Mathematics Grade 11 P1 Gauteng June 2023 QP (Eng)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2023 GRADE 11 MATHEMATICS PAPER 1 TIME: 2 hours MARKS: 100 7 pages P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 (PAPER 1) GRADE 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. Answer ALL the questions. 2. This question paper consists of 6 questions. 3. Present your answers according to the instructions of each question. 4. Clearly show ALL calculations, diagrams, graphs, et cetera, which were used in determining the answers. 5. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the answers correctly according to the numbering system used in the question paper. 10. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (PAPER 1) GRADE 11 QUESTION 1 1.1 If x  {0; 1; 2; 3; 4; 5}, determine the values of x for which: 16 4 x 1.1.1 is not defined. (2) 1.1.2 is a natural number. (2) 1.1.3 is an irrational number. (2) 1.2 Solve for x: 1.2.1 3x 2  4 x  0 (3) 1.2.2 3x  14  6 x 2 (4) 1.2.3 ( x  1)( x  3) > 12 (4) 1.2.4 2x 2 x (4) 40 1.2.5 If x  6  0 is one of the solutions of the equation x + = 16, determine ONE x 40 value of y for which 2 y  3   16. 2y  3 (3) 1.3 Solve for x and y simultaneously: y  1  2x x 2  xy  3 x  y  2  0 (5) 1.4 Show that the equation x 2  px  p 2  2 has TWO real and unequal roots for all real values of p. (3) 1.5 A farmer constructs a rectangular enclosure using 100 m of fencing. He uses one existing boundary wall as one side of the rectangular enclosure. Calculate the dimensions of the rectangle to obtain the maximum enclosed area. (7) [39] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 1) GRADE 11 QUESTION 2 2.1 Simplify WITHOUT the use of a calculator: 3n2 .9 n1 2.1.1 27n1 (3) x2 2.1.2 if x = 1 + 3 1 x (4) 5 a 2  b 2  ( a  b) 2 2.1.3 1 if a  b ( a  b) 2 (4) 2 8 2.2 Prove that: – = –2 1 2 8 (4) 2.3 Given: Isosceles  JKL with JK = 2 + 3 and LK = 4. J 2 3 L M K 4 Calculate the area of  JKL correct to ONE decimal place. (6) [21] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 1) GRADE 11 QUESTION 3 3.1 The FIRST three terms of a linear sequence are: x; 4 x  5; 10x  5; … Determine the numerical value of x. (2) 3.2 Consider the linear sequence: 17; 14; 11; …; –106 3.2.1 Determine n if the n th term is given as Tn  3n  20. (2) 3.2.2 Which term is the FIRST negative term in the sequence? (2) 3.2.3 Determine the value of the 20th ODD term in the sequence. (3) 3.3 Consider the pattern: 3; a; 10; b; 21 The pattern has a second difference of 1. Determine the values of a and b. (4) [13] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 1) GRADE 11 QUESTION 4 The diagram shows the graph of f ( x )  ax 2  bx  c with the following essential properties:  A(2 ; y ) is the turning point of f.  B and C(–1 ; 0) are the x-intercepts of f.  D(6 ; 7) is a point on f. y D(6 ; 7) C(–1 ; 0) B x O A(2 ; y) 4.1 Write down the coordinates of B. (2) 4.2 Show that the equation of f can be written as: f ( x)  x 2  4 x  5 (3) 4.3 Determine the equation of a line h(x) passing through point C which is perpendicular to the line passing through point B and the y-intercept of f. (3) 4.4 For which values of x will x. f ( x)  0 ? (2) [10] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 (PAPER 1) GRADE 11 QUESTION 5 6 6 Given: g ( x)   1 and p( x)   2. x2 x 3 5.1 Sketch the graph of g showing clearly the asymptotes and the intercepts with the axes. (3) 5.2 Determine the equation h, the line of symmetry of g, that has an angle of inclination of 135 in the form y = … (3) 5.3 Determine value(s) of x for which g ( x)  h( x). (1) 5.4 If the graph of g is shifted so that it coincides with the graph of p, 5.4.1 by how many units must the graph be shifted horizontally? (1) 5.4.2 by how many units must the graph be shifted vertically? (1) [9] QUESTION 6 6.1 Given: h( x )  3.2 x  6 6.1.1 Write down the equation of the asymptote of h. (1) 6.1.2 Determine the x-intercept of h. (2) 6.1.3 Determine the y-intercept of h. (1) 6.1.4 Determine for which values of x will h(x) > 0. (1) 6.2 Draw a neat sketch of the graph of g(x) = a.bx + q if:  a=1  0<b<1  q = –1 (3) [8] TOTAL: 100 END