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1 Stud Guide COPYRIGHT RESERVED ANY UNAUTHORISED REPRODUCTION OF THIS MATERIAL IS STRICTLY PROHIBITED

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3 Our videos are available at : For a full list of the videos with links please look at the last page Educ8 tuition centre s would like to thank ou for our support. We have spent over a ear designing this product which we feel will improve students understanding in mathematics at the GR and GR level. This product is not meant to be used as a substitute for work covered at schools but rather as a compliment to work covered at school. Onus is on the student to ensure that the follow the instructions carefull and do all of the prescribed work before progressing on with further tutorials. Whilst ever effort has been made to ensure the accurac of this product, there ma still be errors as it is onl in its pilot phase, we apologize for an inaccuracies but accept no liabilit.

4 CONTENTS: PAPER : Eponents, logs and surds 5 Algebra 0 Functions 7 Calculus 8 Financial Maths Number patterns 5 Linear Programming 0 PAPER : Analtical Geometr Trigonometr 50 Transformations 59 Data handling 60

5 5 Eponents, logs and Surds Eponents Eponents, practice eamples : Break the following numbers into their simplest surd form: ) 96 ) ) 798 ) 8 5) 0 Eponents, Practice eamples : Simplif: ) 8. 6 ) 6 ) ( 5 ) ( ) 8 ) 8 5) 6. Solve for : ). ) ) 6 5 ) 0 8 5) 7 5

6 6 Eponents, eercise: Simplif the following: ) ) ( 8 ) ) n 7 5 ) n 08 n. n n 5) ( ) 6) ). 5 8) ) ) Solve for : ) 8 ) 9 ) 5) 5 6 ) 8 8 6) ( )( 8) ) 7 0 8) ( ) 5 5 9) 50 ( ) 0). 9

7 7 Eponents, Logs and Surds Logs Logs, Practice eamples : Simplif the following: ) log ) log 8 log8 ) log 6 log 8 ) log 7 5) log 8 Solve for : ) log ) log ) log 7 log 0 ) log log5 log 5) log 6 Simplif: Logs, eercise ) log 8 ) ) log 6 log 8 ) 5) log log log 5 6) 7) log 8 log 7 log 6 log log9 8) log 5 5 log8 log 7 log6 log9 log log 6 log 6 log log9 ( log5 log ) Solve for : ) log ) log ) log ) log 5) log 8 6) ( ) log 5 7) log log log( ) log 8) log log log ) log log 0) log 6 log

8 8 Eponents, Logs and Surds Cumulative ) 75 Simplif: Cumulative practice eamples : ) 8.(. ) ) 5) log log log 5 ) log log 5 log log5 Solve for : ). ) 6. a. a ( ) ) a ) log log 5) log ( ) log Cumulative eercise: Simplif: n n 8 ) n ) 8. ) ) ( 75 ) 5) n 6 9 n n n.5 n 5. 6) ( ) 7) log 6 log5 log 0 8) 7 log 9) log9 7 log 7 0) log log 5 log5 9

9 9 Solve for : ) ) ) 9 ( 7 ) 5). 0 ) ) 7) 7 log ( ) log 8) log5 9 9) log 7 log 0) 6 0 log

10 0 Algebra Basic factorization Factorize full: Algebra practice eamples ) ) ) a 6a ) 6 9 5) 8 9 6) 56 7) a b 8) 60 Algebra practice eamples Factorize full: ) 5 ) 9 6 ) 70 ) 9 5 Algebra eercise: Factorize full: ) 7 0 ) 5 ) 9 0 ) 0 5) 5 6) 0 7) ) 0 8 9) 0 0) 0

11 Algebra Quadratic formula and completing the square Algebra practice eamples Solve for unknown variable b completing the square: ) ) ) 7 0 ) 9 0 5) 0 0 Algebra practice eamples Solve for unknown variables b using the quadratic formula: ) 0 0 ) 6 0 ) ) ) 8 0 Algebra eercise: Solve, using an method: ) 7 0 ) 5 5 ) ) 0 5) 5 6) 05 7) 6 7 8) 0 8 9) 0 0) 0

12 Algebra Basic simultaneous ) 5 Algebra practice eamples Solve for unknown variables simultaneousl: ) ) ) z z 6 9 z 6 Solve for unknown variables: Algebra eercise: ) ) ) ) 5) z z z

13 Algebra 5 Dealing with fractions Algebra 5 practice eamples Solve for unknown variable: (Remember our LCD s) ) 9 6 ) 9 6 ) 6 ) 6)( ( ) ) ( 5) Algebra 5 eercise: Solve for unknown variable: ) ) ) ) 5)( ( ) 6) ( 6 5) 9

14 Algebra 6 Inequalities basic Algebra 6 practice eamples Find the value(s) of the unknown variables: 9 ) ) ) ) 9 ( ) 6 5) 6 Algebra 6 eercise: Find the value(s) of the unknown variables: 9 ) 8 ) ) ) ( ) ) 7

15 7 Functions Basic functions Functions practice eamples Using the tables provided, sketch the following functions: f f() ) ( ) ) g ( ) ) h ( ) 5 ) j( ) 0 h() j() 5) k( ) k() Sketch the following functions using an method B 6) A ( ) 7) ( ) 8) C( ) 9) D( ) 0) E( ) Functions practice eamples Think of possible scenarios to match the following functions: (Note that there is no one right answer, what I do on-screen is merel an illustration) 0 ) g ( ) 9 ) h ( ) 6 0 ) l( ) Functions eercise: g() Sketch the following: ) A ( ) 5 ) B( ) ) j( )

16 8 Functions Straight line Functions practice eamples Sketch the following functions: ) 9 8 ) 5 6 ) 5 ) 5) 6) 9 Functions eercise: Sketch the following: ) 5 ) 8 ) ) 5) 7 8 6) 5 8 7) 6 8) 5 Functions The parabola Functions practice eamples Sketch the following functions using steps: ) g ( ) ( ) ) f ( ) ( ) 8 ) j ( ) ( ) 8 ) k ( ) ( ) 5) h ( ) 8 6 Functions practice eamples Sketch the following functions using steps: 8 ) f ( ) ) g ( ) ) h ( ) ( 5 )( 6) ) l ( ) ( ) 5 k 5) ( )

17 9 Functions practice eamples ) b ( ) a( p) q (-;9) 7.) determine a, p and q.) find distance AB a b ) c ( ) a b c -.) determine a, b and c.) the other intercept.) the intercept (;-5) ) (p;q) 5 ( ) a( p) q h.) find a, p and q - ) 5 k().) determine the equation k().) can k() 0? (;)

18 0 Functions eercise: Sketch the following: ) f ( ) 6 ) g ( ) 6 5 k ) h ( ) ( )( 8) ) j ( ) ( 5) 5) ( ) 6) m( ) 5 Sketch the following: Functions Hperbola Functions practice eamples : 5 ) c( ) ) d ( ) ) e ( ) ) f ( ) Sketch the following: Functions eercise: ) f ( ) ) g ( ) 7 ) h ( ) ) j ( )

19 Functions 5 Eponential Sketch the following: f Functions 5 practice eamples ) ( ) ) g( ) ) h ( ) ) j ( ) Functions 5 practice eamples Sketch the following: ) log ) log ) 5 Functions 5 eercise 0 Sketch the following, indicating all intercepts with the ais: ) ( ) g ( ) ) ( ) log ) ( ) log f ) ( ) h j Function 6 Trigonometric graphs Functions 6 practice eamples : Sketch the following using the table/s provided: ) cos ) tan Sketch the graph of sin Functions 6 eercise:

20 8 Calculus Basic differentiation ) f ( ) Calculus practice eamples Differentiate using first principals: ) g ( ) 6 8 Differentiate using an method: ) ) f ( ) 6 8 6) g ( ) ) f ( ) 5 Calculus eercise: Differentiate using first principals: ) g ( ) 6 7 Differentiate using an method: ) 7 7 ) f ( ) 5 7) g ( ) 8 5

21 9 Calculus Long division, remainder & factor theorem Calculus practice eamples, solve for g() 0 ) If ( ) is a factor of g ( ) 0 ) Use the remainder theorem to find the remainder when f ( ) divided b h ( ) ) If f ( ) m 6 is divisible b: g ( ) 8 m? ) Solve for :.) g ( ) 0 0.) h ( ) 7 7 0, what is the value of is.) f ( ) 9 0.) k ( ) 0 Calculus eercise: Solve for : ) ) ) ) what is the remainder when ( ) 8 5 f is divided b g ( )

22 0 Calculus rd degree (cubic) graphs Sketch the following graphs: 7 ) g ( ) 7 ) h ( ) f Sketch the following graphs: 5 9 ) ( ) g ) ( ) Calculus practice eamples Calculus eercise:

23 Financial Mathematics Basic financial mathematics Financial Math Eercise ) What will the value of a R investment be in 5 ears time if interest is calculated at 6%p.a., simple interest? ) How much would ou have to invest toda to receive a paout of R in ten ears time if our investment would ield 8% p.a., simple interest? ) If interest is compounded annuall, after 0 ears, what would an investment of R ield if the interest rate is 7% p.a.? ) Assuming inflation to be a constant 7% p.a. what would our same investment be worth (of above)? 5) Interest is measured at 6% p.a., compounded monthl. How much should be invested to ield a paout of R in 5ears from now? 6) If we intend to settle an outstanding balance of R that is owed in 8months time, how much would we have to pa now to settle the amount? Assuming interest at 5% p.a., compounded monthl. Financial Maths, eercise: Financial Maths Timelines ) If we invest R00 toda, R800 in a ears time and R000 in two ears time, how much will we have at the end of 5ears if our investment earns an interest of 8% p.a. compounded annuall? ) A mother wishes to give each of her three kids a gift of R on each of their st birthdas. Her eldest kid is 8 ears old, the second is and the oungest is two. How much should she invest toda if the investment option available to her ields an interest rate of 6% p.a. compounded quarterl? ) We start an investment with an amount of R In a ears time we deposit a further R and another R in two ears time. If after ears we draw R50 000, what will our investment be worth at the end of 5ears if interest rate is % p.a. compounded twice earl? ) Of above, what would our investment be worth had we not withdrawn the R50 000?

24 Financial Maths Annuities and loans Financial Maths, Eercise ) If we deposit R00 monthl into an annuit paing out 7% p.a., compounded monthl, how much would we have at the end of 0 ears? ) Annual paments are made b a parent into a fund ielding 6% p.a., compounded earl. If the first pament is on the child s first birthda, how much would the fund be worth on the child s st birthda? ) Using the same scenario as above, imagine the child takes over paments at the age of and continues until their 65 th birthda, how much would the fund then be worth on their 65 th birthda? ) You take out a loan to bu a car costing R How much will our monthl repaments be over five ears if interest is calculated at % p.a. compounded monthl? 5) Using the same scenario as above, ou are able to put down a 5% deposit on the car. What will our new monthl repaments be? 6) If ou can afford a monthl repament of R000, with interest at % p.a., compounded monthl, what size loan ma ou be granted over a 0 ear period?

25 5 Number patterns Arithmetic sequences Number patterns, practice eamples : ) Determine the general solution of the following ; 6; 8.. ) Determine the general solution of the following: 9; 6; ; 0.. ) Of the series; 7; 9.5; ; what is the rd term? ) Of the series; 0; 9.7; 9.; what is the 7 th term? 5) Of the series; 5; 0; 5; 0; which term is 00? 6) Of the series; 66; 58; 50; which term is the first term that is less than zero? 7) If the first, second and third terms add up to 0 and the fourth term is 6, what is the first term, the common difference and the general solution? Number patterns, practice eamples : ) What is the sum of the first 0 terms of the series:? ) What is the sum of the first 800 terms of the series: ? ) How man terms of the series ; ; ; must be added to reach a total of 500? ) How man terms must be added in the series to reach a total of -600? 5) 5 is the sum of ten terms of the series z. Determine the values of, and z if the 7 th term is 8. ) i Number patterns, practice eamples : Determine the solution of the following: n n ) i 0 0 n 8 i i ) i ( i ) n 0 i ) 6i i

26 6 Number patterns, eercise : ) Determine the general solution of the series: 5; 7; 9; and the sum of 5 terms ) Determine the general solution of the following series: -5; -5; -0; and the sum of 0 terms ) What is the 0 th term of the series starting at -7, with a common difference of 8? And determine the sum of terms ) If the fourth term of an arithmetic series is, the siteenth term is 08, determine the 5 th term and the sum of 5 terms n 8 i 5) Solve: i ( i ) Number patterns Geometric sequences Number patterns, practice eamples : ) In the geometric sequence: ; ; 8; determine the general solution as well as the 0 th term. ) Of the series: 8; 7; 9; determine the general solution as well as the 9 th term. ) Consider the series: ; ; :.) What is the ratio?.) For which r values will the series diverge?.) For which r values will the series converge? ) Of the series: ; ;, which term is ? 5) How man terms in the series: ; ; 8; lie between 8 and 08?

27 7 Number patterns, practice eamples : n 8 ) Determine the solution of: i i i ) Determine the solution of: n 5 i 5 ) Of the series 5 5 how man terms need to be added to reach a total 9 of? 5 6 ) Consider the series: 6.) What is the sum of 0 terms?.) What is the sum of 00 terms?.) What is the sum of 000 terms?.) Is the series convergent or divergent? Number patterns, practice eamples : 6 ) Find the sum to infinit of the series: 6 ) Determine the solution of: i ) Determine the solution of: 5 Number patterns, practice eercise: i ) Determine the general solution of the series: ; 8; 56; and the sum of 0 terms i ) Determine the general solution of the following series: -8; 6; -; and the sum of 00 terms ) What is the 0 th term of the series starting at, with a common ratio of 8? And determine the sum of 5 terms ) If the fourth term of a geometric series is, the siteenth term is 08, determine the 5 th term and the sum of 5 terms i

28 8 n 5) Solve: 5 i i n 6) Solve: i 5 i Number patterns nd Difference: Number patterns, practice eamples : Consider the following sequence: 6; ; 8; ) determine the net two terms ) find the general solution Number patterns, eercise: ) Consider the following sequence: ; ; 9; 8; a) determine the net two terms b) find the general solution ) Consider the following sequence: 7; 5; ; -5; a) determine the net two terms b) find the general solution

29 0 Linear Programming Linear programming, eercise: ) A factor manufactures two tpes of beds, namel foams and springs ( and ). Suppose the factor manufactures according to the following constraints: The profit per foam () is R50 and R0 per spring (), a) Sketch the inequalities and determine the feasible region b) Determine the maimum profit function c) Find the point that maimizes profit d) Calculate the maimum profit ) According to a recommended diet plan, at least 0mg of vitamin A and 6mg of vitamin B must be taken dail. A tablet () contains mg of vitamin A and mg of vitamin B. A capsule () contains mg of vitamin A and mg of vitamin B. a) Determine the inequalities using the following table: vitamin A B Tablet () Capsule () Min req. 0 6 b) Sketch the inequalities and determine the feasible region c) What is the minimum amount of tablets one needs to take? ) A compan makes two tpes of chairs, X and Y. The compan onl has 00m² of storage space available. X requires.5m² of storage space and Y requires m². The compan can onl afford to invest R0 000 in equipment, costs are R0 per X and R80 per Y. Not more than 50 of Y ma be manufactured per da due to a glue dring process. Profit per X is R50 and R0 per Y. a) Determine and sketch the inequalities b) Find the feasible region c) Determine the objective profit function d) Determine the point that will ield the maimum profit e) Determine the maimum profit

30 Analtical Geometr Basics Analtical Geometr, practice eamples : ).) Determine the lengths A (;5) of BC, AB and AC.) Is ABC a right angle triangle with BC the α B (5;) hpotenuse? M.) What are the co-ordinates of C (-;0) M, the midpoint of BC?.) what is the value of angleα? ).) What is the value of δ?.) determine the co-ordinates of M, the midpoint of AB.) Determine the distance CM if AC BC A (-;) δ M C B (;5) ).) If PQ 8 units, and δ is 0, Q (a;b) determine the values of a and b. P δ R (c;d).) what would c and d s values have to be for PQR to be an equilateral triangle? Analtical Geometr, eercise: ) Sketch the following points on a cartesian plane: A(; 5); B(; -6); C(-5; ); D(-;-) ) Using the above sketched points, determine: a. The distances AB and CD b. The gradients of AC and AB and their respective angles of inclination c. Calculate the co-ordinates of E such that it is the midpoint of AD d. What is the gradient of EF if it is perpendicular to AD and goes through E

31 Analtical Geometr Equations and gradients Analtical Geometr, practice eamples ; ).) determine the length of AB B (5;6).) what are the co-ordinates of M M, the midpoint of AB.) Equation of AB.) Equation of perpendicular A (;) bisector through M ) P (a;) B (;).) Point P is equidistant from A and B. What is the value of a? A (-;-) Analtical geometr, eercise: ) Sketch the following points on a cartesian plane: A(; 5); B(; -6); C(-5; ); D(-;-) ) Using the above sketched points, determine: a. The equations of AB and CD b. The gradients of AC and AB and their respective angles of inclination c. Calculate the co-ordinates of E such that it is the midpoint of AD d. What is the equation of EF if it is the perpendicular bisector of AD ) Determine the co-ordinates of F such that it lies on the line BC as well

32 Analtical geometr Triangles: medians, midpoints and heights. Analtical Geometr, practice eamples : ) B (5;5).) Determine equation of AP if AP is a Median P.) Length of AP C (7;).) Is AP also a height of the triangle? A (-;-) ) A.) If AB AC, determine the equation of AD. (AD CB).) Is AD a median as well as a height? C (-;-) D B (;-) Analtical geometr, eercise: ) If the equation of ac is given b: 6, determine the co-ordinates of C and D such that CD is the median and height of Triangle ABC. A D B 0 C

33 Analtical Geometr Basic cumulative Analtical Geometr, Practice eamples : ) Given the points: P ( 6 ; 7 ), Q ( ; -7 ) and R ( ; a ).) Determine the length of PQ.) Determine the value of a if PQ PR ) OABC is a parallelogram (AB // OC and BC // OA) B (-;) Equation of OA given b: δ 5 A O δ C Determine:.) the equation of CB.) the equation of AB.) the co-ordinates of A and C.) distance of AC.5) size of angle AOC ) Determine: Q (;5).) value of b, the -co-ordinate of R.) co-ordinates of M, the midpoint of PR P(-;-) α O S M R ( ;b).) size of α (the angle RPQ).) co-ordinates of S such that PQRS is a rectangle. ) A (6;).) calculate the value of p such that C and B are equidistant from A C (p;).) Calculate the size of δ. δ B (;-)

34 R (-;a) 5) P (-;b) PQR is an equilateral triangle. PQ cuts the ais at QR cuts the ais at - Q (5;) M 5.) find values of a and b 5.) is QM a height of triangle? 5.) what are co-ordinates of M, the midpoint of PR? Analtical geometr, eercise: A ) The co-ordinates of the triangle are as follows: A (5;5), B(-7;), C (;-7) a. show that ABC is an isosceles triangle b. determine equation of AD, the perpendicular bisector of BC c. determine the equation of the line through A and perpendicular to AD. B D 0 C ) A (-;), B(-;-), C (;) are the vertices of a triangle. a. Determine the equation of the median BE b. Calculate BC c. Determine co-ordinates of D if ABCD is a parallelogram d. Prove that D is collinear to BE (i.e.: lies on the same line) A ^ ) Find the values of a and b if the equation of AB: and CB: What is size of angle ABC? A ( ;) B (a;b) C (7;) D 0

35 50 Trigonometr Basics Trigonometr, practice eamples : Solve for the following to two decimal places: ) sin 0 ) cos 80 ) tan 0 ) sin 50 5) cos 0 Solve for to two decimal places: ) sin 0.5 ) cos 0.5 ) tan 5 ) cos ) tan Trigonometr, practice eamples : Sketch the following on the same set of ais: ) 0 ) 0 ) 60 ) 0 5) 5 Trigonometr, practice eamples : ) ) 5) Sketch right-angled triangles for the following: sin δ ) cosδ tan α ) 8 tan 5 Trigonometr, eercise: sin β 5 Solve to two decimal places: ) sin 0º ) tan 7º ) cos 87º ) sin 58º 5) cos 875º 6) tan 55º 7) sin -97º 8) cos -70º Solve for to one decimal place: ) sin 57º ) cos 788º ) tan ) Sketch the following on a set of ais: 8 sinδ ) cosδ 6 ) tanδ

36 5 Trigonometr Reduction Trigonometr, Practice eamples : Reduce the following using the -reductions to acute angles: ) sin 50 ) cos 0 ) tan 0 ) cos 0 5) sin 90 6) sin 90 7) tan 65 8) tan 0 9) cos 6 Trigonometr, Practice eamples : Reduce the following using the -reductions to acute angles: ) sin 50 ) cos 0 ) tan 0 ) cos 0 5) sin 90 6) sin 90 7) tan 65 8) tan 0 9) cos 6 Trigonometr, Practice eamples : Reduce the following to acute angles: ) sin 6 ) tan 80 ) cos 5 ) tan 5 5) cos 0 6) sin -80 7) tan -6 8) cos -59 9) sin ) cos -500 Trigonometr, eercise: Reduce the following to acute angles: ) sin ) tan 75 ) cos ) tan 85 5) cos 65 6) sin -5 7) tan -87 8) cos ) sin -75 0) cos -

37 5 Trigonometr Special angles Trigonometr, practice eamples : Solve for the following without the use of the calculator: ) sin 90 ) tan 5 ) cos 0 ) tan 60 5) cos 0 Trigonometr, practice eamples : ) Solve for the unknown angles without the use of a calculator: cos δ ) tan δ ) cos δ ) 5) sin δ 0 sin δ Trigonometr, practice eamples : Solve for the following without the use of a calculator: ) sin 5 ) cos 00 ) tan 80 ) tan -0 5) sin -5 6) cos -750 Trigonometr, eercise: Solve for the following without the use of a calculator: ) sin 5 ) cos 90 ) tan 60 ) tan 0 5) sin 0 6) cos 50 7) cos 0 8) sin 50 9) tan -5 0) sin -50

38 5 Trigonometr Identities Prove the following identities: tan ( sin ) ) sin cos cos Trigonometr, practice eamples : cos sin cos ) sin sin.cos cos ( sin ) tan ) cos sin sin cos cos cos cos ) ( tan )( tan ) 5) sin.cos cos.sin sin 6) cos sin tan cos.sin cos Trigonometr, eercise: Prove the following identities: tan sin cos tan sin ) ( ) ) cos ( 80 ) tan sin ( 90 ) cos( 90 ) ( 80 ) tan ) sin sin tan ( sin ) ) sin tan cos cos cos cos sin cos

39 5 Trigonometr 5 General solution Trigonometr 5, practice eamples : Find the general solution for the following: ) sin δ 0. 5 ) cosδ ) tan δ ) sinδ. 8 5) sin δ cosδ 6) 5 tanδ cosδ cosδ Trigonometr 5, practice eamples : Find the general solution for the following: ) sin cos ) sin cos( 60 ) ) cos sin( 50 ) ) 6sin sin Find the general solution: Trigonometr 5, eercise: ) cos δ ) sinδ ) tan δ. 5 ) cos sin( 5 ) 5) sin sin 6) tan 0 tan

40 55 Trigonometr 6 Trigonometric graphs Trigonometr 6, practice eamples : Sketch the following graphs for the period E { 60 ; 60 } ) a) sin b) sin c) sin d) sin ( 0 ) ) a) cos b) cos c) cos d) cos ( 0 ) ) a) tan b) tan c) tan d) tan ( 0 ) Trigonometr 6, practice eamples : Sketch the following on the same set of ais: ( ) sin and g ( ) cos( 0 ) f Trigonometr 6, practice eamples : Using the graphs f() and g(), determine: ) Points of intersection ) values for which f() g() ) values for which f() g() ) values for which f() is increasing while g() is decreasing Trigonometr 6, practice eamples : On the same set of ais, for the period E { ; 80 } f ( ) sin( 5 ) and g( ) cos 80, sketch the graphs: Using the graphs determine: ) values for which f() g() ) values for which f() g() ) values for which f() is increasing while g() is decreasing Trigonometr 6, eercise: 80 ; 80, sketch the graphs: cos 0 g sin On the same set of ais, for the period E { } f ( ) ( ) and ( ) Using the graphs determine: ) values for which f() g() ) values for which f() g() ) values for which f() is increasing while g() is decreasing

41 59 Transformations Transformations. Sketch the following transformations: ) ( ; ) ( ; ) ) ( ; ) ( ; -) ) ( ; ) ( ; ) ) ( ; ) (- ; ) 5) ( ; ) ( ; ) 6) ( ; ) ( ; ) Transformations, practice eamples : D(-;5) O A (;) D (-;-) C (8;-) Transformations, practice eamples : Sketch the following rotations and determine new co-ordinates: ) 90 clockwise ) 80 clockwise ) 70 clockwise P (;5) Q(;) O R (;) Transformations, practice eamples : Consider the following sketch with co-ordinates: A (0 ; ), B ( ; ), C (- ; 0) and D (-; ) Find co-ordinates of A B C D if figure: ) rotated 90 clockwise ) rotated 90 anticlockwise D ) rotated 80 ) rotated 60 clockwise 5) rotated 60 anticlockwise 6) What are co-ordinates of A B C D if figure is rotated 90 clockwise then enlarged b a factor of? C 7) Is the transformation from ABCD to A B C D rigid or not? 8) Write down the general transformation of ABCD to A B C D 9) What is the ratio of the area of A B C D : ABCD A O B

42 60 Data Handling Basic data analsis Data handling, practice eamples : ) Of the following set of data, determine the Mean, median and mode and sketch the Bo and Whisker plot diagram: Which measure of central tendenc is better? ) The following are running times of learners in a particular class, calculate the mean and variance of the data: There is no eercise for this section.

43 EXPONENTS ALGEBRA FUNCTIONS lphqj7wds

44 CALCULUS FINANCIAL MATHS