Mathematics Grade 11 IEB June 2019 Question Paper

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Downloaded from hlayiso.com JUNE EXAMINATION 2019 MATHEMATICS PAPER 1 GRADE 11 JUNE 2019 Time: 2 Hours Total:100 PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 8 pages plus a data sheet. Please check that your question paper is complete. 2. Read the questions carefully. 3. Answer all questions, showing all the necessary working. 4. Please note that diagrams are not necessarily drawn to scale. 5. Approved non-programmable, non-graphing calculators may be used, unless otherwise stated. 6. Round off your answers to TWO decimal digits where necessary, unless otherwise stated. 7. Ensure that your calculator is in DEGREE mode. 8. It is in your own interest to write legibly and to present your work neatly. 1|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 QUESTION 1 (a) Solve for x: Show all working steps. (1) (2 x  1) 2  4  0 (3) (2)  x  5  2x 2  0 (rounded to 1 decimal digit) (3) (3) x  2x  1  2 (4) (4) ( x  2)(2 x  3)  3 (4) (5)  4 x 2  12x  8  0 (by completion of the square-leave answer in surd form) (5) (6) 32 x2  1  10.3x (5) (b) (1) Solve for x and y simultaneously: 3 x y  2 and y 1  (6) x 1 1 1 (2) Hence, or otherwise, determine the value(s) of:    (4) x y [34] 2|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 QUESTION 2 (a) Without using a calculator, evaluate each of the following:   2 (1) 98  50 (3) 3  1  5     x  3 4 0 (2) (4)  16  (b) Simplify the following expressions: pq 1  p 1q (4) q 1  p 1 [11] QUESTION 3 The first term of a linear number pattern is 92 and the constant difference is -4. a) Write down the values of the second and third terms. (2) b) Determine an expression for the nth term of the number pattern, (2) c) Find the value of the eighteenth term. (2) d) If 𝑇𝑝 + 𝑇𝑞 = 0 , determine the value of (𝑝 + 𝑞). (4) [10] 3|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 QUESTION 4 Consider the following picture pattern which continues in the same way indefinitely. Calculate the number of square blocks in the 50th pattern. [4] QUESTION 5 5 Given: the graph of f ( x)  x 5 Determine the equation of the new graph formed if the graph of f ( x)  is: x (a) shifted 4 units upward. (1) (b) shifted 2 units to the left and then 3 units down. (2) (c) reflected about the y-axis. (1) [4] 4|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 QUESTION 6 The sketch below shows the graph of 𝑓(𝑥) = 2𝑎 𝑥 − 1. The point A(1 ; 5) is found on the graph. a) Show that 𝑎 = 3. (2) b) Determine the y-intercept of 𝑓. (2) c) Write down the range of 𝑓. (1) d) What will be the equation of 𝑔(𝑥) if f is reflected about the x-axis followed by a translation of two units to the left. (2) [7] 5|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 QUESTION 7 Given: 𝑇 (−2 ; 8) ; 𝐾 (2 ; 6) and 𝑃 (−4 ; −2) are the vertices of ∆ 𝑇𝐾𝑃. 𝐴𝐵 𝑇𝑃 and 𝑇𝑅 𝑦 − 𝑎𝑥𝑖𝑠. 𝑃𝑇̂𝑅 = 𝛼. a) Determine the co-ordinates of B , the midpoint of PK. (2) b) The equation of TP is 𝑦 − 5𝑥 = 18 , show that the equation of AB is 1 9 𝑦=− 𝑥+ . (3) 5 5 c) Find the value of 𝛼, correct to one decimal place. (4) d) Given 𝑁 (𝑛 ; 5). Determine the value of 𝑛 such that T , K and N are collinear. (4) e) If 𝑇𝐾𝑃𝑄 is a parallelogram, determine the coordinates of point 𝑄. (4) 6|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 [17] QUESTION 8 A rocket is fired upwards. It follows a path that fits the equation h(t )  120t  3t 2 , 0  t  40 where h is the height in metres and t is the time in seconds from launch time. (a) Sketch the graph of : h(t )  120t  3t 2 ; 0  t  40 on the grid provided on the ANSWER SHEET. Clearly show all turning points and intercepts with axes. (4) (b) Use your graph to determine: (1) the time when the height of the rocket is zero. (1) (2) the flight time of the rocket. (1) (3) the maximum height of the rocket. (1) (4) how long after launching does the rocket reach its peak height. (1) (5) how long is the rocket above 900 m. (4) (c) Explain why there is a restriction on t. (1) [13] 7|Page

Downloaded from hlayiso.com JUNE EXAMINATION 2019 ANSWER SHEET - QUESTION 8 (a) 8|Page Powered by TCPDF (www.tcpdf.org)