Mathematics Grade 12 P2 North West Mock 2016 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 BO ee ee ae Ge a eed he apc en rd # — MATHEMATICS P2 __ * ss SEPTEMBER 2016 i. 2 ‘ AS MARKS: 150 TIME: 3 hours This question paper consists of 9 pages, 1 information sheet and a 20-pages answer book.

Downloaded from hlayiso.com Mathematics/P2 2 NW/September 2016 NSC 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 that you used to determine the answers. 4. Answer only will NOT necessarily be awarded full marks. 5. If necessary, round off answers to TWO decimal places, unless stated otherwise. 6. Diagrams are NOT necessarily drawn to scale. 7. ‘You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. 8. An INFORMATION SHEET with formulae is included at the end of the question paper. 9. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 QUESTION 1 A Mathematics teacher wants to create a model by which she can predict a learner’s 3 NSC final marks. She decided to use her 2015 results to create the model. NW/September 2016 Preparatory | 55 | 35 | 67 |85|91| 48 | 78 | 72 | 15 | 75 | 69|37 exam (x) ana 57 | 50 | 74 | 80}92] 50 | 80 | 81 | 23 | 80 | 75} 42 gl Determine the equation of the least squares regression line in the form y=atbx. 1.2 Use the equation of the regression line to predict the final exam mark for a learner who attained 46% in the preparatory examination. 1.3 Could you use this equation to estimate the preparatory exam mark for a learner who attained 73% in the final exam? Give a reason for your answer. 1.4 Show that the point (x ; y) lies on the regression line. 1.5 Determine the correlation coefficient of the data. 1.6 Describe the correlation between preparatory and final exam results. QUESTION 2 G3) (2) Q) @) qd) (2) {14] The table below shows the results from a survey of cellphone expenditure for 100 learners from a secondary school in Rustenburg. Expenditure (in rand) | Frequency Cumulative frequency 50 < x <100 24 100 < x <150 52 150 < x <200 14 200 < x <250 a 250 < x <300 4 21 Determine the value of a. 2.2 Complete the cumulative frequency table in the ANSWER BOOK. 2.3 Draw an ogive (cumulative frequency graph) for the data. 24 What is the modal class for the data? Copyright reserved q) (2) (3) qd) [7] Please turn over

Downloaded from hlayiso.com Mathematics/P2 4 NW/September 2016 NSC QUESTION 3 In the diagram below, A(4 ; 5) , B(-3 ; -2 ) and C(6 ; —5) are the vertices of AABC. AD is drawn perpendicular to BC. 3.1 3.2 3.3 3.4 3.5 3.6 y Z A(4; 5) BC-3 ; -2, Calculate the length of BC. Determine the equation of BC. Determine the equation of AD. Determine the coordinates of D. Calculate the size of B AD 7 CO ;-5) (2) (3) (3) 3) (5) Calculate the coordinates of a point E if the area of AEBC = area of AABC and E is a point on the positive x axis. Copyright reserved (4) [20] Please turn over

Downloaded from hlayiso.com Mathematics/P2 > NW/September 2016 NSC QUESTION 4 In the diagram below, O(0; 0) and N(2; y) are two points on the circumference of a circle with centre M(4 ; 2). The tangents at O and N meet at R. Jy | NQsy R -M(4; 2) > (0) x 4.1 Determine the equation of the circle. (3) 42 Calculate the value of y (4) 4.3 Determine the equation of OR. (3) 4.4 — Calculate the coordinates of R. (6) 4.5 Determine, with a reason, the type of quadrilateral represented by MNRO. (2) [18] QUESTION 5 0 -t ° — x). sin2(90° — : 5.1. Determine the value of cos(180°+ x) an(360 2).sin (00° =) + sin? x (6) sin(180° — x) 52 5.2.1 Prove the identity: cos(A —B) — cos(A + B) = 2sin A sinB (3) 5.2.2 Hence calculate, without using a calculator, the value of cos 15° — cos 75° (4) 5.3 Find the value of tan 0, if the distance between A(cos 6 ; sin 0) and B(6 ; 7) is 86. (4) (17] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 6 NW/September 2016 NSC QUESTION 6 Consider: f(x) = cos(x— 45°) and g(x) = tan x for xe [-180° ; 180°] 6.1 Use the grid provided to draw sketch graphs of f and g on the same set of axes for xe [-180° ; 180°]. Show clearly all the intercepts on the axes, the coordinates of the turning points and the asymptotes. (6) 6.2 Use your graphs to answer the following questions for xe [—180° ; 180°] 6.2.1 Write down the solutions of cos(x — 45°) =0 (2) 6.2.2 Write down the equations of asymptote(s) of g. (2) 6.2.3 Write down the range of f. (1) 6.2.4 How many solutions exist for the equation cos(x — 45°) = tan x u 6.2.5 For what value(s) of xis f(x).g(x) >0 (3) [15] QUESTION 7 In the diagram below, ABCD is a cyclic quadrilateral with DC = 6 units, AD = 10 units, ADC = 100° and CAB = 40° _ Calculate the following, correct to ONE decimal place: 7A The length of BC (6) 72 The area of AABC (3) [9] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 7 NW/September 2016 NSC Give reasons for ALL statements in QUESTIONS 8, 9 and 10 QUESTION 8 8.1 Complete the following statement: 8.1.1 The angle subtended at the circle by a diameter is «0.0.0.4... qd) 8.1.2 The angle between a tangent to a circle and a chord drawn from the point of contact is equal tO... eects qd) 8.2 In the diagram below, ED is a diameter of the circle with centre O. ED is produced to C and CA is a tangent to the circle at B. AO intersects BE at F. BD||AO. Let E =x Cc 8.2.1 Write down, with reasons, THREE other angles each equal to x. (6) 8.2.2 Determine, with reasons, CBE interms of x. (3) 8.2.3. Prove that F is the midpoint of BE. (4) 8.2.4 Calculate the length of the diameter if it is further given that EB =8cm and OF =3 cm. (4) [19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 8 NW/September 2016 NSC QUESTION 9 In the diagram below, CE is a common chord of the circles ACE and CBDE. CD is a tangent to circle ACE at C and AEH is a tangent to circle CBDE at E. ACB and BDH are straight lines. AC =ED. 9.1 Prove that AB||ED. (5) 9.2 What type of quadrilateral is ACDE? Give reasons. (2) 9.3 Prove that af = BE (4) CB EA {11] QUESTION 10 10.1 In the diagram alongside, AABC and ADEF are given. Prove the theorem which states that: A If A=D, B=E andC=F hen ee DE DF E F Cc B Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 9 NW/September 2016 NSC ) 10.2 In the diagram below, PQRS is a cyclic quadrilateral. PS and QR are produced to meet at T. RE is a tangent to the circle at R, with E on PT and RE | Qs. Prove that: 10.2.1 QR = RS (4) 10.2.2 ARST ||| APQT (4) 10.2.3 EOE SE (5) PT ET [20] TOTAL: 150 Copyright reserved Please turn over

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Downloaded from hlayiso.com Mathematics/P2 NW/September 2016 NSC INFORMATION SHEET pe bt Vb? —4ac 7 2a A=P(i+ni) A=P(l-ni) A=P(-i)" A= P(1+i)" T,=at+(n-ld_ S, = 5a +(n-1a] ¢7 pl l-r eee ali)" -1| p-alna+)") L t fat+h)- fa) Oe) =i Fe) 30 h xX, +x. y, +y. d=y (x, -x,)7 +0, -9,)7 M| 12-1 2 2 2 y=mx+e y-y, =m(x-x,) m=22 1 m=tand 02) acs (x-a) +(y-by =r In AABC: = = a = a a? =b2 +¢7 ~2be.cos A sinA sinB_ sinC area AABC =F absin€ sin(a + B) = sina.cos B + cosa.sin B sin(a — 8) = sina.cos B — cosaz.sin B cos(a+ B)=cosa.cos # -sina.sin B cos(a— 8) = cos@.cos # + sina.sin B cos’ a@—sin’ @ cos2a@=41—2sin? a sin 2@ = 2sina.cosa@ 2cos* a-1 - Dre > Xx, -x) x= et o = ___ n n n(A) P(A)= AS) P(A or B) = P(A) + P(B) — P(A and B) n x-x\(y-y jsatbe pau! \o-y) Si@-x)y Copyright reserved