# Mathematics Grade 11 P2 National Exemplar November 2014 QP > Grade 11 Mathematics Paper 2 question paper from the National Exemplar November Exam 2014, 14 pages. Read online or download the free PDF. - Page: https://www.hlayiso.com/library/2014-grade-11-final-exam-nov-math-paper-2/9158becc-51bf-454c-bcde-b658df2cc550 - Updated: 2026-09-27 - Subject: Mathematics - Grade: Grade 11 - Document type: Question paper - Year: 2014 - Exam period: National Exemplar November Exam - Paper: 2 - Curriculum: CAPS - Pages: 14 Breadcrumbs: [Home](https://www.hlayiso.com/) › [Library](https://www.hlayiso.com/library) › [Grade 11](https://www.hlayiso.com/library/grade-11) › [Mathematics](https://www.hlayiso.com/library/grade-11/mathematics) › [Mathematics Grade 11 P2 National Exemplar November 2014 QP](https://www.hlayiso.com/library/2014-grade-11-final-exam-nov-math-paper-2/9158becc-51bf-454c-bcde-b658df2cc550) ## About this document Mathematics · Grade 11 · National Exemplar November Exam · 2014. Question paper, 14 pages. Read online or download the PDF. Read it free online on the page above; download the PDF from there. ## Document text Text extracted from the PDF. Layout, diagrams and tables may not survive extraction. ### Page 1 Downloaded from hlayiso.com Copyright reserved Please turn over ### Page 2 Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2014 CAPS – Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 10 questions. 2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may 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. Write neatly and legibly Copyright reserved Please turn over ### Page 3 Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2014 CAPS – Grade 11 QUESTION 1 1.1 The number of delivery trucks making daily deliveries to neighbouring supermarkets, Supermarket A and Supermarket B, in a two-week period are represented in the box- and-whisker diagrams below. Supermarket A 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 Supermarket B 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 1.1.1 Calculate the interquartile range of the data for Supermarket A. (2) 1.1.2 Describe the skewness in the data of Supermarket A. (1) 1.1.3 Calculate the range of the data for Supermarket B. (2) 1.1.4 During the two-week period, which supermarket receives 25 or more deliveries per day on more days? Explain your answer. (2) 1.2 The number of delivery trucks that made deliveries to Supermarket A each day during the two-week period was recorded. The data is shown below. 10 15 20 x 30 35 15 31 32 21 x 27 28 29 If the mean of the number of delivery trucks that made deliveries to supermarket A is 24,5 during these two weeks, calculate the value of x. (3) [10] Copyright reserved Please turn over ### Page 4 Downloaded from hlayiso.com Mathematics/P2 4 DBE/November 2014 CAPS – Grade 11 QUESTION 2 The 2012 Summer Olympic Games was held in London. The average daily temperature, in degrees Celsius, was recorded for the duration of the Games. A cumulative frequency graph (ogive) of this data is shown below. Cumulative frequency graph of average daily temperature recorded 30 25 Cumulative frequency 20 15 10 5 0 17 19 21 23 25 27 29 31 33 35 Average daily temperature (in degrees Celsius) 2.1 Over how many days was the 2012 Summer Olympic Games held? (1) 2.2 Estimate the percentage of days that the average daily temperature was less than 24 °C. (2) 2.3 Complete the frequency table for the data on DIAGRAM SHEET 1. (3) 2.4 Hence, use the grid provided on DIAGRAM SHEET 1 to draw a frequency polygon of the data. (4) [10] Copyright reserved Please turn over ### Page 5 Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2014 CAPS – Grade 11 QUESTION 3 In the diagram A(–9 ; 12), B(9 ; 9) and C(–3 ; –9) are the vertices of ABC. N(a ; 7) is a point such that BN = 5 5 . R is a point on AB and S is a point on BC such that RNS is parallel to AC and RNS passes through the origin. T lies on the x-axis to the right of point P. AĈB  θ , AM̂O   and BP̂T   . y A(–9 ; 12) R B(9 ; 9) 5 5 N(a ; 7) x M O P T S  C(–3 ; –9) 3.1 Calculate the gradient of the line AC. (2) 3.2 Determine the equation of line RNS in the form y = mx + c. (2) 3.3 Calculate the value of a. (4) 3.4 Calculate the size of . (5) [13] Copyright reserved Please turn over ### Page 6 Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2014 CAPS – Grade 11 QUESTION 4 In the diagram A(–8 ; 6), B, C and D(3 ; 9) are the vertices of a rhombus. The equation of BD is 3x – y = 0. The diagonals of the rhombus intersect at point K. D(3 ; 9) A(–8 ; 6) K C O B 4.1 Calculate the perimeter of ABCD. Leave your answer in simplest surd form. (3) 4.2 Determine the equation of diagonal AC in the form y = mx + c. (4) 4.3 Calculate the coordinates of K if the equation of AC is x + 3y = 10. (3) 4.4 Calculate the coordinates of B. (2) 4.5 Determine, showing ALL your calculations, whether rhombus ABCD is a square or not. (5) [17] Copyright reserved Please turn over ### Page 7 Downloaded from hlayiso.com Mathematics/P2 7 DBE/November 2014 CAPS – Grade 11 QUESTION 5 5.1 If cos 23° = p, express, without the use of a calculator, the following in terms of p: 5.1.1 cos 203° (2) 5.1.2 sin 293° (3) 5.2 Simplify the following expression to a single trigonometric term: sin(360  x). tan( x) (6) cos(180  x).(sin 2 A  cos 2 A) cos x 1  sin x 2 5.3 5.3.1 Prove the identity:   (5) 1  sin x cos x cos x 5.3.2 For which values of x in the interval 0° ≤ x ≤ 360° will the identity in QUESTION 5.3.1 be undefined? (2) 5.4 Determine the general solution of: sin 2 x  4 cos 2 x (5) 5.5 In the diagram below P( x ; 3 ) is a point on the Cartesian plane such that OP = 2. Q(a ; b) is a point such that TÔQ   and OQ = 20. PÔQ  90 . y P( x ; 3 ) 2  x O  T 20 Q(a ; b) 5.5.1 Calculate the value of x. (2) 5.5.2 Hence, calculate the size of α. (3) 5.5.3 Determine the coordinates of Q. (5) [33] Copyright reserved Please turn over ### Page 8 Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2014 CAPS – Grade 11 QUESTION 6 In the diagram below the graphs of f(x) = a cos bx and g(x) = sin (x + p) are drawn for x  [–180° ; 180°]. f g 0 6.1 Write down the values of a, b and p. (3) 6.2 For which values of x in the given interval does the graph of f increase as the graph of g increases? (2) 6.3 Write down the period of f (2x). (2) 6.4 Determine the minimum value of h if h(x) = 3f(x) – 1. (2) 6.5 Describe how the graph g must be transformed to form the graph k, where k(x) = – cos x. (2) [11] Copyright reserved Please turn over ### Page 9 Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2014 CAPS – Grade 11 QUESTION 7 Surface area =  r 2   r S where S is the slant height. 1 Volume = area of base  perpendicular height 3 1 Volume =  r 2 h 3 7.1 In the diagram, the base of the pyramid is an obtuse-angled ABC with  = 110°, B̂ = 40° and BC = 6 metres. The perpendicular height of the pyramid is 8 metres. T 8 A B 110° 40° 6 C 7.1.1 Calculate the length of AB. (3) 7.1.2 Calculate the area of the base, that is ABC. (2) 7.1.3 Calculate the volume of the pyramid. (3) Copyright reserved Please turn over ### Page 10 Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2014 CAPS – Grade 11 7.2 The perpendicular height, AC, of the cone below is 2 metres and the radius is r. AB is the slant height. BÂC  36 A 36° 2 B r C Calculate the total surface area of the cone. (6) [14] Copyright reserved Please turn over ### Page 11 Downloaded from hlayiso.com Mathematics/P2 11 DBE/November 2014 CAPS – Grade 11 GIVE REASONS FOR YOUR STATEMENTS AND CALCULATIONS IN QUESTIONS 8, 9 AND 10. QUESTION 8 8.1 In the diagram below, PT is a diameter of the circle with centre O. M and S are points on the circle on either side of PT. MP, MT, MS and OS are drawn.  M 2 = 37° M 2 T 1 37° O 2 1 S P Calculate, with reasons, the size of:  8.1.1 M1 (2)  8.1.2 O1 (2) Copyright reserved Please turn over ### Page 12 Downloaded from hlayiso.com Mathematics/P2 12 DBE/November 2014 CAPS – Grade 11 8.2 In the diagram O is the centre of the circle. KM and LM are tangents to the circle at K and L respectively. T is a point on the circumference of the circle. KT and TL are joined. Ô1 = 106°. K O 1 106° 1 T 2 M L 8.2.1 Calculate, with reasons, the size of T̂1 . (3) 8.2.2 Prove that quadrilateral OKML is a kite. (3) 8.2.3 Prove that quadrilateral OKML is a cyclic quadrilateral. (3) 8.2.4 Calculate, with reasons, the size of M̂ . (2) [15] Copyright reserved Please turn over ### Page 13 Downloaded from hlayiso.com Mathematics/P2 13 DBE/November 2014 CAPS – Grade 11 QUESTION 9 In the diagram M is the centre of the circle passing through points L, N and P. PM is produced to K. KLMN is a cyclic quadrilateral in the larger circle having KL = MN. LP is joined. KM̂L  20 . K 1 2 L 2 1 20° 1 M 2 4 3 1 1 2 2 N P 9.1 Write down, with a reason, the size of NK̂M . (2) 9.2 Give a reason why KN | | LM. (1) 9.3 Prove that KL = LM. (2) 9.4 Calculate, with reasons, the size of: 9.4.1 KN̂M (4) 9.4.2 LP̂N (3) [12] Copyright reserved Please turn over ### Page 14 Downloaded from hlayiso.com Mathematics/P2 14 DBE/November 2014 CAPS – Grade 11 QUESTION 10 10.1 Use the sketch on DIAGRAM SHEET 4 to prove the theorem which states that BÂT  Ĉ . (6) C B O P A T 10.2 In the diagram PQ is a tangent to the circle QST at Q such that QT is a chord of the circle and TS produced meets the tangent at P. R is a point on QT such that PQRS is a cyclic quadrilateral in another circle. PR, QS and RS are joined. P 1 2 1 S 2 3 1 Q 2 1 2 3 T R 10.2.1 Give a reason for each statement. Write down only the reason next to the question number. Statement Reason Q̂1  T̂ 10.2.1 (a) Q̂ 2  P̂2 10.2.1 (b) (2) 10.2.2 Prove that PQR is an isosceles triangle. (4) 10.2.3 Prove that PR is a tangent to the circle RST at point R. 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