Mathematics Grade 12 P2 North West Mock 2018 Question Paper

Downloaded from hlayiso.com Education and Sport Development Department of Education and Sport Development Departement van Onderwys en Sportontwikkeling Lefapha la Thuto le Tihabololo ya Metshameko NORTH WEST PROVINCE NATIONAL SENIOR CERTIFICATE | ‘GRADE 12 APT SSSR SSR RRR RRS SHR RST RS RSE RR RRR " MATHEMATICS P2 ; 1 " " SEPTEMBER 2018 1 erererirrirTrrtr Tt Trt r tr Terre rere rrr MARKS: 150 TIME: 3 hours This question paper consists of 13 pages, 1 information sheet and an answer book of 23 pages. Copyright reserved Please turn over

Mathematics/P2 Downloaded from hlayiso.com NW/September 2018 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 10 questions. Answer ALL the questions in the ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. . If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. An information sheet with formulae is included at the end of the question paper. Write neatly and legibly. Copyright reserved ° Please turn over

Downloaded from hlayiso.com Mathematics/P2 3 NW/September 2018 NSC QUESTION 1 The distances (in cm) of the best attempts of 11 long jump athletes during an athletics event are given below: 287 328 374 486 492 501 522 583 601 619 685 1.1 Calculate the mean distance of the athletes’ best attempts. (2) 1.2 Calculate the standard deviation of the above data. (2) 1.3 Determine how many distances lie outside ONE standard deviation from the mean attempt. Show ALL your calculations. @) 1.4 The official that measured the distances of the long jump athletes, mistakenly measured y cm short from the correct measuring mark. Hence all distances measured were y cm shorter than what it was supposed to be. This scenario is shown in the diagram below. e A=The correct mark from where the distance should have been measured. e B=The incorrect mark from where the distances were measured. e C=The mark up to where the distance was measured. When the correction is made to the distances, the sum of the athletes’ best jumps is i now 5555 cm, i.e. Dk, = 5555. n=l 1.4.1 Calculate the value of y. (2) 1.4.2 Write down the standard deviation of the new correct distances. (2) [1] Copyright reserved Please turn over

Mathematics/P2 QUESTION 2 NSC Downloaded from hlayiso.c om NW/September 2018 The goal-scorers in a netball game practice scoring at training during the week. In the tournament during the weekend, the number of goals they score from the total number of attempts they made, is recorded as a percentage. This statistic is referred to as the successful goal-shoot average. The table below shows the number of goal shots practiced during the week and the successful goal-shoot average during the tournament for 8 goal-scorers. Number of goal shots 280 | 400 | 540 | 595 | 375 | 430 | 500 | 650 racticed Successful goal shoot 73175183 | 89 | 80 | 76 | 92 | o1 average (%) 2.1 Determine the equation of the least squares regression line. (3) 2.2 Calculate the correlation coefficient for the data. (2) 2.3 Comment on the correlation between the number of goal shots practiced and the successful goal-shoot average. (2) 2.4 A player practiced 465 goal shots. What is her expected successful goal-shoot average for the next tournament? (2) 19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 5 NW/September 2018 NSC QUESTION 3 In the diagram below, A(—3 ; 0), B, C and D(-8 ; 5) are the vertices of a quadrilateral with BCD = 105°. E(-11 ; 0) and F are points on the x-axis. ED is a straight line. FG || AD with G on ED. jy Cc 105° B DC-8 ; 5) G x E(-11 ; 0) F AC3;0) 9 3.1 Prove that the perimeter of A ADE, rounded off to TWO decimal places, is 20,90 units. 6) 3.2 It is given that F is the midpoint of AE. 3.2.1 Give a reason why G is the midpoint of DE. qd) 3.2.2 Hence, determine the coordinates of G. @) 3.2.3. Write down the length of FG. qd) 3.2.4 Determine the equation of FG. (4) 3.3 Calculate the size of DAO. (2) 3.4 It is given that ABCD is a cyclic quadrilateral and that the equation of CB is =12+5¥3 | 2445/3 nn a Determine the coordinates of B. oO) [23] Copyright reserved a oe a Please tui over

Downloaded from hlayiso.com Mathematics/P2 NW/September 2018 NSC QUESTION 4 4.1 Determine the equation of a circle with its centre at the origin in the Cartesian plane and with a radius of 24/3 units. Q) 4.2 A circle is defined by the equation x? -6x+y?-2y =6. 4.2.1 Rewrite the equation of the circle in the form (x-al +(y-bP =P? (2) 4.2.2 Write down the coordinates of M, the centre of the circle. (2) 4.2.3. Write down the length of the radius of the circle. qd) 4.2.4 — A tangent PQ is drawn from the point P(6 ; -2) to the circle, with Q the point of contact. Calculate the length of the tangent PQ. (4) 43 In the diagram below are two circles that touch each other externally in the point 20 95 C3). 13°13 The radius of circle A with centre A(-k; 5) is 6 units. The radius of circle B with centre B(2k ; 10) is 7 units. ACB is a straight line. y ACk;5) x 4.3.1 If k>0, prove that the gradient of AB is = (5) 4.3.2 Hence, or otherwise, determine the equation of the common tangent to the circles A and B. (3) [19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 7 NW/September 2018 NSC QUESTION 5 vk 5.1 Given: cos16°= ——. Without using a calculator, determine in the simplest form, the value of each of the following in terms of k and ft: 5.1.1 sin 106° (2) 5.1.2 sin 16° (3) 5.1.3 cos 8° (4) 5.2 Prove that: 4(1—cos8)(1+cos?) 1 sin 20 . cos@ @) 5.3 It is given that sin p+J3 cos p =1. 5.3.1 Show that the equation can be written as sin(60° + p) = ; (3) 5.3.2 Hence, determine the general solution of sin ptv3 cosp =1. (4) 54 Without using a calculator, determine the value of: cos 0° + cos 1° + cos 2° +... + cos 178° + cos 179° + cos 180° +2 (3) [23] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 NW/September 2018 NSC QUESTION 6 In the diagram below, the graphs of f(x) = cos(x+p) and g(x) = sinx+q are drawn on the same set of axes for - 240° < x <$180°. A(-150° 3-1) is a point on g. y 180 6.1 Determine the values of p and q. (4) 6.2 Determine graphically the values of x, for —240° < x < 180°, where 1 F(x) = g(x) + 5 (2) 63 Describe the transformation that the graph of J has to undergo to form the graph of h, where h(x) =—sinx. (2) [8] Copyright reserved Please turn over

Downloaded from hlayiso.com NW/September 2018 Mathematics/P2 NSC QUESTION 7 circle in a horizontal plane. pole in the vertical plane through C, elevation of E at A is f. A, B and C are three points on the circumference of a semi- AC is the diameter of the semi-circle. EC is a slanted forming an angle of @ with the vertical. The angle of BC x and ACB =a. SEN \ \ \ (2) x cosa Show that AC 7.1 (3) AEC in terms of 6 and /. Determine an expression for 7.2 (3) [3] x.sin B cos a.cos(Z~@) Prove that EC 73 Please turn over Copyright reserved

Downloaded from hlayiso.com Mathematics/P2 NW/September 2018 NSC Give reasons for your statements in QUESTIONS 8, 9 and 10. QUESTION 8 8.1 In the diagram below, A, B and C are points on a circle having centre O. DC is a construction line drawn through the centre O to the point C, Use the above diagram to prove the theorem which states that AOB = 2¢. (5) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 Il NW/September 2018 NSC 8.2 In the diagram below, the circle having centre O, passes through A, B, C and D, with AOB = 130°. EBFisa tangent to the circle at B with EF||AD. BOG is a straight line. E Calculate, with reasons, the size of: 8.2.1 D, (2) 8.2.2 B, (2) 8.2.3 BAD (1) 824 ¢ (2) 825 8B, (3) 8.2.6 Calculate the length of GD, if AD = ut units. (3) [18] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 NW/September 2018 NSC QUESTION 9 Two equal circles cut each other in A and C. BA and BC are tangents to one circle at A and C respectively and they are chords of the other circle. Eis a point on the circumference of one circle and AE produced cuts the other circle in D. Chords AE and CD are equal. Prove that: 9.1 ¢, =¢, (4) 9.2 C, =A, (3) 9.3 E is the centre of the circle that passes through A, C and D. (4) 9.4 AECD is equilateral. (2) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 13 NW/September 2018 NSC QUESTION 10 10.1 Complete the following theorem to make the statement TRUE: Ifa line divides two sides of a triangle in the same proportion, then the line is... (1) 10.2. Two circles with centres P and S touch each other externally at C. SP produced intersects circle P at B. A common tangent at R and Q meets SB produced at T. Prove that: 10.2.1 PQ\ISR (4) 10.22 P= cer ae ® 10.2.3. ATQP ||| ATRS (3) 2 2 1024 Js? leg? _ VTP? + BP 21 BPeos8) .CS 6 [18] TOTAL: 150 Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 14 NW/September 2018 NSC INFORMATION SHEET: MATHEMATICS =b+/b2 —4dac 2a A=P(l+ni) A=P(l~ni) A= P(-i)" A=P(+i)" T,=a+(n-ld S, =F pa+m—1a] T, =ar"" s, <=! pre S,= pcs ler <li po -r L t d= VX, =x)" +(¥2 -»)? mi yomxte Y-yY, =mM(x-x,) (x-a)’ +(y—b) =r? in ABC: 2-2 = © snA sinB sinC area AABC = > ab.sinC sin(a + 8) =sina.cos B + cosa.sin B i) cos(a + 8) = cosa.cos B —sin a.sin B cos? a —sin? @ . cos2a =41~2sin? a 2cos”? a —1 Copyright reserved poi") ‘y) = Him Let LO) X1 + Xq Jy t yo — > ne] v2 7M" n=——— XX, m=tan@ a? =b? 402 ~2be.cos A sin(a — 8) = sina.cos 8 —cosa.sin B cos(a - B) =cosa.cos # +sina.sin 8 sin 2@ = 2sina.cosa a 2 Xx, -x) oats n P(A or B) = P(A) + P(B) — P(A and B) p= eH -W) — Y@-3x