Mathematics Grade 11 P1 Gauteng June 2017 Question Paper

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION JUNE 2017 GRADE 11 MATHEMATICS PAPER 1 TIME: 2 hours MARKS: 100 6 pages + 1 answer sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 Paper 1 GRADE 11 GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION MATHEMATICS (Paper 1) TIME: 2 hours MARKS: 100 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of SEVEN questions. Answer ALL questions. 2. Number your answers according to the numbering system used in this question paper. 3. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 4. Round-off the final answer correct to TWO decimal places, unless instructed otherwise. 5. Show ALL calculations, diagrams, graphs etc. that you have used in determining the answers. 6. Answers only will not necessarily be awarded full marks. 7. Diagrams are NOT necessarily drawn to scale. 8. It is in your interest to write legibly (in blue ink) and present all answers neatly and logically. P.T.O

Downloaded from hlayiso.com MATHEMATICS 3 Paper 1 GRADE 11 QUESTION 1 [19] 1.1 Solve for x: 1.1.1 𝑥 2 − 2𝑥 = 15 (3) 1.1.2 4𝑥 2 − 𝑥 − 5 < 0 (3) 1.1.3 √2𝑥 − 1 + 2 = 𝑥 (5) 2 1.1.4 2𝑥 3 − 8 = 0 (3) 1.2 If a𝑥 2 + b𝑥 + c = 0 and 𝑎 + 𝑏 + 𝑐 = 0, calculate ONE numerical value of x. (5) QUESTION 2 [15] 2.1 Solve simultaneously for x and y 3𝑦 + 𝑥 = 2 𝑦 2 + 𝑥 = 𝑥𝑦 + 𝑦 (6) 2.2 Prove that √𝑏√𝑎 − 𝑏 . √𝑏√𝑎 + 𝑏 = 𝑏√𝑎 − 1. (4) 2.3 If 3a = 21b and 7c = 21b , show that ac b= where a + c ≠ 0. (5) a+c P.T.O

Downloaded from hlayiso.com MATHEMATICS 4 Paper 1 GRADE 11 QUESTION 3 [18] 3.1 Given the sequence −3 ; 1 ; 5 ; ... 3.1.1 Write down the 5th term of the sequence. (1) 3.1.2 Determine the general term of this sequence. (2) 3.1.3 Show that 394 is NOT a term in the sequence. (3) 3.2 The quadratic sequence 0 ; 5 ; 12 ; ... has the general term, 𝑇𝑛 = 𝑛2 + 2𝑛 + 𝑐. 3.2.1 Show that c = −3. (2) 3.2.2 Calculate the 10th term of the sequence. (2) 3.2.3 Determine which term in the sequence has a value greater than 360. (4) 3.3 The table below represents the total number of handshakes exchanged between random people. Each person shakes the hand of another person only once. Number of people 2 3 5 100 Number of handshakes 1 3 a b 3.3.1 Determine the value of a. (1) 3.3.2 Determine the value of b. (3) QUESTION 4 [6] √𝑥−2 Given: 𝑘 =2+ 4 4.1 For what value(s) of x is k real? (2) 4.2 Determine the minimum value of k. (1) 4.3 If x = 3, calculate g(k) if g(a) = 𝑎2 − 1 . (3) P.T.O

Downloaded from hlayiso.com MATHEMATICS 5 Paper 1 GRADE 11 QUESTION 5 [12] Given: h(x) = 3𝑥 - 1 5.1 Determine the x and y-intercepts of h. (3) 5.2 Sketch the graph of h on the ANSWER SHEET provided on page 7. Clearly indicate the points of intersection with the axes as well as the asymptote of the graph. (3) 5.3 Write down the range of h. (1) 5.4 Given: p(x) = h(x+ 2) 5.4.1 Determine the x-intercept of p. (1) 5.4.2 Determine for which value(s) of x is p(x) > 2. (1) 5.5 Determine the x coordinate of a point J on h if 3ℎ(𝑥) = 726. (3) QUESTION 6 [10] 3 Given the function f(x) = –2. 𝑥−1 6.1 Write down the equations of the asymptotes of f. (2) 6.2 Calculate the x and y-intercepts of the graph with the axes. (3) 6.3 Sketch the graph of f on the answer sheet provided on page 7, clearly illustrating the asymptotes and the intercepts of the graph with the axes. (3) −3 6.4 Describe, in words, the transformation of f to g if g(x) = −2. (2) 𝑥+1 P.T.O

Downloaded from hlayiso.com MATHEMATICS 6 Paper 1 GRADE 11 QUESTION 7 [20] The graphs of 𝑘(𝑥) = 2𝑥 2 + 8𝑥 + 3 and 𝑝(𝑥) = 2𝑥 − 4 are sketched below. y k p 0 x L D E M 7.1 Determine 7.1.1 the coordinates of point D, the turning point of k. (3) 7.1.2 for which values of x is 𝑘(𝑥) ≥ 3. (2) 7.1.3 the minimum length of LM, where LM is parallel to the y- axis, with points L on k and M on p respectively. (4) 7.1.4 the average gradient between k (-2) and k (3). (3) 7.1.5 the value of t such that the straight line, y = 2x + t, touches the graph of 𝑘(𝑥) = 2𝑥 2 + 8𝑥 + 3 only ONCE. (5) 1 7.2 A quadratic function f has f (1 ) = 0 , f (−4) = 0 and f (1) = -5. 2 Draw a sketch graph of f in your ANSWER BOOK. (3) TOTAL: 100 END

Downloaded from hlayiso.com MATHEMATICS 7 Paper 1 GRADE 11 ANSWER SHEET Please detach and place in your ANSWER BOOK. Name:_____________________________________________________ Grade: 11____ QUESTION 5.2 y x QUESTION 6.3 y x