MIND ACTION SERIES. MATHEMATICS PRACTISE EXAMINATION (Original Paper set up by Mark Phillips) GRADE 12 PAPER 2 OCTOBER 2016 TIME: 3 HOURS MARKS: 150

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1 1 MIND ACTION SERIES MATHEMATICS PRACTISE EXAMINATION (Original Paper set up by Mark Phillips) GRADE 1 PAPER OCTOBER 016 TIME: 3 HOURS MARKS: 150 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 10 questions.. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 4. Answers 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 nongraphical), unless otherwise stated. 8. An INFORMATION SHEET with formulae is included at the end of the question paper. 9. Write neatly and legibly.

2 QUESTION The following table gives the frequency distribution of the daily travelling time (in minutes) from home to work for the teachers at Kutlwanong. Daily travelling time (x) in minutes Midpoint of class interval Frequency (no of teachers) 0 x x x x x Calculate the estimated mean time Calculate the estimated standard deviation for the time. () () 1. An ogive was constructed from the given data Construct a box-and-whisker plot on the scaled axes below the ogive curve to summarise the data. Show on the ogive (by means of dotted lines), where you have read off the data required for the box-and-whisker. Use the diagram provided in the ANSWER BOOK. 1.. Is the data positively or negatively skewed? Provide a reason. () [10]

3 3 QUESTION Mr Matsibela is retired and he supplements his pension by mowing lawns for customers who live in his neighbourhood. As part of a review of his charges for this work, he measures the approximate areas (x) in m of a random sample of 1 lawns and notes the time (y) in minutes, that it takes him to mow these lawns. His results are shown in the table below. Area (x) ( m ) Time (y) (minutes) Use your calculator to determine the equation of the least squares regression line. Give your answers correct to 4 decimal digits.. Calculate the value of r, the correlation coefficient for the data, correct to 4 decimal digits..3 Given that Mr Matsibela charges a flat call out fee of R150, as well as R50 per half hour (or part thereof), estimate the charge for mowing a customer's lawn that has an area of 560 m. (For example: 100 minutes would be taken as hours) () [9]

4 4 QUESTION 3 In the figure below, ABCD is a parallelogram with vertices A(0 ;1), B( ; 4), C(8 ;1) and D( k ; 6). AF is perpendicular to BC and parallel to CG. E is the point of intersection of the diagonals of ABCD. D( k;6) A(0 ;1) E C(8;1) G( p;0) B( ; 4) Determine: 3.1 the length of BC in simplest surd form. 3. the gradient of BC 3.3 the equation of AF 3.4 the coordinates of E 3.5 the value of k 3.6 the value of p 3.7 the size of rounded off to two decimal places. () () () () () (6) [17]

5 5 QUESTION 4 A circle with equation x y 8x 9 cuts the y-axis at P and Q. and has its centre on the x- axis at M. RPS is a tangent to the circle at P and cuts the x-axis at R. SM is joined. S( a; b) 4.1 Determine the coordinates of M. 4. Determine the length of PM. 4.3 Determine the equation of the tangent to the circle at P. 4.4 Calculate the area of PRM rounded off to two decimal places. 4.5 If PS 5 units, calculate the value of a and b. (5) (5) (6) [0]

6 6 QUESTION If tan 3 and 0 180, determine, without using a calculator, the value of sin( ) (5) 5. Prove the following identity: cos sin 1 sin 1 sin 5.3 Determine, without using a calculator, the general solution of the equation: cos(90 x) tan 495. cos( 10 ) (6) 5.4 Given: f ( x) tan( x 45 ) For which values of x will f ( x ) be undefined? () 5.4. Prove, without using a calculator, that sin x cos x tan( x 45 ) sin x cos x (5) Hence show that tan [6] QUESTION 6 Given: f ( x) cos x and g( x) sin x for the interval 180 x Sketch the graphs of y f ( x) and y g( x) on the set of axes provided in the ANSWER BOOK for the interval 180 x If the graph of f is shifted 30 left, write down the equation of the new graph formed. 6.3 If the graph of g is reflected in the x-axis and then shifted unit down, write down the equation of the new graph formed. 6.4 Determine graphically the values of x for which f ( x). g( x) 0 () [8]

7 7 QUESTION In ABC shown below, Ĉ1 150 and BC,61 cm. In ADC, CD 5 cm and AD 13 cm. The area of ABC 6,46 cm Calculate the length of AC to the nearest whole number Calculate the size of Ĉ to the nearest degree. () () 7. In the diagram below, a flag pole of length 5 metres is leaning at 10 to the vertical line AB. EF is drawn parallel to BA and meets CA at F. An observer at C notes that the angle of elevation of E, the top of the flag pole, is 5. Another observer stands at D, which is in the same horizontal plane as C, F and A. In CDF, CDF ˆ 78 and CD 10 metres and CFD ˆ Show that CF 11 m (rounded off to the nearest whole number) [11]

8 7.. Calculate the size of to the nearest degree. QUESTION In the diagram below, O is the centre of the circle passing through A, B and C. Use the diagram provided in the ANSWER BOOK to prove that theorem which states that the angle subtended by an arc at the centre of the circle is twice the angle subtended by the same arc at the circumference of the circle. (6) 8. In the diagram below, O is the centre of the circle passing through A, B, D and C. AB CD and BOD is an equilateral triangle Why is Ĉ 30? 8.. Why is  30? 8..3 Calculate, with reasons, the size of Ê Calculate, with reasons, the size of ˆF 1. () () () [13]

9 9 QUESTION CD is a tangent to circle ABDEF at D. Chord AB is produced to C. Chord BE cuts chord AD in H and chord FD in G. AC FD and chord FE chord AB Why is D ˆ ˆ 1 D3? 9.1. Prove that D ˆ ˆ D Prove that BCDH is a cyclic quadrilateral. 9. In ABC, BS SE, SD AEFC and BE DF Prove that EF : FC :1 (5) [17]

10 Prove that QUESTION 10 DC BD DF BS In the diagram below, ED is a diameter of the circle centre O. ED is extended to C and CA is a tangent to the circle at B. AO intersects BE at F. BD AO, OD DC and Ê x Write down, with reasons, three angles equal to x. 10. Why is AEOB a cyclic quadrilateral? 10.3 Why is OB a tangent to the circle passing through A, F and B? 10.4 Express ˆB 1 in terms of x Prove that F is the midpoint of BE Prove that AB BC Prove that CBD CEB Prove that EF.CB CE.BD () () [19]

11 11 TOTAL MARKS: 150