Mathematics Grade 10 P1 National November 2017 QP (Eng)

Se basic education 4 Sy Department: UG) Basic Education . YE REPUBLIC OF SOUTH AFRICA N ONAL SENIOR CERTIFICATE GRADE 10 en TTR SRR RRR SRR RRR RRR RRR RRR ER RRR RR RRR RS RSS RR EEE " MATHEMATICS P1 a rr u Ll} i NOVEMBER 2017 : Woje = 'e)s Stes 2 Se ee S Sis Soe StS 2 Ses Ses Spee Se es = = Se ee ees? MARKS: 100 TIME: 2 hours This question paper consists of 7 pages. GAUTENG Please turn over Copyright reserved

Mathematics/P1 Downloaded from hlayiso.com DBE/November 2017 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 7 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used to determine the answers. Answers only will NOT necessarily be awarded full marks. You must use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 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 UUM A Please tim over

Downloaded from hlayiso.com Mathematics/P1 DBE/November 2017 CAPS — Grade 10 QUESTION 1 1.1 Given: g= Vb? -4ac 1.1.1 Determine the value of g if a=2, b=-1 and c=~-4. Leave your answer in simplest surd form. (2) 1.1.2 State whether q is rational or irrational. (1) 1.1.3 Between which TWO consecutive integers does gq lie? qd) 1.2 Factorise the following expressions fully: 1.2.1 P(r—-s)-rt+s G3) 3 220 eet (2) x x41 1.3 Simplify the following completely: 13.1 (2y +3)(7y* -6y-8) @) 1.3.2 — (3) ~ x -9 (x-3) ft 1-2 1.3.3 3-3 2.3' -3' (3) [17] QUESTION 2 2.1 Given: 4-2x<16 where xeR 2.1.1 Solve the inequality. (2) 2.1.2 Hence, represent your answer to QUESTION 2.1.1 on a number line. qd) 2.2 Solve simultaneously for x andy: -2x—y=10 and 3x-4y=-4 (4) 2.3 Solve for x: 23.1 *=9)_1 29 GB) 6 2.3.2 c=Va+2x (2) 2.4 Tabelo is currently four times as old as his daughter, Linda. Six years from now, Tabelo will be three times as old as Linda. Calculate Linda's age currently. (4) [16] Cone TL cre GAUTENG

Downloaded from hlayiso.com Mathematics/P1 DBE/November 2017 CAPS — Grade 10 QUESTION 3 3.1 Consider the linear sequence: 5;8;11;0;17;... 3.1.1 Write down the value of 5. 3.1.2 Determine the n™ term of the sequence. 3.1.3 Calculate the value of the 15" term of the sequence. 3.1.4 Which term in the sequence is equal to 83? 3.2 Consider the number pattern below created by using the numbers of the sequence 2;6;10;14;18;... 6 10 14 18 9-22 2% 30 34 38 42 3.2.1 Calculate the sum of the numbers in the 8” row. 3.2.2 Determine the mean of the numbers in the 20" row. QUESTION 4 4.1 Seven years ago, Mrs Grey decided to invest R18 000 in a bank account that paid simple interest at 4,5% p.a. 4.11 Calculate how much interest Mrs Grey has earned over the 7 years. 4.1.2 Mrs Grey wants to buy a television set that costs R27 660,00 now. If the average rate of inflation over the last 5 years was 6,7% p.a., calculate the cost of the television set 5 years ago. 4.1.3 At what rate of simple interest should Mrs Grey have invested her money 7 years ago if she intends buying the television set now using only her original investment of R18 000 and the interest earned over the last 7 years? 4.2 On a certain day the exchange rate between the US dollar and South African rand is $1 =R12,91. At the same time the exchange rate between the British pound and the South African rand is £1 = R16,52. Calculate the exchange rate between the British pound and US dollar on that day. Comyrigh reserved UIUC AU EU AU A Please tm ove GAUTENG 2) (2) (2) (2) (3) 2) [3] Q) (3) (3) (2) [10]

Downloaded from hlayiso.com Mathematics/P1 DBE/November 2017 CAPS — Grade 10 QUESTION 5 The diagram shows the graphs of g(x)=ax’+q and f(x)=mx+c. R and S(2;0) are the x-intercepts of g and T(0; 8) is the y-intercept of g. Graph / passes through R and T. y TO; 8) g x R (@) SQ ; 0) f 5.1 Write down the range of g. ¢0) 5.2 Write down the x -coordinate of R. qd) 53 Calculate the values of a and gq. G) 5.4 Determine the equation of (- G6) 5.5 Use the graphs to determine the value(s) of x for which: 5.5.1 F(x) = g(x) (2) 5.5.2 x. g(x) <0 (3) 5.6 The graph / is obtained when g is reflected along the line y=0. Write down the equation of A inthe form h(x) = px’ +k. (2) [15] copie NALINI eo

Downloaded from hlayiso.com Mathematics/P1 DBE/November 2017 CAPS — Grade 10 QUESTION 6 6.1 The function p(x) =k* +q is described by the following properties: 6.2 e k>0;k¥1 e x-intercept at (2 ; 0) e The horizontal asymptote is y=-9 6.1.1 Write down the range of p. qd) 6.1.2 Determine the equation of p. (3) 6.1.3 Sketch the graph of p. Show clearly the intercepts with the axes and the asymptote. G) The sketch below shows the graphs of f(x) = Lg +w and g(x)=-x-1. x The graph g is an axis of symmetry of f/. The graphs f and g intersect at P and Q. y (6) x & Q fi 6.2.1 Write down the value of w. qd) 6.2.2 The point (—2 ; 7) lies on f Calculate the value of k. (2) 6.2.3 Calculate the x-coordinates of P and Q. (4) : . -16 6.2.4 Write down the values of x for which ——>-x. Q) x [16] Conese AA ALUN) GAUTENG

Downloaded from hlayiso.com Mathematics/P1 DBE/November 2017 CAPS — Grade 10 QUESTION 7 71 Two events, A and B, are complementary and make up the entire sample space. 72 Also, P(A’) =0,35. 7.1.1 Complete the statement: P(A)+P(B) =... qd) 7.1.2. Write down the value of P(A andB). (1) 7.1.3. Write down the value of P(B). qd) A survey was conducted among 150 learners in Grade 10 at a certain school to establish how many of them owned the following devices: smartphone (S) or tablet (T). The results were as follows: © 8 learners did not own either a smartphone or a tablet. e 20 learners owned both a smartphone and a tablet. e 48 learners owned a tablet. e x learners owned a smartphone. 7.2.1 Represent the information above in a Venn diagram. (4) 7.2.2. How many learners owned only a smartphone? (G3) 7.2.3 Calculate the probability that a learner selected at random from this group: (a) Owned only a smartphone qd) (b) Owned at most one type of device (2) [13] TOTAL: 100 coma