WTS TUTORING WTS TERM: 2 CAMP GRADE : 11 : PROF KWV KHANGELANI SIBIYA : WTS TUTORS CELL NO. : :

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1 1 WTS TUTORING WTS TERM: 2 CAMP GRADE : 11 COMPILED BY : PROF KWV KHANGELANI SIBIYA : WTS TUTORS CELL NO. : FACEBOOK P. : kwvsibiya@gmail.com : WTS MATHS & SCEINCE TUTORING

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4 4 QUESTION 4 The equations of h and p are given by: 1 h ( x) 2 and p ( x) 4 x 2 x Write down the x and y asymptotes of h. (2) 4.2 Determine the x and y intercepts of h. (3) 4.3 Determine the x and y intercepts of p. (3) 4.4 Write down the equation of the asymptote of p. (2) 4.5 Sketch the graphs of h and p on the same set of axes provided. Indicate ALL intercepts with the axes and asymptotes clearly and name your graphs. (6) QUESTION 5 Consider the following functions; g(x) = 3 1 x 2 h(x) = State the x and y intercepts of g. 5.2 Write down the y asymptote of h. 5.3 State the range for g 5.4 Sketch both graphs on the system of axes provided.

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11 11 QUESTION 3 The graphs of ( ) and ( ) are drawn below: intersects at S and T, and f passes through the origin O. 5 T (-1; 3) is the turning point of f. P and Q( ;0) are x-intercepts of f and g 2 respectively and R is the y-intercept of g. y g R S P O x f 3.1 Determine the values of m and c and hence the length of OR. (3) 3.2 Determine the values of a and b and hence the length of OP. (6) 3.3 Calculate the co-ordinates of S. (3) 3.4 Write down the range of f. (2) 3.5 Use your graphs to solve for x where: ( ) 0 (2) f is decreasing (1) f ( x) g( x) 0 (2) g ( x) 0. (1) 3.6 For which values of k will f ( x) k have equal roots? (2)

12 x= -1 WTS TUTORING 12 QUESTION The sketch below shows the sketch of; f(x) = ax 2 + bx + c, with the line of symmetry x = 1 g(x) = k ; x < 0 x and the line y = 2. The curves of f and g and the line y = 2 intersect at A Write down the co-ordinates of A. (1) Show that a = 2, b = + 4 and c = 2 (4) Determine the equation of g. (3) Write down the equations of the line of symmetry of g. (2) For what values of x is f increasing? (1) Determine the average gradient on the curve of f between x = 1 and x = 0 (2)

13 If the graph of f is shifted 2 units to the right and 3 units down, write down the equation of the new graph. (2) 4.2 Given y = 2 x 2 + 8x + 10 and y = 2 x Determine the x and y intercepts of y = 2 x 2 + 8x + 10 (4) Sketch both graphs on the system of axes provided. (6) Determine the coordinates of the points of intersection of the two graphs. (2)

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21 21 QUESTION If tan, and 180 o < < 270 o, determine with an aid of a sketch the 4 value of: sin θ (3) cos (180 o + θ) (2) θ (answer to 2 decimal places). (2)

22 Simplify, without the use of a calculator: 2 o o 1 tan.cos.cos 360. tan 225 o o o sin90 sin 180 sin90 cos(90 ) (6) 3.3 Consider the functions below: f(x) = sin 2x and g(x) = cos (x + 60 o ) Draw a neat sketch of the curves of f and g for on the axes provided on the diagram sheet. Clearly indicate the intercepts with the axes. (6) Write down the range for g (1) Write down the period of f (1) For which value(s) of x is the graph of g decreasing. (2) 3.4 Determine the general solution of the equation: 2 sin 2 x 5 sin x = 3 (5) 3.5 Prove the following identity: 1 cosa sin A 2 sin A 1 cosa sin A (5)

23 23 QUESTION FOUR 4.1 Prove for any acute angled ABC that: c sinc a sin A A D c b B a 4.2 Complete: In any ABC: Area of ABC = 1 ab. 2 C (4) 4.3 The figure consists of a rectangle KLMN and NMP. The area of pentagon KLMPN is 63 square units. KN = 6 units, NM = 8 units and NP = 7 units. K L 6 N 8 M S P Determine the area of NMP (2) Calculate the size of acute M Nˆ P. (3) If MS is drawn to meet NP at S and SM = 5,2 units, calculate N ŜM. (3) 4.4 Given PQR, with PQ = 140 mm, QR = 123,4 mm and PR = 199,2 mm. Calculate the size of the largest angle of PQR. (4)

24 24 QUESTION THREE 3.1 If 3 sin θ = 2 and cos θ 0, with the aid of a sketch calculate the value of tan 2 θ. 5 cos θ. (5) Leave your answer in surd form cos (180 o θ). (2) Leave your answer in surd form θ. (2) 3.2 If tan 20 = m determine the following in terms of m without the use of a calculator sin 70 (3) tan sin (3) 3.3 Simplify, without a calculator: o 2 sin(360 x ). 1 cos x o o 3sin(90 x).cos( 180 x) (5) o o o tan150.cos10 sin o o o sin80.cos225 sin135 (5) 2sin x cosx tan x 3.4 Prove that: tan x 2 2 cos x sin x (5) 3.5 Determine the general solution for 2 sin 2 x - sin x = 0. (7)

25 25 QUESTION FOUR 4.1 Sketch the following graphs on the same system of axes provided on Annexure A. Show clearly the intercepts with the axes and the turning points. g( x) sin3x and h ( x) cos( x 30 o ) o o for x [ 90 ; 120 ] (8) 4.2 State the period of g(x). 4.3 For which values of x is g(x) h(x) 4.4 If A and B are two points on g(x) and h(x) respectively, determine the length AB at x = 90.

26 26 QUESTION FIVE are drawn below for the domain x 0 ; 360 f ( x) tan ax and g( x) bsin x 2 1 g(x) P (120 o ; ) 0,5 120 o 90 o 60 o 30 o O 90 o 180 o 270 o 360 o x 0,5 1 g(x) Q Determine the values of a and b. (4) 5.2 For what value(s) of x is f undefined if 0 ; 360 x? (1) 5.3 State the range for g(x). (2) 5.4 If P(120 ; ) is a point of intersection of both the graphs and P and Q are symmetrical find the co-ordinates of Q. (2)

27 27 MERCY!!!!! WHERE TO START MATHS AND SCIENCE TUTORING Where to Start Maths and Science tutoring is aiming at assisting learners with understanding of basic skills for Maths and Sciences and also changes the stigma of learners towards Maths and Science subjects, we also help Schools around the country TO: LEARNERS JOIN US ON WHATSAP GROUP: WTS VISITING SCHOOL PROGRAM DAYS SUBJECTS TIME : FRIDAYS, SATURDAYS & SUNDAYS : MATHS, MATHS LIT AND PHYSCS : ANY TIME AND EVEN CROSSNIGHTS BOOK US ON : WTS PRIVATE CLASSES PLACE : RICHARDS BAY ARBORETUM GRADES : 8 TO 12 WTS SATURDAY & SUNDAYS CLASSES LEARNERS FROM DIFFERENT SCHOOLS ARE ALLOWED TIME : 09:00 TO 12:00 SUBJECTS : MATHS & SCIENCES

28 VENUE GRADE 12 GRADE 10 & : SIPHUMELELE SCHOOL [MZINGAZI RESERVE] : SUNDAYS : SATURDAYS WEEKDAYS: PRIVATE CLASSES MONDAY TO THUERDAY TIME : 17:30 TO 19:00 SUBJECTS : MATHS & SCIENCES WTS FINISHINING SCHOOL PLACE SUBJECTS : KZN RICHARDS MZINGAZI : MATHS, PHYSCS, ACCOUNTING & LIFE SCIENCES TIME : 15:00 TO 16:30 ACCOMMODATION IS AVAILABLE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ACKNOWLEDGEMENTS DEPARTMENT OF EDUCATION PAST PASTS ANY EDITIONS AND COMMENTS ARE ALLOWED I THANK YOU!!!!!!!!!!!!!! NB: WE CONDUCT CROSSNIGHTS AND CAMPS PER TERM WHERE TO START MATHS & SCIENCE IS FOR THE NATION