Mathematics Grade 9 November EC 2011 Question Paper (Eng)

Downloaded from hlayiso.com Province of the EASTERN CAPE EDUCATION SENIOR PHASE GRADE 9 NOVEMBER 2011 MATHEMATICS MARKS: 100 TIME: 2 hours This question paper consists of 14 pages, including annexures.

Downloaded from hlayiso.com 2 MATHEMATICS (NOVEMBER 2011) INSTRUCTIONS AND INFORMATION 1. Answer all the questions. 2. Write neatly and legibly. 3. Do not change the numbering of the questions. 4. Show all your calculations, correct your answer to TWO decimal places where necessary. 5. A non-programmable calculator may be used.

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 3 QUESTION 1 In QUESTION 1, there are multiple choice questions. Four possible answers are given for each question. Only one answer is correct. Select the best answer and use the answer sheet provided in ANNEXURE 1 to make a cross on the corresponding letter for the correct answer. Example: 1.11 √8 is ... A 24 B 2 C 2,7 D 512 The correct answer is 2 which is letter B. 1.11 A B C D 1.1 . = ... A 6x10 B 6x10 C 0,6x10 D 0,6x10 (1) 1.2 The equation for the line graph AB below is: Y A 3- B 2- 1- | | | | | | | | | | X -5 -4 -3 -2 -1 0 1 2 3 4 5 -1- -2- A x=3 B y=3 C x=y+3 D y=x+3 (1)

Downloaded from hlayiso.com 4 MATHEMATICS (NOVEMBER 2011) 1.3 The sequence 11; 14; 17; 20; ..., 101 consist of ... A 30 terms B 31 terms C 33 terms D 34 terms (1) 1.4 The expression (x + 3)( x – 2) + 2x2 is ... A 3x2 + x – 6 B 3x2 – x – 6 C 3x2 + 2x – 6 D 3x2 + 5x – 6 (1) 1.5 Uncle Zondi bought 4 boxes of pencils for his niece. He placed them in a pencil case so that they do not get lost. The pencil case had 7 pencils in it already. The total number of pencils in the case is 27. How many pencils are in each box? A 38 B 35 C 5 D 10 (1) 1.6 In the regular octagon below MN bisects  QNP. The size of each angle of a regular octagon is 135°. Therefore  MNR is … R M P N Q A 60° B 67,5° C 45° D 75° (1)

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 5 1.7 50 cm 15 cm 10 cm The area of the figure given above is … A 528 cm² B 150 cm² C 825 cm² D 750 cm² (1) 1.8 Zelha has prepared her mother’s birthday-present tied with a ribbon as shown. The bow knots and ends used 47 cm of ribbon. Bow knot ends 10 cm 20 cm 15 cm The total length of the ribbon used in metres is … A 30,47 m. B 0,45 m. C 0,92 m. D 1,57 m. (1) 1.9 Tommy, Andile and Temba dig a hole in 6 days. If they are assisted by 6 friends, how long will they take, working at the same rate, to dig a hole of the same size? A 9 days B 2 days C 4 days D 18 days (1)

Downloaded from hlayiso.com 6 MATHEMATICS (NOVEMBER 2011) 1.10 Two coins are tossed. The probability of obtaining the same outcome twice is … 2 A 3 3 B 4 1 C 4 1 D 2 (1) [10] QUESTION 2 2.1 Mr. Ceolo needs R12 000 to renovate his house. The financial institution has agreed to offer him a loan at one of the following rates: 8,8% per annum compound interest, or 9% per annum simple interest 2.1.1 If Mr. Ceolo wants to pay over 2 years. Show by calculation which offer is a better option. Compound Interest or Simple Interest. (4) 2.1.2 How many US dollars should his friend in the USA send him for the renovations? HINT: exchange rate $ 1 = R 7,12 (1) 2.2 Water is being pumped into a tank at a rate of 150 litres per minute. How long will it take to fill a tank with a volume of 81 000 litres? Give your answer in hours. (2) [7] QUESTION 3 3.1 Simplify: 3.1.1 4 10 (3) 3.1.2 4 3 3 2 7 1 2 (4) 3.2 Factorise: 3.2.1 36 16 4 (2) 3.2.2 25 49 (2) 3.3 Evaluate 5 3 using factorisation. (Do not use a calculator.) (2)

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 7 3.4 Solve for : 3.4.1 1 5 (2) 125 3.4.2 3 2 4 4 8 16 (4) 3.5 Consider the table below and answer the questions that follow: 1 2 3 4 5 17 B N 0 3 8 15 24 A 528 ? 3.5.1 What is the general rule for the pattern? (2) 3.5.2 Find the value of A, i.e. when = 17. (1) 3.5.3 Find the value of B, i.e. when = 528. (2) 3.6 3.6.1 Use ANNEXURE 2 to draw the graphs of 2 + 3 = 6 and = + 2 for  R on the same system of axes. Label the graphs. (6) 3.6.2 Determine the point of intersection of the two graphs. (1) [31] QUESTION 4 4.1 P 45° 80° 10 cm 20 cm 9 cm 80° S 45° R p Q In the above figure; ΔPQR||| ΔSPR. 4.1.1 Work out the length of p. (2) 4.1.2 Using the answer from QUESTION 4.1.1 and give reasons for  PQR|||  SPR (1)

Downloaded from hlayiso.com 8 MATHEMATICS (NOVEMBER 2011) 4.2 In the diagram below LO = MQ = 6 cm; OM = 3 cm; O P̂ Q = 30°; PQ = LN; PO  LQ and MN  LQ. L P O M N Q 4.2.1 Show with reasons that LM = QO. (2) 4.2.2 Prove that ΔPOQ ΔNML. (3) 4.3 Shown below is  XYZ with X(1;2) , Y(0;4) and Z(3;2). 5_ 4 _ Y(0;4) 3_ 2_ X(1;2) Z(3;2) 1_ | | | | | | | | X 1 2 3 4 5 6 7 8 4.3.1 If ΔXYZ is enlarged by a factor of 2 (i.e. doubled), draw the image of ΔXYZ on ANNEXURE 3. (2) 4.3.2 On the same Cartesian plane in ANNEXURE 3, reflect the image of ΔXYZ (the enlarged triangle) in the -axis. (2) 4.3.3 Write down the co-ordinates of the reflected triangle. (2)

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 9 4.4 The figure below shows that LK // MN; LKˆ M = 3 ; KMˆ L = 2 and NMˆ Q = . K 3 N 2 P L M Q 4.4.1 Calculate with reasons the value of . (3) 4.4.2 What is the size of LKˆ M ? (1) 4.4.3 Which type of triangle is ΔMKL? (1) [19] QUESTION 5 5.1 The perimeter of the rectangle HIJK is 48 m. The length is equal to one third (i.e. ) the size of the perimeter. H K 1 b b 2 3 l 4 I l J 5.1.1 Calculate the length and the breadth of rectangle HIJK. (2) 5.1.2 3 1 If the length of the unshaded rectangle is of IJ and the breadth 4 2 of HI, work out the perimeter of the unshaded portion. (2)

Downloaded from hlayiso.com 10 MATHEMATICS (NOVEMBER 2011) 5.2 In the given cone below, the vertical height VO is 12 cm and the radius of the base circle OA is 5 cm. Determine the size of VA (slant height). (2) V 12 cm O A 5 cm [6] QUESTION 6 6.1 The pie chart below shows how R94 000 was allocated to 4 schools in a school district nutrition programme. School B School A (22%) (44%) º School C (12%) School D (22%) 6.1.1 How much did school A receive? (1) 6.1.2 Find the value of º. (2) 6.1.3 School A decided to donate an amount of R 5 300 to School C. How much will School C have now? (2)

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 11 6.2 The stem and leaf diagram below represents the ages of 50 parents who attended a parents’ meeting in Active Children J.S.S. Stem Leaf 7 1 2 3 6 1 2 2 3 5 9 5 1 2 3 4 5 6 7 7 9 9 4 1 1 2 2 3 4 4 5 6 6 9 3 2 2 3 4 5 6 7 8 8 9 2 1 2 3 4 8 9 1 7 8 8 9 6.2.1 Determine the range of the data. (1) 6.2.2 What is the median? (1) 6.2.3 Draw a frequency table to represent the data in intervals of 0 – 10; 11 – 20; 21 – 30;... (3) 6.3 The body mass in kilograms of the first 5 parents to arrive in the parents meeting are 51; 56; 54; 59 and 53. If the sixth parent arrive, their average body mass is 56 kg. Calculate the body mass of the sixth parent. (3) 6.4 The table below shows the percentage of marks obtained by Aliva in 6 Mathematics tests in the second term. Test Number 1 2 3 4 5 6 Marks as a Percentage 13 17 20 22 16 4 6.4.1 Draw a broken line graph to show Aliva’s performance. (4) 6.4.2 Determine the average percentage of the test marks. (6) 6.5 A grade R class has bags where it keeps counters. One bag is carrying two green, one white and one black counter. One counter is randomly taken out, its colour noted and then put back into the bag. The bag is shaken and then a second counter is taken out at random. Draw a tree diagram and use it to list all possible outcomes. (4) 6.6 What is the probability of randomly selecting … 6.6.1 a white counter twice? (1) 6.6.2 a white and black counter? (1) 6.6.3 at least one black counter? (2) [27] TOTAL: 100

Downloaded from hlayiso.com 12 MATHEMATICS (NOVEMBER 2011) ANNEXURE 1 SURNAME NAME DATE ANSWER SHEET FOR MULTIPLE CHOICE QUESTIONS QUESTION 1 Example: 1.11 √8 is ... A 24 B 2 C 2,7 D 512 The correct answer is 2 which is letter B. 1.11 A B C D 1.1 A B C D 1.2 A B C D 1.3 A B C D 1.4 A B C D 1.5 A B C D 1.6 A B C D 1.7 A B C D 1.8 A B C D 1.9 A B C D 1.10 A B C D

Downloaded from hlayiso.com (NOVEMBER 2011) MATHEMATICS 13 ANNEXURE 2 SURNAME NAME DATE QUESTION 3.6.1 y 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 0 x -6 -5 -4 -3 -2 -1 -1 -2 -3

Downloaded from hlayiso.com 14 MATHEMATICS (NOVEMBER 2011) ANNEXURE 3 SURNAME NAME DATE QUESTION 4.3.2 y 10 9 8 7 6 5 4 Y(0;4) 3 2 X(1;2) Z(3;2) 1 1 2 3 4 5 6 7 0 x -6 -5 -4 -3 -2 -1 -1 -2 -3