Mathematics Grade 10 P1 National November 2016 QP (Eng)

Downloaded from hlayiso.com basic education WE ulahys Department: i) A A) Basic Education RX REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 : F: NOVEMBER 2016 “ w SRR COCOOOOOCOCOCOCO OCC CCC ee eee eee eee eee eee eee ee ee | SECC CORE CC CREE OCC CREO OC CORE CC CREE OCC ROE EO 8 eee MARKS: 100 TIME: 2 hours This question paper consists of 8 pages. III) *K6* GAUTENG Please turn over Copyright reserved

Downloaded from hlayiso.com Mathematics/P1 2 DBE/November 2016 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 8 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your 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. If necessary, round answers off 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 served FANN AMALIA EA Please fm over

Downloaded from hlayiso.com DBE/November 2016 Mathematics/P1 3 QUESTION 1 11 Factorise the following expressions fully: 11.1 x =x 1.1.2 3x? +3 px —2mx—2mp 1.1.3 2p? —2p-12 1.2 Simplify the following: a+l a-l 1.2.1 ue 7 122 x? -x41 2x ~ xt] | 2x42 QUESTION 2 2.1 Solve for x: 2.1.1 x(x—-1)=20 2.1.2 3x2 ay 2.2 Given: -4s-dm<5 where meER 2.2.1 Solve for m. 2.2.2 Write the answer to QUESTION 2.2.1 in interval notation. 2.3 Given: 4x” —y? =171 and 2x-y=9 CAPS — Grade 10 2.3.1 Calculate the value of 2x+y. 2.3.2 Solve simultaneously for x and y. Copyright reserved FANN AMALIA EA Please turn over (1) (3) (3) (3) (4) [14] (4) (G3) (3) (1) (2) G3) [16]

Downloaded from hlayiso.com Mathematics/P1 4 DBE/November 2016 CAPS — Grade 10 QUESTION 3 Dark tiles (D) and light tiles (L) are used to create patterns on a floor. The first four patterns are shown below. For the patterns that follow the tiles are arranged in a similar manner. sa Pattern 1 Pattern 2 Pattern 3 Pattern 4 3.1 How many dark tiles were used in pattern 5? (1) 3.2 How many light tiles were used in pattern 6? qd) 3.3 Write down the general term (D,) for the number of dark floor tiles used in each pattern. (2) 3.4 Write down the general term (L,) for the number of light floor tiles used in each pattern. (2) 3.5 Which pattern will have exactly 64 light floor tiles? (3) 3.6 Each dark tile is 0,3 m wide and 0,6m long. Calculate the total area covered by all the dark tiles in the first 100 patterns. (3) [12] Copyright served FANN AMALIA EA Please fm over

Downloaded from hlayiso.com Mathematics/P1 5 DBE/November 2016 CAPS — Grade 10 QUESTION 4 4.1 Mary wants to buy a fridge that costs R15 550. She has to pay a deposit of 15% of the cost and the balance by means of a hire-purchase agreement. The rate of interest on the loan is 16,25% p.a. simple interest. The repayment period of the loan is 54 months. In addition to the hire-purchase agreement, an annual insurance premium of 1,5% of the total cost of the fridge should be added. The annual insurance premium should be paid in monthly instalments. 4.1.1 Calculate the value of the loan that Mary will take. 4.1.2 Calculate the total amount that must be repaid on the hire-purchase agreement. 4.1.3 Calculate the monthly repayment, which includes the monthly insurance premium. 4.2 The table below shows the rand equivalent of one British pound and one US dollar. COUNTRY CURRENCY RATE OF EXCHANGE OF THE RAND Britain (United Kingdom) Pound (£) 21,41 United States of America Dollar ($) 13,45 A South African nurse works in the United States of America. 4.2.1 The nurse saves the equivalent of R4 800 per month. Calculate the amount, in US (American) dollars, that she saves per month. 4.2.2 She ordered a book from the United Kingdom (Britain) and paid $85 for it. Calculate the price of the book in pounds (£). 43 A sum of money doubles in 5 years when the interest is compounded annually. Calculate the rate of interest. Copyright served FANN AMALIA EA Please turn over (2) (3) GB) (2) (3) (3) [16]

Downloaded from hlayiso.com Mathematics/P1 6 DBE/November 2016 CAPS — Grade 10 QUESTION 5 The graphs of f(x)=x?—4 and g(x)=—x+2. are sketched below. A and B are the x-intercepts of f/ C and D are the y-intercepts of f and g respectively. K isa point on g such that BK || x-axis. f and g intersect at A and E. x Cc 5.1 Write down the coordinates of C. qd) 5.2 Write down the coordinates of D. qd) 5.3 Determine the length of CD. qd) 5.4 Calculate the coordinates of B. (3) 5.5 Determine the coordinates of E, a point of intersection of f and g. (4) 5.6 For which values of x will: 5.6.1 fo) < gx) Q) 5.6.2 — f(e.g(x)20 (2) 5.7 Calculate the length of AK. (4) [18] Copyright served FANN AMALIA EA Please fm over

Downloaded from hlayiso.com Mathematics/P1 7 DBE/November 2016 CAPS — Grade 10 QUESTION 6 The graph of g(x)=-2*+8 is sketched below. A and B are the y- and x-intercepts respectively of g. g fa) B \ 6.1 Write down the range of g. () 6.2 Determine the coordinates of B. (3) 6.3 If g is reflected over the x-axis to form a new graph h, determine the equation of h. (2) 6.4 Explain why the x-intercepts of g and h are both at B. (2) [8] QUESTION 7 A hyperbola, h, is described with the following characteristics: e The equation of the vertical asymptote is x = 0 e The range of / is (2 33)UG; oo) e The x-intercept of h is (2; 0) Determine the equation of h. [4] Copyright served FANN AMALIA EA Please fm over

Downloaded from hlayiso.com Mathematics/P1 8 DBE/November 2016 CAPS — Grade 10 QUESTION 8 8.1 In a certain class of 42 boys: 27 play hockey (H) 32 play soccer (S) 7 do not play hockey or soccer An unknown number (x) play both hockey and soccer eecee The information is represented in the Venn diagram below. HW Ss 8.1.1 Calculate the value of x. (2) 8.1.2 If a boy from the class is chosen at random, calculate the probability that he: (a) Does not play hockey or soccer qd) (b) Plays only soccer (2) 8.2 A bag contains 3 blue balls and x yellow balls. 8.2.1 Write down the total number of balls in the bag. qd) 8.2.2 If a ball is drawn from the bag, write down the probability that it is blue. (2) 8.3 8.3.1 Complete the following statement: If A and B are two mutually exclusive events, then P (A and B)=... qd) 8.3.2 Given that A and B are mutually exclusive events. The probability that event A occurs is 0,55. The probability that event B does not occur is 0,7. (3) Calculate P (A or B). [12] TOTAL: 100 Copyright reserved FANN AMALIA EA