Mathematics Grade 9 ANA 2014 Question Paper (English)

Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA MARKS ANNUAL NATIONAL ASSESSMENT 2014 GRADE 9 MATHEMATICS TEST MARKS: 140 TIME: 2+ hours PROVINCE DISTRICT SCHOOL NAME EMIS NUMBER (9 digits) CLASS (e.g. 9A) SURNAME NAME GENDER (Vv) BOY GIRL DATE OF BIRTH This test consists of 21 pages, excluding the cover page.

Downloaded from hlayiso.com Instructions to the learner Noa PP w . Read all the instructions carefully. Question 1 consists of 10 multiple-choice questions. You must circle the letter of the correct answer. Answer Questions 2 - 12 in the spaces provided. All working must be shown. Give a reason for each of your statements in Question 9 and Question 10. The test is out of 140 marks. The test duration is 22 hours. 8. The teacher will lead you through the practice question before you start the test. 9. Approved scientific calculators (non-programmable and non-graphical) may be used except in Question 2.2 and Question 12. Practice question Circle the letter of the correct answer. 1. The next number in the sequence 3; 6; 11; 18; ... is A 25 B 24 Cc 26 D 27 You have done it correctly if you circled ©. The test starts on the next page. Grade 9 Mathematics Test 1

Downloaded from hlayiso.com QUESTION 1 1.1 Vi6x!é =... A 8x8 B 8x4 Cc 4x4 D 4x8 1.2 The LCM of 5a? and 60a? is ... A 60a° B 30a° Cc 60a? D 300a® 1.3 The product of a number and 6 decreased by 4 is equal to 20. Which of the following equations matches the statement? A 6x+4=20 B 6x —4= 20 Cc 6(x +4) = 20 D 6— 4x =20 Grade 9 Mathematics Test 2

Downloaded from hlayiso.com 1.4 The value of —x? — 2(2x — 1) when x = —2is ... A 6 B 1 C —6 D -1 1.5 What is the value of @? ? A —6 9 5 B = 6 C 8 27 D 27 8 1.6 (a+b)y?= A at+b B 2 Cc 1 D 0 1.7 What is the value of x if 3* = =? A -3 B 3 Cc —2 D 2 Grade 9 Mathematics Test 3

Downloaded from hlayiso.com 1.8 *_4= y A y7* x B y7* y Cc x-y D x7y y 1.9 If 3 is a root of the equation x? + x+t=0 the value of tis... A 12 B —12 Cc a 12 D a 12 1.10 If T is a point on the line defined by y = x, the co-ordinates of T are ... A (5; -5) B (5; 0) c (-5; 5) D (-5; -5) [10] Grade 9 Mathematics Test 4

Downloaded from hlayiso.com QUESTION 2 2.1 Write 0,000 000 207 mm’? in scientific notation. 2.2 Calculate without using a calculator. Show in each case all the calculation steps. 2.2.1 73-3 2.2.2 Between which two consecutive integers does ¥110 lie? 2.2.3 3x5? 57 2.3 Calculate leaving the answer in decimal form. 1,03 x 10°? + 3,8 x 10% Grade 9 Mathematics Test 5 (1) (2) (2) (2) (2) [9]

Downloaded from hlayiso.com QUESTION 3 Simplify each of the following expressions. The denominators in the fractions are not equal to zero. 3.1 2(x+2)?—(2x-1)(x +2) 3.2 15x*y3+9x7y3 8x73 (2) 3.3 x? — 4x x?-—2x-8 (3) Grade 9 Mathematics Test 6

Downloaded from hlayiso.com 3.4 x? 2x 7x? 2 3 6 (3) 3.5 6x? 3y3 7xy ra (2) [14] QUESTION 4 Factorise fully: 4.1 3x*y—9xy? + 12x3y3 (2) 42 2(x+y)-t(x+y) (2) 4.3 4x?-y? (2) 44 x?-11x+18 (2) [8] Grade 9 Mathematics Test 7

Downloaded from hlayiso.com QUESTION 5 Solve for x: 5.1 (x«-—2)?4+3x-2=(x+3)* (4) 5.2 x?—5x—-6=0 x+2 x-3 5.3 _ =0 [9] Grade 9 Mathematics Test 8

Downloaded from hlayiso.com QUESTION 6 6.1 Complete the table below: Position in 1 2 3 4 5 pattern (2) Term 1 8 27 6.2 Write down the general term T,, of the above number pattern. 6.3 If T,, = 512, determine the value of 7. Grade 9 Mathematics Test 9

QUESTION 7 Downloaded from hlayiso.com Study the graph below. wn 5 -4 3 -2 -1 -2 3 -4 7.1 Use the graph to calculate the gradient of the straight line. Grade 9 Mathematics Test 10 (3)

Downloaded from hlayiso.com 7.2 Determine the equation of the straight line. (2) 7.3 Write down the gradient of any other straight line which can be drawn parallel to the given line. [6] QUESTION 8 8.1 Decrease 240 kg by 15%. (2) 8.2 Nthabi’s car uses 1 litre of fuel to travel 12 km . How much fuel will be needed to travel 420 km? (2) Grade 9 Mathematics Test 11

Downloaded from hlayiso.com 8.3 There are 44 boys and girls in Mary’s class. The ratio of the number of boys to the number of girls is 5:6. How many boys are there in Mary’s class? (3) 8.4 Study the table below. The length ofa side ofa 2 3 4 square in cm Area of the square in cm? 4 9 16 Is this an example of a direct or an indirect proportion? Give a reason for your answer. (2) 8.5 Calculate how long it will take for an investment of R4 000 at 3% per annum simple interest to earn an interest of R840. (6) 8.6 Calculate the final amount that | will have in my savings account if | invest R600 for 2 years at a rate of 6% per annum compound interest. (4) [19] Grade 9 Mathematics Test 12

Downloaded from hlayiso.com QUESTION 9 9.1 Complete each of the following statements: 9.1.1. D and F are complementary angles if 9.1.2 The sum of the interior angles of a triangle is equal to 9.1.3. The sum of the exterior angles of any polygon is equal to 9.1.4 A trapezium is a quadrilateral with one pair of sides. 9.1.5 The diagonals of a rectangle are in length. 9.2 A t v In the figure above, AB|| TC, C, = 65° and C, = 43°. Calculate the size of A, B, and B,. Statement Reason Grade 9 Mathematics Test 13

Downloaded from hlayiso.com 9.3 B A In AABC, AB = AC and € = x°. Determine the size of A in terms of x. Statement Reason (3) [11] QUESTION 10 10.1 F Q R B D Which triangle is congruent to APQR? Statement Reason (2) Grade 9 Mathematics Test 14

Downloaded from hlayiso.com 10.2 In the given figure, P and T are points on a circle with centre M. N is a point on achord PT such that MN 1 PT. PLO Ns NY Prove that PN = NT. Statement Reason Grade 9 Mathematics Test 15 (8)

Downloaded from hlayiso.com 10.3 B In the above diagram, AC = DF, AB = DE and BF = CE. 10.3.1 Prove that BC = EF. Statement Reason (2) 10.3.2 Prove that AABC = ADEF. Statement Reason (5) Grade 9 Mathematics Test 16

Downloaded from hlayiso.com 10.3.3 Why is B = £? Statement Reason B=E 10.3.4 What is the relationship between AB and ED? Statement Reason Grade 9 Mathematics Test 17

Downloaded from hlayiso.com 10.4 In the figure, 8 = C, AD = 9 cm, AE =7 cmand CE = 21cm. 10.4.1 Prove that AABD |j| AACE. Statement Reason (6) 10.4.2 Calculate the length of BD. Statement Reason Grade 9 Mathematics Test 18

Downloaded from hlayiso.com QUESTION 11 A 12cm D 5cm CO B 3cm T c In parallelogram ABCD, AB =5 cm, AD = 12 cm, BT = 3 cmand AT 1 BC. 11.1 Calculate the length of AT. (3) 11.2 Calculate 11.2.1. the perimeter of trapezium ADCT. (1) 11.2.2 the area of trapezium ADCT. (3) Grade 9 Mathematics Test 19

Downloaded from hlayiso.com 11.3 The circumference of a circle is 52 cm. Calculate the area of the circle correct to 2 decimal places. (4) 11.4 The length of a rectangle is doubled. Write down the value of k if the area of the enlarged rectangle = k x the area of the original rectangle. [12] Grade 9 Mathematics Test 20

Downloaded from hlayiso.com QUESTION 12 Solve for x without using a calculator. Show the calculation steps. 12.1 x=(V¥8+ v2)? (3) 12.2 i] WwW (3) TOTAL: 140 Grade 9 Mathematics Test 21

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