Mathematics Grade 12 Paper 1 Limpopo November 2019 Question Paper

Downloaded from hlayiso.com LIMPOPO PROVINCIAL GOVERNMENT REPUBLIC OF SOUTH AFRICA DEPARTMENT OF EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 12 (ORS B SSG SS SSGRRSSSSRRR SSSR SSE SSSEESGG SHEE S REE RRS i MATHEMATICS P1 a la a " SEPTEMBER 2019 " UNUM f EMATHP1 MARKS: 150 TIME: 3HOURS This question paper consists of 10 pages including formula sheet and answer sheet. Copyright reserved Please turn over |

Downloaded from hlayiso.com Mathematics P14 2 LimpopoDoE/September 2019 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1 This question paper consists of 11 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, etc. that you have used to determine your answers. 4. Answer only will not necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. 9. ANSWER SHEET given for QUESTION 5.1.3. 10. Write neatly and legibly. 11. Use black or blue pen only. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P4 3 LimpopoDoE/Sepiember 2019 N3c QUESTION 1 L.L Solve for x: Lil. (4+2)@-N)=0 (2) 11.2, x? -x=5 (correct to two decimal piaces) (4) 143. x-V54x=7 (4) Lid 4x2 ales (4) —xt2 =x 12 Given: p= 2 =l6a a *+4q7*! L2A Simplify P and show P= a(a-4) (4) 1.2.2 Hence solve for P=0 (2) 1.3 Prove thatthe rootsof a?x? +abx+b? =0 are non-real for all real values of a and b, a#0 and b¥0 (3) 14 Solve for x and y: 34x=2y and x7 4+4y" =2xy+7 (3) [28] QUESTION 2 The sequence 3;9;17;27;...... is a quadratic sequence. 2.1 Write down the next term. qd) 2.2 Determine an expression for the n™ term of the sequence. (4) 2.3 What is the value of the first term of the sequence that is greater than 269? (4) {9] _ Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 4 LimpopoDcoE/September 2019 NSC QUESTION 3 The first two terms of an arithmetic series A, and a geometric series to infinity B, are the same: 3.1 write down in terms of a: 3.1.1 the third term of the geometric series, B. (2) 3.1.2 the third term of the arithmetic series , A. (2) 3.2 The sum of the first three terms of the arithmetic series A is the same as the third term of the geometric series B. Write down an equation and determine the value of a. (5) 3.3. If a=—, determine if the geometric series converge. @) [12] QUESTION 4 4.1 The sum to »—terms of a sequence of numbers is given as: S,, = 5 (ne 9). 4.1.1 Calculate the sum to 23 terms of the sequence. @G) 4.1.2 Hence calculate the 23” term of the sequence, (2) 4.2 If x is areal number, show that the following sequence can NOT be geometric: Ti xtlix-35 ec... (4) [9] QUESTION 5 5.1 Consider the function: (x)= = -1. 5.1.1 Calculate the y—intercept of f. (2) 5.1.2 Calculate the x-intercept of /. (3) 5.1.3 Sketch the graph of f, showing the asymptotes and the intercepts with the axes. Use the ANSWER SHEET given. (4) 5.1.4 For which values of x is f(x) > 0? @ Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 $ LirmpapcDoE/September 2019 NSc 5.1.5 Calculate the average gradient of f between x =—2 and x=0. (4) 5.2 Draw a sketch graph of yrax +bxtc, a<0, b<0,c<0 and ax? +bx+ce=0 has only ONE solution. 4 {19] QUESTION 6 Tn the diagram below {(x)=2* and f T are given. AandC are points on /. Bisa pointon f —). CB and AB are perpendicular to each other. > v 6.1 Write down the equation of ramaes) in the form y=... (2) 6.2 Calculate the length of AB. (5) 6.3 Calculate the length of CB, where CB 1 AB. (3) 6.4 Write down the domain of f~!(x). a [14] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P1 6 LimpopoDoE/September 2019 NSC QUESTION 7 7.1 Peter invests R12 500 for & years at a compound interest rate of 9% p.a. compounded quarterly. At the end of the & years his investment is worth R30 440. Calculate the value of k. i) 7.2 Sam bought a car for R500 000 on an agreement in which he will repay it in tmoonthly instalments at the end of each month for 5 years, starting one month after the loan was granted. Interest is charged at 18% p.a. compounded monthly. 721 Calculate the annual effective interest rate of the loan. ~ (3) 7.2.2. Calculate Sam’s monthly instalments. (4) 7.2.3. Sam decided to pay R12 700 each month as his repayment. Calculate the outstanding balance of the loan after 2 years. (4) [15] QUESTION 8 8.1 Given: fQ)= 3x? 1. Determine f ‘ (x) from first principle. (5) 8.2 Determine: g2i LY ir yasxt ade (3) dx 8.2.2 p,| 4) (3) 3x 8.3 Given s(=P. Show that the gradient of any tangent to s will never be negative. Q) (13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P41 7 LimpopaDoE/Sepiember 2019 NSC QUESTION 9 The sketch below shows the graph of the function / (x) =x? -x? -8x412. Ais an x-intercept and B a turning point of the graph. The points C (0: 2) and D (2;0) . the other turning point, are given on the sketch. ¥ 8 C(0.12) A Di2:0) x 4 9.1 Determine the coordinate of A. (4) 9.2 Determine the coordinate of B. (5) 9.3 Calculate the x—coordinate of the point of inflection. Q) 9.4 Write down the value(s} of x for which / f (x} >0 (2) 9.5 How many real roots will the equation x* -x? -8x412=k have if k <0? 2) {15] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics P41 3 LimpopoDaE/September 2019 NSC QUESTION 10 PQRS is a rectangle with P on the curve h(x) = x? and with the x-axis and the line x = 6 as boundaries. y 10.1 Show that the area of rectangle PQRS can be expressed as: A= 6x? —x3. @) 10.2 Determine the largest possible area for rectangle PORS. Show all your calculations. (4) [7] QUESTION 11 ii... A and B are mutually exclusive events. If it is given that the P(A) = 0,35 and P(B) = 0,52 determine: Ila P(A’) Q) 11.1.2 P(A and B) qd) 11.1.3. P(A orB) (2) 11.2. Three married couples — Mr and Mrs Brown, Mr and Mrs Green and Mr and Mrs White are to be seated on a bench. 11.2.1 How many different arrangements are possible? (1) 11.2.2 If Mr and Mrs Green must be seated in the middle, how many different arrangements are possible for the remaining persons? (2) 11.2.3. Determine the probability that Mr and Mrs Green will sit next to each other. (4) (12) TOTAL:150 Copyright reserved Please turn over