Mathematics Grade 10 P1 National November 2018 QP (Eng)

Downloaded from hlayiso.com ie =Ze basic education a & Department: (O): Basic Education Sad REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 gee TE SSS SSSR SRR R SSSR SSSR RRS SSSR RRR RRS ESSE " MATHEMATICS P1 ‘ i NOVEMBER 2018 “ Me eee! MARKS: 100 TIME: 2 hours This question paper consists of 7 pages. Copyright reserved Please turn over — — = —=

Downloaded from hlayiso.com Mathematics/P1 2 DBE/November 2018 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of EIGHT questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, etc. 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 reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 3 DBE/November 2018 CAPS —Grade 10 QUESTION 1 1.1 Factorise the following expressions fully: 1.1.1 4x—x? (2) 11.2 x? 4+15x-54 (2) 1.1.3 yrxytx-l (3) 1.2 Simplify the following expressions fully: 121 (x+2)(x? -x+3) (2) 1.2.2 oe x+3 2-x (3) 123 221s" 3.5% (3) 1.3 Determine the value of p+q)’ if 9p? +q? =12 and pq=-3. (3) [18] QUESTION 2 2.1 Solve for x: 241 px+gx=a @) 212 2x?~5x4+2=0 (3) 2.13 (y" =32 GB) 2 2.2 Given: -11<3m-8<4 2.2.1 Solve for m. (2) 2.2.2 Hence, write down the number of integers that satisfy the inequality. (1) 2.3 Solve simultaneously for x and y if: 5x+4y=21 and 2x=3-y (4) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 4 DBE/November 2018 CAPS — Grade 10 QUESTION 3 Consider the finite linear pattern: 20; 17; 14; ...; -103 3.1 Write down the 4" term of the pattern. 3.2 Determine the expression for the n™ term. 3.3 Calculate the number of terms in the sequence. 3.4 Which term is the first to have a negative value? 3.5 What is the value of the 19" even-valued term in the sequence? QUESTION 4 Samantha is investigating a pattern of dots represented in the diagram below. ° e e e e e e fo} e @ @ e @ e Pattern number: 1 2 3 Number of dots: Pel 14+3=2? =4 1434+5=3? =9 4l Write down: 4.1.1 The number of dots in the 4" pattern 4.1.2 The number of dots in the 13" pattern 4.1.3 A formula for the number of dots in the n™ pattern 4.2 Hence, or otherwise, calculate the value of: 14+34+54..443 Copyright reserved Please turn over qd) (2) (2) (3) (2) [10] (1) a) (1) (3) [6]

Downloaded from hlayiso.com Mathematics/P1 5 CAPS — Grade 10 QUESTION 5 DBE/November 2018 Sketched below are the graphs of f(x) = ax® +q and g(x) = (3) -4. A and B are the x-intercepts of f The graphs intersect at A and point E (1 ;3) lies on f. C is the turning point of f and D is the y-intercept of g. y E(1 33) 5.1 Write down the: 5.1.1 Coordinates of D Q) 5.1.2 Range of g qd) 5.2 Calculate the: 5.2.1 Coordinates of A (2) 5.2.2 Values of a and g (4) 5.3 Determine the: 5.3.1 Length of CD (2) 5.3.2 Equation of a straight line through A and D G) 5.4 For which values of x is: 541 f(x) >0? Q) 5.4.2 Ff decreasing? 65) [17] Copyright reserved Please turn over

Mathematics/P1 6 DBE/November 2018 Downloaded from hlayiso.com CAPS - Grade 10 QUESTION 6 The equation of the function g(x)= a +q passes through the point (3;2) and has a range of x ye(-~; NUCL). 6.1 Determine the: 6.1.1 Equation of g 6.1.2 Equation of h, the axis of symmetry of g which has a positive gradient 6.2 Sketch the graphs of g and # on the same system of axes. Clearly show ALL the asymptotes and intercepts with axes. 6.3 Write the equations of the asymptotes of f if f(x)=—g(x)+5. QUESTION 7 Read the advertisement below. 7.1 Calculate the total amount to be paid over a period of 24 months. 72 The monthly instalment, quoted in the advertisement, is calculated on a hire purchase agreement which charges interest of 7,5% p.a. on the cash price of the cellphone. Show that the price of the cellphone is R4 779,13. 73 Calculate the total interest paid over a period of 24 months if the cellphone is bought with this hire purchase agreement. 74 The cellphone is insured at 11,5% p.a of the cash price. The total insurance is calculated and then split up over 24 months. It is then added to the monthly instalment. Calculate the new monthly instalment if the customer wants to insure the cellphone. 15 The cost of the cellphone is subject to inflation and increases to a cash price of RS 100,00 after 2 years. Calculate the annual inflation rate. Copyright reserved Please tur over Buy a Samsung J5 for only R229 per month. You have 24 months to pay. No deposit is required. (3) 2) (4) @) [12] qd) @) () G) (4) [14]

Downloaded from hlayiso.com Mathematics/P1 7 DBE/November 2018 CAPS — Grade 10 QUESTION 8 8.1 In a random physical sciences experiment, A and B are two different events. It was found that: 5 P(A) = , PB’) == and P(A orB) => 8.1.1 Calculate: (a) P@) 2) (b) P(Aand B) GB) 8.1.2 Hence, determine whether events A and B are mutually exclusive. Motivate your answer. (2) 8.2 The Venn diagrams below represent different scenarios of events A and B. Write down the probability of the shaded region for EACH of the diagrams below. ee e@ q) 8.2.3 QQ) 8.3 Which diagram(s) in QUESTIONS 8.2.1, 8.2.2 or 8.2.3 represent mutually exclusive events? qd) f14] TOTAL: 100 Copyright reserved