3 Calculate the value of 2𝑥 2 − 4 if 𝑥 = 3 (2) 3.2 Simplify the following: 3.2.1 (5𝑥)3 𝑦 × (2𝑥𝑦 2 )2 (3) 15𝑥 5 𝑦 2 2𝑥 + 4𝑦 3.2.2 (2) 𝑥 + 2𝑦 3.3 Factorise fully: 3.3.1 𝑥² − 𝑥 − 6 (2) 3.3.2 18𝑥 2 − 200 (2) [16] QUESTION 4 4.1 Solve the following equations: 4.1.1 3(𝑥 + 1) = 8𝑥 − 2 (2) 𝑥 + 7 3𝑥 − 1 4.1.2 + =0 (3) 4 3 4.2 Solve for x and y: 𝑥 + 3𝑦 = 6 … . . (1) (4) −𝑥 + 8𝑦 = 5 … … . (2) [9] Page 6 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 QUESTION 5 Pattern 1 Pattern 2 Pattern 3 5.1 Copy the table and complete the table by writing down a pattern representing the number of sticks that makes each pattern: Pattern 1 2 3 4 5 6 Number of sticks (3) 5.2 Describe the pattern in your own words. (1) 5.3 Write down the general term of the given sequence in the form: Tn= _________________ (2) 5.4 Without drawing the figures determine the number of sticks needed to build the (2) 17th figure [8] QUESTION 6 6.1 On the grid (ANNEXURE B) plot the following two points and then join them. 6.1.1 (-3 ; 4) (1) 6.1.2 (2 ; -1) (1) 6.2 Determine the gradient of the line (2) 6.3 Determine the equation of the line in the form𝑦 = 𝑚𝑥 + 𝑐 (2) [6] Page 7 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 QUESTION 7 Prove with reasons that ∆ FGH is congruent to ∆ GHJ (4) 7.1 B D A C 7.2 Prove with reasons that ∆ ABE is simillar to ∆ DCE (4) A B 1 2 E C D [8] QUESTION 8 Study the following diagram and answer the questions that follows: A E 𝑧 58° 3𝑥 𝑦 𝑥 D B C AE ⃦DC 8.1 Determine , with reasons without using a protractor, the size of: 8.1.1 𝑥 (3) Page 8 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 8.1.2 𝑦 (2) 8.1.3 z (2) 8.2 Calculate the area of a rectangular carpet if the width is 8m and the diagonal measures 10m. (3) 8.3 Given the diagram below, answer the following questions: 8.3.1 Identify the figure represented above. (1) 8.3.2 Calculate the surface area of the above figure.. (3) [14] QUESTION 9 Do this question on ANNEXURE C 9.1 ∆ABC with A(3;0), B(2;4) and C(0;2) is enlarge using the rule (𝑥; 𝑦) → (2𝑥; 2𝑦). The resulting image is A1B1C1 (2) Draw ∆ABC and its image on the given grid. 9.2 ∆ABC word gereflekteer om die y-as. Die refleksie is A11B11C11 . 9.2.1 Draw the image on the given grid. A11B11C11 (3) 9.2.2 What is the distance between A and A11 ? (1) [6] Page 9 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 QUESTION 10 10.1 During the two days before Christmas, a clothing store sold a number of women’s dresses in the following sizes. 30 18 26 42 40 20 24 34 26 42 36 32 40 32 18 38 26 30 10.1.1 Calculate the mean of the data. (3) 10.1.2 What is the mode of the data. (1) 10.1.3 Determine the median of the data. (1) 10.1.4 What is the range of the data. (1) 10.2 A bag contains three coloured discs: green, pink and brown. The tree- diagram shows the possible outcomes when a disc is pulled out of the bag green green pink brown green Disc pink pink brown green brown pink brown 10.2.1 Write down all the possible outcomes. (2) 10.2.2 Write down the total number of outcomes. (1) 10.2.3 Write down the probability of pulling out a brown and a brown (1) 10.2.4 Write down the probability that the first disc is a pink and the second disc is a green. (1) 10.2.5 Write down the probability of pulling out a purple disc (1) [12] TOTAAL: 120 Page 10 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 ANNEXURE A: NAME:---------------------------------------------------------------- GRADE 9----------- MATHEMATICS: 2014 NOVEMBER EXAMINATION GRADE 9 SECTION A QUESTION 1 Answer sheet for Multiple Choice 1 A B C D 2 A B C D 3 A B C D 4 A B C D 5 A B C D 6 A B C D 7 A B C D 8 A B C D 9 A B C D 10 A B C D [10] Page 11 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 ANNEXURE B: NAME:---------------------------------------------------------------- GRADE 9----------- QUESTION 6.1 y 5 4 3 2 1 -4 -3 -2 -1 0 1 2 3 4 x -1 -2 -3 -4 -5 Page 12 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 ANNEXURE C: NAME:---------------------------------------------------------------- GRADE 9----------- QUESTION 9.1 and 9.2.1 y 12 11 10 9 8 7 6 5 4 3 2 1 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 Page 13 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 GAUTENG DEPARTMENT OF EDUCATION GRADE 9 NOVEMBER COMMON EXAMINATION 2014 NAME AND SURNAME:_______________________________________________ NAME OF THE SCHOOL:_________________________________________________ Question Topic Max Time Learner’s Moderated Marks Mark Mark TOTAL Page 14 Please turn over

Downloaded from hlayiso.com MATHEMATICS GRADE 9 NOVEMBER 2014 Page 15 Please turn over