KING DAVID HIGH SCHOOL LINKSFIELD MATHEMATICS PAPER 1 GRADE 11 NOVEMBER EXAMINATION 2017

Transcription

1 KING DAVID HIGH SCHOOL LINKSFIELD MATHEMATICS PAPER 1 GRADE 11 NOVEMBER EXAMINATION 2017 Total: 100 marks Reading Time: 10 minutes Writing Time: 2 Hours Name: This paper comprises a question paper of 8 pages (including the front cover) and a data sheet. Check that your paper is complete. Write your name in the space above. Please read the following instructions carefully: 1. Number all questions exactly as they appear on the question paper. 2. Pay careful attention to time management and mark allocation. 3. Write legibly and not in pencil. 4. Non programmable calculators may be used unless otherwise instructed. 5. All answers to be given to 2 decimal places where appropriate. 6. All necessary calculations must be clearly shown. You will NOT receive full credit if you write down only the answers and show no working out. Q1 [16] Q2 [11] Q3 [10] Q4 [11] Q5 [19] Q6 [7] Q7 [8] Q8 [12] Q9 [6] TOTAL [100]

2 Page 2 of 8 Grade 11 Mathematics Paper 1 November 2017

3 Question 1 a) Simplify x x x 1 x 2 (4) b) Solve for x: x x (i) (6) (ii) 2x 1 2 x (6) Question 2 a) Solve for x leaving answers in SIMPLEST surd form where necessary: (i) x 2 + 4x 5 = 6 (3) (ii) (x + y)(2x 1) = 0 (2) b) Determine k if the equation x 2 + k 2 = 4x has real roots. (6) Question 3 a) Ari has R18600,00 and he needs to have R24380,00 in 4 years. At what rate should he invest the money if interest is compounded half- yearly? (4) b) R12000 was invested in the bond market for 5 years. The interest rate was fixed at 11.5% per annum compounded quarterly for the first 3 years. (i) Calculate the annual effective interest rate. (2) (ii) After 3 years the interest rate changes to 11,25% compounded monthly. What is the investment worth at the end of the 5 year period? (4) Question 4 Consider the quadratic sequence: 12; 9; 2; 9; x;... a) What is the value of x? (1) b) Determine a formula for T n of this sequence. (4) c) A new sequence, P n, is formed by adding 6 to each term of the ORIGINAL sequence (T n ) above. (i) Write down the formula for P n in the form P n = dn 2 + en + f. (2) (ii) Which term of this sequence has a value of 400? (4) Page 3 of 8 Grade 11 Mathematics Paper 1 November 2017

4 Question 5 1 The diagram below shows sketch graphs of f(x) = 1 and g(x) = x 3 graph of f intersects the X axis at A and the Y axis at B. f and g intersect at C and D. Y f 1 x. The 2 g A O X C B D Graphs NOT drawn to scale. a) Write down the equations of the asymptotes of f. (2) b) What is the domain of f? (2) c) Calculate the lengths of OB and OA (5) d) Determine the co ordinates of C and D. (6) e) Use the graphs and your answers above to obtain the solution to 1 x 2 x 3 2 (4) Page 4 of 8 Grade 11 Mathematics Paper 1 November 2017

5 Question 6 The graphs of y = mx + 6 and y = x 2 + 8x 5 are shown on the sketch below. D is the turning point of the parabola and CDE // Y axis. Y C O E D X Graphs NOT drawn to scale. a) Determine the co-ordinates of D. (3) b) Write down the co-ordinates of C in terms of m. (2) c) If CD = 3 units, determine the value of m. (2) Page 5 of 8 Grade 11 Mathematics Paper 1 November 2017

6 Question 7 Use the table on the next page to match the description(s) to the appropriate graph: The equations of the graphs are in the form : y = ax 2 + bx + c or y = a(x p) 2 a + q or y = q x p 1 Description A Graph b 2 4ac =16 (2) 2 B b 2 4ac + 25 = 0 (2) 3 C b 2 = 4ac (2) 4 D a > 0; p < 0; q < 0 (1) 5 E a < 0; p < 0; q > 0 (1) a < 0; p > 0; q > 0 a > 0; p < 0; q = 0 a > 0; p > 0; q > 0 Page 6 of 8 Grade 11 Mathematics Paper 1 November 2017

7 Question 7 continued NB Each of the graphs satisfies at least one of the descriptions given. Graph Description(s) Example Q 1 ; 4 A B C D E (8) Question 8 A survey is conducted among the 174 grade 11 students. The results are shown below 37 study Life Sciences 111 study Mathematics 60 study Physical Science 50 study Mathematics and Physical Science 29 study Life Sciences and Mathematics 13 study Physical Sciences and Life Sciences 45 do not study any of Life Sciences, Mathematics or Physical Sciences x students study all three a) Draw a Venn diagram to represent the information above (6) b) Show that x = 13 (2) c) If a student is selected at random, calculate the probability that she studies: (i) Mathematics and Physical Sciences but not Life Sciences. (2) (ii) Only one of Mathematics or Physical Sciences or Life Sciences. (2) Page 7 of 8 Grade 11 Mathematics Paper 1 November 2017

8 Question 9 A and B are two events so that P(A) =0,4; P(A or B) = 0,6 and P(B) = k. Determine k in each of the following cases if: a) A and B are mutually exclusive events. (2) b) A and B are independent events. (4) End of examination Page 8 of 8 Grade 11 Mathematics Paper 1 November 2017