Gr9 Math (English) November 2018 Question Paper_hlayiso.com_.pdf

Downloaded from hlayiso.com testpapers.co.za GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION NOVEMBER 2018 GRADE 9 MATHEMATICS NAME OF LEARNER: _____________________________________________________ GRADE / CLASS: _____________________ TIME: 2 hours MARKS: 100 18 pages + 1 formula sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 2 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS TIME: 2 hours MARKS: 100 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 9 questions and 19 pages, including the attached FORMULA SHEET. 2. Answer ALL the questions. 3. A non-programmable calculator may be used unless otherwise stated. 4. Clearly show all calculations, diagrams and graphs that you have used in determining your answers. Answers only will not necessarily be awarded full marks. 5. If necessary, round-off answers to TWO decimal places, unless otherwise stated. 6. Diagrams are not necessarily drawn to scale. Reasons MUST always be given when doing geometric calculations. 7. Answer Questions 2 to 9 of Section B in the spaces provided on the question paper. 8. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 3 SECTION A QUESTION 1 Circle the letter of the correct answer. 1.1 Which one of the following numbers is irrational? A ̇ B C √ D √ (1) 1.2 √√ … A B C D (1) 1.3 The ratio written in its simplest form is ... A B C D (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 4 1.4 ( x  2) 2 = ... A x2  4 B x 2  4x  4 C x 2  4x  4 D x 2  4x  4 (1) 1.5 , … A 0 B 6 C 1 D undefined (1) 1.6 The general rule for the pattern is … A Tn  4n  1 B Tn  4n  1 C Tn  4n  1 D Tn  4n  1 (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 5 1.7 Complete the flow diagram by using the given rule. Input Rule Output 𝑦 𝑡+ … A B C D (1) 1.8 Complete: If two straight lines are parallel, then the ... A product of the gradients is . B gradients are equal. C product of the gradients is 1. D sum of the gradients is . (1) 1.9 12 m³ = … A 12 000 000 kℓ B 12 000 kℓ C 12 kℓ D 0,012 kℓ (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 6 1.10 The length of a rectangle and the width . Complete: If both the length and the width of the rectangle are doubled, then the area of the rectangle will be ... A B ( + ) C D ( + ) (1) [10] P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 7 SECTION B QUESTION 2 2.1 Write in decimal form. ____________________________________________________________ ____________________________________________________________ (1) 2.2 Decrease by . ____________________________________________________________ ____________________________________________________________ (2) 2.3 Simplify: 2.3.1 ( ) ( ) ____________________________________________________________ ____________________________________________________________ (4) 2.3.2 √ ( ) ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ (2) 2.3.3 + + ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) [12] P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 8 QUESTION 3 Factorise fully: 3.1 ____________________________________________________________ ____________________________________________________________ (2) 3.2 ____________________________________________________________ (2) 3.3 ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ (2) [6] QUESTION 4 Solve for . 4.1 + ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (4) 4.2 ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 9 4.3 + ___________________________________________________________________ ___________________________________________________________________ (2) [9] QUESTION 5 5.1 Joe travelled 3 hours by car at a speed of 110 km/h. Calculate the distance that Joe travelled. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) 5.2 8 boys each contribute R115, 50 towards the purchase of a tent. Calculate how much each boy will have to contribute to buy the same tent, if there were 10 boys in the group. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) 5.3 How long will it take for an investment of R5 000, at 6% per annum simple interest, to earn R1 200 interest? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 10 5.4 Calculate what R15 000 will amount to if it is invested at 5,5 % per annum compound interest for 5 years. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) [12] QUESTION 6 6.1 Determine the equation of the given straight-line graph. Use + . ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (4) 6.2 Determine the gradient of the straight line perpendicular to the given graph. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) [7] P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 11 QUESTION 7 7.1 The stem-and-leaf diagram below represents the marks of the learners in a Grade 9 class for a Mathematics test. Stem Leaves 1 0 0 1 1 8 2 2 3 5 5 6 8 9 3 0 1 2 3 3 3 4 5 7.1.1 How many learners wrote the test? _____________________________________________________________ (1) 7.1.2 Calculate the average mark obtained by the class. _____________________________________________________________ _____________________________________________________________ (2) 7.1.3 Determine the modal mark for the test. _____________________________________________________________ (1) 7.1.4 Determine the median mark. _____________________________________________________________ _____________________________________________________________ (2) 7.2 Cards numbered 1 to 6 are put into a bag. Athletes draw a card to decide the lane in which they will run in a track event. 7.2.1 What is the probability that a particular athlete will draw the card for lane one? _____________________________________________________________ _____________________________________________________________ (1) 7.2.2 What is the probability of the next athlete choosing any one of the remaining numbers? _____________________________________________________________ _____________________________________________________________ (1) [8] P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 12 QUESTION 8 8.1 In the diagram below, , ̂ ,̂ , Â ° and ̂ °. A B C 𝑥 𝑦 2 ° 70° 40° 2 D E F Determine the values of and . Statement Reason _______ + _______ = _______ _______________________________ _______ _______ _______________________________ (5) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 13 8.2 In , is produced to . and ̂ . Calculate the size of ̂. E 2 1 C D F Statement Reason ̂ +̂ _______ ̂ _______ ̂ ̂ ̂+ ̂+̂ ________ ̂ _________ (6) 8.3 A 1 2 1 2 T B C In the diagram above, ̂ ̂ and ̂ ̂. Complete: Statement Reason 1) (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 14 8.4 The diagonals of ABCD bisect each other at T. A D 2 1 1 2 2 T 3 4 1 2 1 1 2 B C Prove that . Statement Reason In and ____________________________ (4) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 15 8.5 In , , and ̂ ̂ A 1 2 1 2 B D C 8.5.1 Prove that . Statement Reason In and (4) 8.5.2 Calculate the length of if and BD = 9 cm. Statement Reason In and proportional sides of similar  AB  ______ (3) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 16 8.6 8.6.1 Use your pair of compasses, ruler and a sharp pencil to construct triangle in the frame below, so that (2) 8.6.2 By measurement: The size of ̂ _______________ (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 17 8.7 The co-ordinates of A are ( ) A O 8.7.1 Write down the co-ordinates of if is the reflection of A in the x– . ________________________________________________________ (1) 8.7.2 Write down the co-ordinates of if is the reflection of A in the y . ________________________________________________________ (1) 8.7.3 Write down the co-ordinates of if A is rotated anti-clockwise about the origin through 180°. ________________________________________________________ (1) [29] P.T.O.

Downloaded from hlayiso.com MATHEMATICS GRADE 9 18 QUESTION 9 The cylinder above has a base with a diameter , height = and . 9.1 Calculate the curved surface area of the cylinder. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (4) 9.2 Calculate the volume of the cylinder. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) [7] TOTAL [100] END

Downloaded from hlayiso.com MATHEMATICS GRADE 9 19 FORMULA SHEET Simple interest: Compound interest: ( + ) ( + ) ( + ) ( + ) Perimeter Area Rectangle ( + ) Circle Triangle ( + + )