Mathematics Grade 11 P1 Gauteng June 2024 QP (Eng)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2024 GRADE 11 MATHEMATICS (PAPER 1) TIME: 2 hours MARKS: 100 6 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. This question paper consists of 6 questions. 2. Answer ALL the 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. 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 according to the numbering system used in this question paper. 10. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (PAPER 1) GRADE 11 QUESTION 1 x2 + 4 1.1 Determine the value(s) of x for which the expression: 9− x 1.1.1 has real value(s). (1) 1.1.2 is not defined. (1) 1.1.3 Given, x =1, is the expression rational or irrational? Validate your answer with an appropriate calculation. (1) 1.1.4 Determine a value for x where the expression will yield a recurring decimal (1) value? 1.2 Given: 2 x 2 − 3x − k = 0 . Determine x if: 1.2.1 k =5 (2) 1.2.2 k = 4 (correct to TWO decimal places) (3) 1.3 Solve for x : 1.3.1 x−4 = − x−2 (5) 1.3.2 x2 + 4 > 3x + 2 (4) 1.4 Solve simultaneously for x and y. 2 x = y + 2 and 2 x 2 = 2 − y 2 (6) 1.5 For which values of p will − 2 x 2 + 4 x − 3 = − p : 1.5.1 have two unequal roots? (4) 1.5.2 have roots that are BOTH positive? (2) 1.6 Show that the equation ( p 2 + 1) x 2 = −2 pqx − q 2 has no real roots for p and q  Real numbers and q  0. (5) [35] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 1) GRADE 11 QUESTION 2 2.1 Simplify WITHOUT using a calculator: 2.1.1 (2 −1 + 3−1 ) 2 (3) 2.4 x + 2 − 4 x −3 2.1.2 2 x.2 x (3) 1 − 2.1.3 3 2 [ 12 + 3 3 3 ] (4) 2.2 Solve for x WITHOUT using a calculator: 3 2.2.1 2 x = 164 (3) 2.2.2 5 x +1 + 5 x = 150 (4) 9 − 54 3 2 −2 3 2.3 WITHOUT using a calculator, show that is equal to . 6 2 4 (3) [20] QUESTION 3 Given the number pattern: 4 ; − 3 ; − 10 ; … ; − 227 3.1 Write down the value of the 4 th term of this pattern. (1) 3.2 Determine the general term of the number pattern in the form Tn = an + b . (1) 3.3 Calculate the number of terms of the pattern. (2) 3.4 The given number pattern above is also the FIRST differences of a quadratic number pattern, Tn = an2 + bn + c. Determine if the quadratic pattern will have a maximum or minimum value. Validate your answer with an appropriate calculation. (2) [6] QUESTION 4 Given the quadratic number pattern: 69 ; 0 − 63 ; … 4.1 Write down the value of the next term in the pattern. (1) 4.2 Calculate an expression for the nth term of the quadratic pattern. (4) 4.3 Determine the value of the SMALLEST term in this pattern. (4) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 1) GRADE 11 QUESTION 5 Sketched below are the graphs of f ( x) = ax 2 + bx + c and g ( x) = mx + k. • The x-intercepts of f are at points A and C. • The graphs of f and g intersect at points A and B respectively. • Point P is the turning point of f. • Q is a point on g such that line PQ is parallel to the y-axis. y g P B(0;8) Q A(–4;0) C(2;0) x 0 f 5.1 Determine the equation of g . (3) 5.2 Calculate the values of a, b and c in f ( x) = ax2 + bx + c. (5) 5.3 Show that the coordinates of P are (−1 ; 9). (2) 5.4 Determine the range of f. (1) 5.5 Determine the equation of a line p perpendicular to g passing through point C. (3) 5.6 Calculate the length of line PQ. (2) f ( x) 5.7 For which value(s) of x is  0? g ( x) (2) [18] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 1) GRAAD 11 QUESTION 6 −4 Given: k ( x) = + 1 and h( x) = 2 − x − 4 x+3 6.1 Write down the equations of the asymptotes of k . (2) 6.2 Determine the x and y-intercepts of k. (2) 6.3 Write down the equation of the asymptote of h. (1) 6.4 Sketch the graph of k and h on the same axes. Clearly indicate ALL intercepts with the axes as well as the asymptotes. (4) 6.5 If p( x) = 3h( x) , write down the equation of the asymptote of p. (1) 6.6 Write down the equation of q, the reflection of h in the y-axis. (1) 6.7 Determine the x-values for which h( x) − q( x) = 0 (1) [12] TOTAL: 100 END