Mathematics Grade 11 P2 Eastern Cape November 2017 QP (Eng)

Downloaded from hlayiso.com *Imat2*

Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2017 CAPS — Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. _ 3. This question paper consists of 12 questions. Answer ALL the questions in the ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine the answers. Answers only will NOT necessarily be awarded full marks. Round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. Write neatly and legibly. OS UNA AAA AA Pease wm ove EASTERN C4&PE

Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2017 CAPS — Grade 11 QUESTION 1 1.1 Mr Brown conducted a survey on the amount of airtime (in rands) EACH student had on his or her cellphone. He summarised the data in the box and whisker diagram below. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 Tid Write down the five-number summary of the data. (2) 1.1.2 Determine the interquartile range. (1) oe Comment on the skewness of the data. (1) 1.2 A group of 13 students indicated how long it took (in hours) before their cellphone batteries required recharging. The information is given in the table below. if 5 8 10 _ 20 ay 48 50 50 63 y | 107 1.2.1 Calculate the value of y if the mean for this data set is 41. (2) 1.2.2 If y=94, calculate the standard deviation of the data. (1) 1.2.3 The mean time before another group of 6 students needed to recharge the batteries of their cellphones was 18 hours. Combine these groups and calculate the overall mean time needed for these two groups to recharge the batteries of their cellphones. (3) [10] comment 2 EASTERN CAPE

Mathematics/P2 QUESTION 2 Downloaded from hlayiso.com 4 CAPS ~ Grade 11 DBE/November 2017 A student conducted a survey among his friends and relatives to determine the relationship between the age of a person and the number of marketing phone calls he or she received within one month. The information is given in the table below. AGE OF PERSON FREQUENCY CUMULATIVE IN SURVEY FREQUENCY 20 <x <30 7 7 30<x<40 27 40 <x <50 25 Ll 64 60<x<70 72 7 -D 4 Cl 80 2.1 Complete the frequency and cumulative frequency columns in the table given in the ANSWER BOOK. 2.2 How many people participated in this survey? 23 Write down the modal class. 2.4 Draw an ogive (cumulative frequency graph) to represent the data on the grid given in the ANSWER BOOK. 2.5 Determine the percentage of marketing calls received by people older than 54 years. Copyright reserved UNA AA Please turn over (4) (1) Q) (3) (3) [12]

Downloaded from hlayiso.com Mathematics/P2 5) DBE/November 2017 CAPS ~ Grade 11 QUESTION 3 A(-2 ; -5), B, C and Dare the vertices of quadrilateral ABCD such that diagonal AC is perpendicular to diagonal BD at T. The equation of BTD is givenby 2y+x=18 and AB= 15 units. a Cc B it 15 fe) x A(-2:-5) D 3.1 Determine the gradient of line AC. (2) 32 Determine the equation of AC in the form y=mx+c. (2) 3.3 If the equation of AC is y=2x—1, calculate the coordinates of T. (3) 3.4 If ABCD isa kite with AB = BC: 3.4.1 Determine the coordinates of C (2) 3.4.2 Calculate the length of BT (4) 3.4.3 Write down the length of the radius of the circle passing through points B, C and T (2) {15] CT a UAC AA Pease over EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2017 CAPS - Grade 11 QUESTION 4 C, a point on the x-axis, A(-5 ; -3) and B(4; 12) are the vertices of a triangle. AB intersects the x-axis at E. ABC=0 and BEC=a. 4, B(4: 12) 6 LZ — . ACS ;-3) 4.1 Calculate the gradient of AB. 4.2 Determine the coordinates of point E. 43 Determine the size of a. Round off to the nearest whole number. 4.4 If 0=76°, determine the equation of the line through A parallel to BC. CEE UNA AA AA Pease um ove EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 7U DBE/November 2017 CAPS - Grade 11 QUESTION 5 5.1 Simplify fully: sin(90°— x). cos(180° + x)+tan x. cos x. sin (x-180°) (6) 5.2 Prove, WITHOUT using a calculator, that 5.3 5.4 sin 315°.tan210°.sin 190° —V2 cos 100°.sin 120° 3 (6) In the diagram below, R is a point in the first quadrant such that TOR =a@ . RO is extended to P such that OP=2RO and TOP=f. It is given that sina = 2 : fy R (6 De fe) T ox ly WITHOUT using a calculator, determine: 5.3.1 The value of tana (3) 5.3.2 The value of sin (3) 539 The coordinates of P (4) yee in@—tan@. cos’ Prove the identity: ee = tan@ (4) cos@—1+sin’ 6 [26] cent ANU, EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2017 CAPS ~ Grade 11 QUESTION 6 6.1 Determine the general solution for sin(x—30°)= cos2x (5) 6.2 Consider the functions f(x)=sin(x-30°) and g(x)=cos2x 6.2.1 Write down the period of g. (1) 6.2.2 State the range of /f. (2) 6.2.3 On the grid provided in the ANSWER BOOK, draw the graphs of —|—h—™mr™éi<“—SO—CS—C—sSsSr—s—s Clearly show ALL intercepts with the axes, turning points and end points. (5) 6.2.4 Write down the x-coordinates of the points of intersection of f and g in the interval x €[-90°;180°]. (3) [16] QUESTION 7 In APQR, QR=3 units,PR = x units, PQ = 2x unitsand POR Oo Q 2% 3 P _ R x +3 TA Show that cos 6 = re (3) 7.2 If x=2,4 units: ve | Calculate 0 (3) 7.2.2 Calculate the area of APQR (2) Ts) Calculate the values of x for which the triangle exists. (4) [12] Cd UNO Pease um over EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2017 CAPS ~ Grade 11 QUESTION 8 A pyramid with a square base with a side length of 16 cm is sketched below. P lies on the square base directly below A. The volume of the pyramid is 640 cm’. Volume of pyramid = yan 16 cm 8.1 Show that the perpendicular height of the pyramid, AP, is 7,5 cm. (2) 8.2 Hence, determine the total surface area of the pyramid. (4) [6] Oe, NU A cabana EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2017 CAPS — Grade 11 Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12. QUESTION 9 9.1 In the diagram below, O is the centre of the circle and point T lies on chord RS. Prove the theorem which states that if OT | RTS then RT= TS. (5) 9.2 In the diagram, O is the centre of circle ABD. F is a point on chord AB such that DOF 1 AB. AB=FD=8cm and OF = xcm. D Determine the length of the radius of the circle. (5) [10] Ca UNA A Please um ove

Mathematics/P2 QUESTION 10 Downloaded from hlayiso.com 10 CAPS ~ Grade 11 M is the centre of the circle SVQR having equal chords SV and QR. RP and QP are tangents to the circle at R and Q respectively such that RPQ = 70°. DBE/November 2017 10.1 Calculate the size of R,. 10.2 Calculate the size of Q,. 10.3 Determine the size of M, : Copyright reserved UU AAA Please turn over (4) (2) (3) 19]

Downloaded from hlayiso.com Mathematics/P2 12 DBE/November 2017 CAPS - Grade 11 QUESTION 11 In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. DB bisects ABC. Let B, =% 11.1 Prove that BC|| OD (4) 11.2 Showthat C =90° (3) [7] Cu) UNA A Pease im oes EASTERN CAPE

Downloaded from hlayiso.com Mathematics/P2 13 DBE/November 2017 CAPS — Grade 11 QUESTION 12 In the diagram below, two circles touch each other externally at point P. QPR is acommon tangent to both circles at P. EDRC isa tangent to circle PBFC at C. RCA=y and DAC=x. AD||BC. E 12.1 Name, with reasons, FOUR other angles equal to x. (7) 12.2 Show that EPA=x+y (4) 12.3 Determine the numerical value of x+y, if it is given that DCTP is a cyclic quadrilateral. (4) {15} TOTAL: 150 coer MALE A

Downloaded from hlayiso.com

Downloaded from hlayiso.com

Downloaded from hlayiso.com