Mathematics Grade 10 September Test 2016 Paper & Memo

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watenaice DOWNloaded frog hlayiSO.GQMb sestenrer2016 2 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions: 1, 2. This question paper consists of 6 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers. Answers only will not necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. Ifnecessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale, Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Copyright reserved Please turn over

Copyright reserved Downloaded from hlayisQ.G@sMpiember2016 Mathematics QUESTION 1 1.1. Determine, without using a calculator, the value of V2 cos 45° + tan 30°, cosec60°. (4) 12 If 4tan0+3=0and @ [90° ; 270°], determine with the aid of'a diagram, and without the use of a calculator, the value of: 1.2.1 cosd (4) 1.2.2 1-sin?@ 3) 13 Usea calculator to solve for 0, where 20 € [0°;90°]: sin 20+ 5 =5,83 @) , ; 14 In the diagram below, POX =30°. The coordinates of P are (& 510). y P(k 310) mal 30° aX ¥ 1.4.1 Write down the value of sin 30°. dy) 1.4.2 Hence, determine the length of OP. (1) 1.4.3. Calculate the value of &. (2) [18] Please turn over

matienatics DOWNloaded from HlayiSO.GOMc sepember2016 4 QUESTION 2 2.1 In the diagram below, KMN is a right-angled triangle. Use the diagram to complete the following trigonometric ratios: at cos N = = Come Ge 21.2 secM=— 6) 2.13 == (1) 2.2 In the diagram below, the angle of depression from the top of a cliff to a boat R at sea, in the same horizontal plane as Q, is 42°. The boat is 700m away from the foot of the cliff Q. P - 42° Hy Td 53°? oes Calculate the height of the cliff, PQ, to the nearest metre. (4) (7| Copyright reserved Please turn over

Mathematics QUESTION 3 Downloaded fram HlayiSQ; COM. sone 2016 3.1. Draw the graphs f(x) =—2sinx and g(x) = cosx—-2 for x <{0°;360°] on the same set of axes in your answer book. Indicate clearly the turning points and the intercepts with the axes. (6) Use the graphs to answer the following questions for x € [0° ; 360°] : 3.2 Write down the range of g. 3.3. Write down the amplitude of /. (2) qd) 3.4 If the graph of f is reflected in the x-axis to form the graph of /, write down the equation of A. QUESTION 4 @) [10] 4.1 Ryan buys a double bed which costs R10 500 on hire purchase. He is charged a simple interest rate of 22,3% p.a. over five years. 4.1.1 Calculate the total amount that he will pay for the bed. 4.1.2 How much interest will he pay over this period? 4.1.3 Calculate his monthly instalment. @) 0) (2) 4.2 The price of a loaf of white bread is currently R14 and the average annual inflation rate for South Africa over the past 15 years is estimated at 5,32%. Calculate what a loaf of white bread, made by the same baking company, cost 15 years ago. Copyright reserved (4) [10] Please turn over

Mathematics D own load e 2d from h layi 1 so GRIM Ma sep September 2016 QUESTION 5 5.1. The probability that John will see a movie during the holidays is 0,7. The probability that he will go to a restaurant is 0,6. The probability of him seeing a movie and going to a restaurant is 0,4. The probabilities are represented in the Venn diagram below. Ss M R x Use the Venn diagram to determine the probability that: 5.1.1 he doesn’t go to a movie or a restaurant, (2) 5.1.2 he only goes to a movie. ¢) 5.1.3 he doesn’t go to a restaurant. () 5.1.4 he goes to a movie or a restaurant. (1) 5.2 Customers at a supermarket were asked if they had bought milk, meat or both. 150 were questioned and the answers were: « $125 bought milk ¢ 85 bought meat * 70 bought both meat and milk 5.2.1 Represent this information in a Venn diagram. Let the event that the ( : customer bought milk be A, and the event that the customer bought meat (4) be B. Use the Venn Diagram to caloulate the probability that a randomly chosen customer bought: 5.2.2 either meat or milk? (2) 5.2.3 meat only? Q) 5.2.4 neither meat nor milk? (2) [15] Copyright reserved Please turn over

Mathematics Down loaded from h lAYISQ,, GUD emer 2016 | QUESTION 6 In the diagram below A(2 ; 5), B(-2 ; 7) and C(-4 ; 3) and D(0 ; 1) are the vertices of a quadrilateral. ty BC-2;7) A(2 ; 5) 1 C-4 ; 3) DO; 1) x « 5 —> 4 v 6.1 Calculate the length of BD. QB) 6.2 Show that AC = BD. Q) 6.3. Show that the coordinates of M, the midpoint of BD, are (1 ; 4) (2) 6.4 Calculate the gradient of AM. (3) 6.5 Prove that AM . BD. (3) 6.6 Write down, giving a reason, what type of quadrilateral ABCD is. Q) [15] TOTAL: 75 Copyright reserved

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Downloaded from hlayiso.com CommotinggSeptember 2016 ‘Mathematics 3 Mathematics ‘Common Test September 2016 Grade 10 Memorandum Grade 10 Memorandum QUESTION 2 QUESTION 4 * [RAT [om Y answer A 411 | 4=P0+im) | “correct formula A k . _ @ 4=10500[1 + 0,223(5)] Y 1osoo+0,223;5) A 212 | ke Y¥ answer A Total = R22 207,50 answer aN : n @ @) D3 | tanMor cot Tama A 41.2 | Taterest= R22 207,50 ~ R10 500 a =RI1 707,50 Y answer CA 2.2 | pRQ=42° (parallel lines - alt. Zs=) YPRQ=42° A ) 0, 308 |v i io rati 413 | Monthly instalments = 2220750 vy Zoral $0 tana? aly tan 4y = a correct trigonometric ratio A . lonthly_ 3x12 3x12 cA re = y PQ = 700 tan 42° h = 63025 y simplification CA 370,13 answer ft © -PQ= OO answer 5 -. PQ= 630,28 m we A 4) 42 A=P0+i" ai) _|gcorrect formula, rea K= p(ita) ¥ substitution m7 14 = PQ+0,0532) oy +s 32th) A = i caale en QUESTION 3 pot = 14 ( “simplification CA +0,0532) = 26,43 31° Tt cost R643 ls Vanswer OK y (4) 2 F(x) =—2sinx (20) Y y— intercept (0; 0) , Y x intercepts x Y turing points 2 ze oe g(x) =cosx—-2 a OO Y y~intercept (0 ;—1) & 2 Y turning point Y shape 3 6) 3.2 | Rangeofgis 3<y<-1 vv answer (A Of OR Q) ye f3;-1] 3.3 | Amplitude of f:2 Y answer A © 34 | k@)=2sinx Y answer A @). {10} Copyright Reserved Please tum over Copyright Reserved. Please tum over

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