Mathematics Grade 9 ANA 2011 Question Paper (English)

Downloaded from hlayiso.com LEARNER NUMBER ANNUAL NATIONAL ASSESSMENTS 2010 GRADE 9 MATHEMATICS - ENGLISH FORM B GENDER (TICK
) BOY GIRL SURNAME NAME(S) PROVINCE DATE OF BIRTH SCHOOL NAME EMIS NO. DISTRICT / REGION Instructions to learners: 1. Question 1 consists of 10 multiple choice questions. Learners must circle the letter of the correct answer (see example below). 2. Learners must provide answers to questions 2 to 8 in the spaces provided. 3. Approved scientific calculators (non-programmable and non graphical) may be used. 1 4. The test duration is 2 hours. 2 Example Circle the letter of the correct answer. Which number comes next in the pattern? 2; 4; 6; 8; _____ a. 9 b. 10 c. 12 d. 20 You have done it correctly if you have circled b as above. The test starts on the next page.

Downloaded from hlayiso.com Page 2 of 18 QUESTION 1 1.1 If 4( x + 3)(2x − 1) = 0 then x = 1 A. -3 or 2 1 B. 4 or 2 C. 0 or 3 D. 4 or -3 1.2 (x )(x ) = 4 2 3 (x ) −3 −2 A. x 3 B. x 4 C. x 8 D. x 16 1.3 In rectangle ABCD, DC =12 cm and diagonal BD=15 cm. What is the length of BC in cm? A B A. 3 B. 27 D C C. 369 D. 9 1.4 A circle has a diameter of 6 cm. What is the area in cm 2 of one quarter of the circle? A. 36π B. 9π 9 C. π 4 9 D. π 2 2

Downloaded from hlayiso.com Page 3 of 18 1.5 In the adjacent figure, AB = AC and AE = AD. Why is ∆ ABE ≡ ∆ ACD? A A. S S S B. 90º H S D E C. S < S D. < < S B C 1.6 If   - then the value of   3 4 A. -6 B. 6 C. -14 D. -8 1.7 The 3-D figure which has 5 faces, 5 vertices and 8 edges is a: A. cylinder B. triangular prism C. square-based pyramid D. triangular pyramid 1.8 In scientific notation 4 10   10  = A. 28 × 10 −20 B. 2,8 × 10 −18 C. 2,8 × 10 −20 D. 0,28 × 10 −18 3

Downloaded from hlayiso.com Page 4 of 18 1.9 Study this growing pattern. 1st 2nd 3rd How many dots will there be in the sixth dot array if this dot array is continued? A. 56 B. 36 C. 42 D. 30 1.10 Which angle in rectangle PQRS is the angle of elevation of P from R? P S Q R A. RQˆ S B. PQˆ R C. PRˆ Q D. SPˆ R [10] 4

Downloaded from hlayiso.com Page 5 of 18 QUESTION 2 2.1 Simplify: 2.1.1  2  1 3 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.1.2         _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.1.3       4 1  _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (5) 5

Downloaded from hlayiso.com Page 6 of 18 2.2 Multiply and simplify: 2.2.1 12" 8" 4 ! _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.2.2 " 2" 2" 4 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.3 Factorise fully: 2.3.1 2 # 4 # 10# _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (2) 2.3.2 $ # _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (2) 6

Downloaded from hlayiso.com Page 7 of 18 2.3.3 2 8 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.4 Use prime factors to determine the value of%108$ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (4) 2.5 Solve for x : 2.5.1 3 1 4  & 2 1 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 2.5.2  1 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (3) 7

Downloaded from hlayiso.com Page 8 of 18 2.5.3  2  1  2  4 3 12 _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (5) [39] QUESTION 3 3.1 Calculate the simple interest on R5 400 at 6% per annum for 4 years? _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (4) 8

Downloaded from hlayiso.com Page 9 of 18 3.2 Mark borrowed R8 000 from the bank at 5% per annum compound interest for 3 years. How much must he repay to the bank at the end of 3 years? _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (5) 3.3 The time taken by the different sets of pumps to empty a water tank is given in the table below. Number of pumps 20 10 5 Time in hours 2 4 8 3.3.1 Is this an example of direct or inverse proportion? _________________________________________________ (1) 3.3.2 Calculate how long it will take 16 pumps to empty the water tank. _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (2) 3.4 If 4,5 kg of sugar costs R36, what will 2,5 kg of sugar cost? _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (3) [15] 9

Downloaded from hlayiso.com Page 10 of 18 QUESTION 4 4.1 Write down the next two terms in the given sequence: 5; 9; 13; ... ; ... _______________________________________________________ _______________________________________________________ _______________________________________________________ (2) 4.2 Describe the pattern in QUESTION 4.1 in your own words. _______________________________________________________ _______________________________________________________ _______________________________________________________ (1) 4.3 Write down the general term of the given sequence in the form Tn =________. (2) 4.4 Which term in the sequence is equal to 101? _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (4) [9] 10

Downloaded from hlayiso.com Page 11 of 18 QUESTION 5 5.1 Use the graphs below to answer the questions that follow. a b c Which of the above graphs represents: 5.1.1 A decreasing, continuous, non-linear function? _________________________________________________ (1) 5.1.2 A discrete, increasing, linear function? _________________________________________________ (1) 11

Downloaded from hlayiso.com Page 12 of 18 5.2 Use the grid below. On the same system of axes draw and label the graphs defined by: #  2 , for  ' ( 2) 1) 0) 1* and #  2 3, for  ' + (7) Y 12 10 8 6 4 2 X -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 -2 -4 -6 -8 -10 -12 [9] 12

Downloaded from hlayiso.com Page 13 of 18 QUESTION 6 In QUESTION 6 give reasons for each of your statements. 6.1 In the given diagram AD = BC, AB = CD, AP , BC, AD , TC, AP - TC, AD = 24 cm, BP = 8 cm and AP = 12 cm. A T D 2 1 1 2 B P C 6.1.1 What kind of quadrilateral is ABCD? Give a reason for your answer. __________________________________________________ __________________________________________________ (2) 6.1.2 Calculate the area of quadrilateral APCD. __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (4) 6.1.3 State why is AP = TC? __________________________________________________ __________________________________________________ __________________________________________________ (1) 6.1.4 Prove that ∆ ABP ≡ ∆ CDT __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (4) 13

Downloaded from hlayiso.com Page 14 of 18 6.2 In the figure below, ABCD is a parallelogram. AC = BC and Ĉ1 = 40. . A B 1 2 1 2 D C Calculate the size of BÂD _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (9) 6.3 A B E C D 6.3.1 Which triangle is similar to ∆ ACD? _________________________________________________ _________________________________________________ (1) 14

Downloaded from hlayiso.com Page 15 of 18 6.3.2 If AE/AD = 3 / 8 and AB = 9cm, determine the length of BC. _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ _________________________________________________ (6) 6.4 The base of an given triangular prism is a right-angled triangle with AB = 5 m, AC = 12 m and the height of the prism = 20 m. D A B C 6.4.1 Calculate the volume of the prism. __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (3) 15

Downloaded from hlayiso.com Page 16 of 18 6.4.2 Calculate the surface area of the prism. __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ (8) [38] QUESTION 7 The following marks were obtained by a group of grade 9 learners in a Mathematics test out of 100. 38 52 68 81 72 31 45 55 74 49 52 47 64 58 84 7.1 Draw a stem-and-leaf plot to display the data. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (4) 16

Downloaded from hlayiso.com Page 17 of 18 7.2 From the data set determine each of the following: 7.2.1 The range. _________________________________________________ _________________________________________________ (2) 7.2.2 The mode. _________________________________________________ _________________________________________________ (1) 7.2.3 The median. _________________________________________________ _________________________________________________ (2) 7.2.4 The mean. _________________________________________________ _________________________________________________ (3) 7.3 How many learners obtained more than 55% for the test? _______________________________________________________ _______________________________________________________ (2) [14] 17

Downloaded from hlayiso.com Page 18 of 18 QUESTION 8 8. If the spinner below is rotated, determine the probability that the arrow will point to: 8 1 7 2 6 3 5 4 8.1 a number greater than 6. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (2) 8.2 a prime number. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (2) 8.3 a factor of 8. _______________________________________________________ _______________________________________________________ _______________________________________________________ _______________________________________________________ (2) [6] Total [140] 18