Gr 11 Math P2 (English) June 2023 Question Paper_hlayiso.com_.pdf

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

Downloaded from hlayiso.com MATHEMATICS 2 (PAPER 2) GRADE 11 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 8 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera, that you have used in determining your answers. 4. Answers only will NOT necessarily be awarded full marks. 5. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round-off answers to TWO decimal places, unless stated otherwise. 7. Answer sheets for QUESTION 1.2 and QUESTION 8.1 are provided at the end of the question paper. Write you name in the spaces provided on each answer sheet and submit them together with your ANSWER BOOK. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the answers correctly 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 2) GRADE 11 QUESTION 1 The following box and whisker plot and accompanying 5-number summary, shows the marks obtained by Grade 11A for a Mathematics test out of 50. The 5-number summary for Grade 11A: Min. = 5 ; Q1 = 11 ; Q2 = 21 ; Q3 = 30 ; Max. = 45 Grade 11A The following data shows the marks obtained by the learners in another class (Grade 11B) for the same Mathematics test out of 50. 10 ; 13 ; 17 ; 21 ; 21 ; 23 ; 27 ; 29 ; 31 ; 34 ; 37 ; 38 ; 42 ; 43 ; 46 ; 48 1.1 Determine the 5-number summary for Grade 11B. (3) 1.2 On the diagram sheet provided in ANSWER SHEET A, draw a box and whisker plot of the marks for Grade 11B. (3) 1.3 Calculate the mean mark of Grade 11B. (2) 1.4 Calculate the standard deviation of Grade 11B. (2) 1.5 How many learners in Grade 11B obtained a mark that is higher than one standard deviation above the mean? (2) 1.6 Taking the interquartile range of the two grades into account, comment on the performance of Grade 11A and Grade 11B. (2) 1.7 Determine the percentage of learners in Grade 11A who achieved less than 30 for the test. (1) [15] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 2) GRADE 11 QUESTION 2 In the following diagram D(–10 ; 6), E, F and G(1 ; 9) are the vertices of a quadrilateral. The equation of EG is 3x – y + 6 = 0. The diagonals of the quadrilateral bisect each other at point K. Point F is on the x-axis and β is the angle of inclination of EG. y G(1 ; 9) D(−10 ; 6) K  O x F E 2.1 Determine the size of β. (2) 2.2 Calculate the coordinates of F given the equation of DF is x + 3y = 8. (2) 2.3 Determine the coordinates of E. (4) 2.4 Prove that DGFE is a rhombus. (3) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 2) GRADE 11 QUESTION 3 In the diagram below, A is the point (–2;–1), B(–3 ; 4), C(1 ; 5) and D(5 ; y). y D(5 ; y) C(1 ; 5) B(−3 ; 4) O x A(−2 ; −1) 3.1 Find the length of AC in simplified surd form. (2) 3.2 Determine the gradient of BC. (2) 3.3 Determine the value of y if B, C and D are collinear. (3) 3.4 If H is a new point such that AH  BC, determine the equation of AH. (3) [10] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 2) GRADE 11 QUESTION 4 4.1 In the diagram below, P(x; –24) is a point such that OP = 25, and R(12 ; 0) with RÔP   , where 180    270. y β x O ● R(12 ; 0) 25 P(x ; −24) 4.1.1 Calculate the value of x. (2) 4.1.2 Determine the value of each of the following WITHOUT the use of a calculator. (a) sin β (1) (b) cos(180° – β) (2) (c) tan2 (–β) (2) 4.1.3 T is a point on OP such that OT = 15.  21 72  (a) Show that T  ;   WITHOUT the use of a calculator. (4)  5 5 (b) Determine the area of ΔROT. (4) 4.2 Simplify to a single trigonometric ratio: tan 225  sin (180   ) cos (90   ) cos (90   ) sin (  540) (6) [21] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 7 (PAPER 2) GRADE 11 QUESTION 5 1  1 In the diagram below, f(x) = a cos x   and g(x) = –2sin(x + p) are drawn for 2  2 x   240 ; 240. y 2 1 x O −240º −180º −120º −60º 60º 120º 180º 240º f -1 g -2 5.1 Write down the amplitude of g. (1) 5.2 Determine the period of f. (1) 5.3 Determine the values of a and p. (2) 5.4 For which value(s) of x is f(x).g(x) ≤ 0? (2) 5.5 If h(x) = 2 cos (x + k), and h(x) = g(x), write down a possible value for k. (2) [8] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 8 (PAPER 2) GRADE 11 QUESTION 6 A candle holder is made in the shape of a hemisphere where a conical section is drilled out for the candle wax. In the diagram below, the radius of the hemisphere is represented by R, where ST = VT = R. The radius of the cone is represented by r, where TW = r. The angle at the vertex of the cone is given by θ. 4 3 1 VSPHERE  πR VCONE  πr 2 h 3 3 S T W R r θ V 6.1 Express r in terms of R and θ. (2) 6.2 Show that the remaining volume of the hemisphere can be represented by: R 3    V  2  tan 2    3   2  (4) 6.3 The cone is filled with wax and a wick. The wick is always 1 cm below the level of the wax but the wick must not protrude over the level of the flat surface of the hemisphere. The radius of the hemisphere (R) is 12 cm and the angle of the cone (θ) is 36°. Determine the volume of wax that must be put into each candle holder. (3) [9] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 9 (PAPER 2) GRADE 11 QUESTION 7 CD is a diameter and PC a tangent to the circle. Chord DK is produced to P. PT intersects KC at Q. CD̂P  40 , DP̂T  25 and TQ̂C  65. P K 25° D 1 2 1 40° Q 1 2 65° T 1 1 2 C 7.1 Determine, with reasons, the size of the following: 7.1.1 Ĉ 2 (2) 7.1.2 K̂ 1 (2) 7.1.3 P̂1 (2) 7.2 Prove, with reasons, that TC = QC. (2) [8] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 10 (PAPER 2) GRADE 11 QUESTION 8 In the diagram below, the points T, U and V lie on the circumference of the circle with centre O. T U O V 8.1 On the ANSWER SHEET B provided, prove the theorem which states that TÔV  2TÛV. (5) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 11 (PAPER 2) GRADE 11 8.2 In the diagram below, the two EQUAL circles with centres O and M are drawn. Chords AB and DM are produced to C. Chord OB is produced to meet AD at F. AB is a tangent to the circle with centre M at B, and AD is a tangent at D. DÔB  2 x. A B 1 2 3 O 2 2x C F 1 1 2 2 1 M D 8.2.1 Provide a reason why DOBM is a rhombus. (1) 8.2.2 Provide the geometric reason why each of the following angles are equal to x. (a) Â (1) (b) M̂ 2 (1) (c) D̂1 (1) (d) B̂ 2 (1) 8.2.3 Prove, with reasons, that D̂ 2  Ĉ. (4) 8.2.4 Prove, with reasons, that AB = BC. (4) [18] TOTAL: 100 END

Downloaded from hlayiso.com MATHEMATICS 12 (PAPER 2) GRADE 11 Name and Surname: Grade: ANSWER SHEET A QUESTION 1 1.2 Grade 11A Grade 11B (3)

Downloaded from hlayiso.com Name and Surname: Grade: ANSWER SHEET B QUESTION 8 8.1 T U O V (5)