Mathematics Grade 9 November EC 2017 Question Paper (Eng)

Downloaded from hlayiso.com SENIOR PHASE GRADE 9 NOVEMBER 2017 MATHEMATICS MARKS: 140 TIME: 2𝟏⁄𝟐 HOURS *9MATHS* This question paper consists of 17 pages including 2 annexures

2 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) INSTRUCTIONS AND INFORMATION 1. Read the instructions for each question carefully before answering the questions. 2. Answer ALL the questions. 1. 3. Number your answers exactly as questions are numbered. 2. 4. You may use an approved scientific calculator (non-programmable and non-graphical). 3. 5. Clearly show ALL the calculations, diagrams and graphs you have used in determining your 4. answers. 5. 6. Diagrams are NOT necessarily drawn to scale. 7. Write neatly and legibly. Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 3 QUESTION 1 1. Various options are given as possible answers to the following questions. Choose the answer and write only the letter (A-D) next to the question number Example: If the correct answer for 1.1 is A, write your answer as 1.1 A. 1.1 Which ONE of the following numbers is rational?  A 2, 3 B √−16 C 𝜋 D 3 53 (1) 1.2 The gradient of the straight line drawn below is: A -2 B 2 C -1 D 1 (1) 1.3 The general rule (Tn) for the pattern 3 ; 7 ; 11 ; 15 is: A Tn  4n  1 B Tn  4n  1 C Tn  4n  1 D Tn  4n  1 (1) Copyright reserved Please turn over

4 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) 1.4 12m2 n  6mn2 When is simplified, the answer is: 3mn A 4m  2n B 2m2 n2 C 2m  n 3 D 2m n (1) 1.5 2x  4 x If   1 , then the value of x is: 3 4 A 5 8 B 4 5 C 5  8 D 4  5 (1) 1.6 The following table shows the number of days a certain number of men will take to complete a task. Number of men 1 5 10 15 4 Time taken in hours 20 4 x 3 The value of x is: A 200 B 2 C 4 5 D 8 (1) Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 5 1.7 Pairs of socks are neatly packed in a drawer of a wardrobe. There are 4 pairs of black socks, 2 pairs of blue socks, 3 pairs of yellow socks and 5 pairs of white socks. One pair of socks is taken from the drawer without looking. What is the probability of not taking a pair of white socks? A 5 B 5 14 C 9 14 D 5 9 (1) 1.8 In ABC the size of C is: A 40° B 180° C 60° D 100° (1) 7 1.9 The value (in scientific notation) of 3,7 10  2 10 is: 4 A 0,74 x 103 B 7,4 x 10-3 C 7,4 x 103 D 74 x 10-3 (1) Copyright reserved Please turn over

6 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) 1.10 The surface area of an open top cylinder, with a height of 97 cm and the circumference of its base measuring 85,9 cm, if it is expressed to 2 decimal places, it will be: A 8 919,49 cm2 B 8 919,49 cm3 C 9 506,67 cm2 (1) D 9 506,67 cm3 [10] QUESTION 2 2.1 Write 0,000 014 6 in scientific notation. (1) 2.2 Simplify: 2.2.1 0, 06 y 4  0,1y 4 (2) 2.2.2 3 x6 (4 x 2 ) 0 (2) 2.2.3 (3x 4 y 1 )2 x 2  x 1 y 2 (3) 2.2.4 3( x  3)( x  3)  ( x 1)2 (4) 2.2.5 1 2 1 1 3 x 2 2 x  4 x 4 3 6 2 (4) 2.3 Factorise completely. 2.3.1 2 x 2  6 x  36 (3) 2.3.2 9 x(5a  b)  2(b  5a) (3) 2.4 Solve for x: 2.4.1  2 x  3 2 x  3  0 (2) 2.4.2 3x  2 x  2  7 3 (3) 2.4.3 27.3x  1 (3) [30] Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 7 QUESTION 3 3.1 Study the geometric pattern below and answer the questions that follow: Figure 1 Figure 2 Figure 3 3.1.1 Refer to the table below and write down the value of p and q Figure 1 2 3 4 Number of Triangles 4 8 p q (1) 3.1.2 Determine the general rule ( 𝑇𝑛 ) of the pattern. (1) 3.1.3 Use the rule obtained in question 3.1.2 to determine which figure will have 120 triangles. (3) 3.2 A straight line graph is defined by y  2 x  4 3.2.1 Determine the X - intercept of the graph. (2) 3.2.2 Determine the Y - intercept of the graph. (1) 3.2.3 Draw the graph showing all your intercepts with the axes. Use ANNEXURE 1. (3) 3.3 On the same system of axes (use ANNEXURE 1) to draw the graph of x  4. (2) 3.4 Find the value of y when the graphs of y  2 x  4 and x  4 intersect. (1) 3.5 Read the flow diagram below and answer the questions that follow: Input values x Output values y 3.5.1 What is the input value in A? (2) 3.5.2 What is the output value in B? (2) Copyright reserved Please turn over

8 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) 3.6 Use the table below to answer the questions that follow: x 1 0 1 2 ….. m y 5 3 1 1 ….. 21 3.6.1 Find the rule in the form y  ... . (2) 3.6.2 Determine the value of m. (2) [22] QUESTION 4 4.1 Craig invests 𝑅15 000 for 3 years at 16% per annum compound interest. Calculate the interest he receives after 3 years. (3) 4.2 The combined ages of a father and his son are 36. In seven years’ time the father will be four times as old as his son. Find their current ages. (5) 4.3 A certain distance is covered in 3 hours at an average speed of 120𝑘𝑚/ℎ. How long will it take to cover the same distance at an average speed of 90𝑘𝑚/ℎ? (4) [12] Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 9 QUESTION 5 5.1 In the diagram ABE  65 . EB∥CD and ABE  EBC. Find with reasons, the size of: 5.1.1 ADC (2) 5.1.2 BCD (2) 5.2 In the diagram below, QTR  140 , QSR  2 x  35 and TRS  3x  10 . 5.2.1 Calculate the value of x. Give reasons for your answer. (4) 5.2.2 Calculate the actual size of QSR. (2) Copyright reserved Please turn over

10 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) In the figure below, O is the centre of the circle. OPS  38 , POS  104 and PRQ  55 . 5.3 5.3.1 Calculate the size of QPR . Give a reason for your answer. (2) 5.3.2 Calculate the size of PSO . Give a reason for your answer. (2) [14] QUESTION 6 6.1 In the figure, AD  AB and CD  BE. Prove that ABC  ADE. . (4) Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 11 6.2 KN  5 cm, MN  2 cm, KM  4 cm, LM  8 cm and KL  10 cm. 6.2.1 Prove that MNK ||| MKL (4) 6.2.2 Calculate the actual size of LKM if it is given that MNP is a straight line. Give a reason for your answer. (3) [11] Copyright reserved Please turn over

12 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) QUESTION 7 7.1 A triangular prism is shown in the figure below. The base is a right-angled triangle with DF= 8 cm, DE= 10 cm FE= 6 cm, and the height 15 cm. 7.1.1 Calculate the surface area of the triangular prism. (2) 7.1.2 Calculate the volume of the triangular prism. (3) Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 13 7.2 A diagram of a kite, ABCD with AB = 5 cm, BE = 4cm, and DE = 10 cm, is given below. 7.2.1 Calculate the length of AE. (2) 7.2.2 Calculate, with a reason, the length of the diagonal AC. (2) 7.2.3 3 Find the area of quadrilateral PQRD which is of the area of kite ABCD. 2 (3) 7.3 A cylinder has a height of 10cm and the circumference of the base is 44cm. 7.3.1 Calculate, correct to the nearest whole number, the radius of the base. (3) 7.3.2 Hence, calculate(correct to TWO decimal digits) the volume of the cylinder. (3) [18] Copyright reserved Please turn over

14 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) QUESTION 8 8.1 Study the diagram given below and answer the questions based on it. 8.1.1 State the rule of the transformation indicated above in the form  x; y   ..... ;.. (2) 8.1.2 Enlarge ABC by a scale factor of 2 and give the coordinates of the vertices of A/ l B / l C / l . (3) 8.2 P( 2 ; 2), Q( 2; 2 ) , and R( 3; 2 ) are the vertices of PQR . 8.2.1 Plot the pointsP(−2 ; 2) , Q(−3 ; −2) , and R(2 ; 0) to form PQR. (2) 8.2.2 Reflect PQR in the line y  x to form P Q R . / / / (3) [10] Copyright reserved Please turn over

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 15 QUESTION 9 9.1 There is a blue pencil, a red pencil, two green rulers and a white ruler on a desk. A pencil and a ruler is taken at random. 9.1.1 Draw a tree diagram to show all possible outcomes. (2) 9.1.2 What is the probability that a red pencil and a green ruler are taken? (1) 9.1.3 What is the probability that a white pencil and a red ruler are taken? (1) 9.2 The table shows the marks(in percentage) obtained by 12 learners in a Maths test and a Natural Science test. Maths 15 40 50 62 65 68 70 75 80 85 88 90 Natural Science 90 45 52 70 65 70 65 80 75 90 80 40 9.2.1 Represent the data in a scatter plot. Use ANNEXURE 2. (3) 9.2.2 Identify ONE possible outlier. (1) 9.2.3 Compare the relationship between performance in Mathematics and Natural Science for the learners (1) 9.3 The following data represents the number of people who visited a farm stall during December over a 10 day period. 18 20 22 23 x 30 35 40 42 46 9.3.1 If the median of the data is 27, determine the value of x . (2) 9.3.2 Determine the mean of the data (2) [13] GRAND TOTAL: 140 Copyright reserved Please turn over

Downloaded from hlayiso.com

16 Downloaded from hlayiso.com MATHEMATICS (EC/NOVEMBER 2017) ANNEXURE 1 QUESTION 3.2.3 NAME: _____________________________________________________ SURNAME: _____________________________________________________ Copyright reserved Please turn over

Downloaded from hlayiso.com

(EC/NOVEMBER 2017) Downloaded from hlayiso.com MATHEMATICS 17 ANNEXURE 2 QUESTION 9.2.1 NAME: _____________________________________________________ SURNAME: _____________________________________________________ Test marks of learners 100 90 80 70 Natural Science mark 60 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Mathematics Mark Copyright reserved Please turn over