CAMI Education linked to CAPS: Mathematics. Grade The main topics in the FET Mathematics Curriculum NUMBER

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1 - 1 - CAMI Eucatio like to CAPS: Grae 1 The mai topics i the FET Curriculum NUMBER TOPIC 1 Fuctios Number patters, sequeces a series 3 Fiace, growth a ecay 4 Algebra 5 Differetial Calculus 6 Probability 7 Eucliia geometry a Measuremet 8 Aalytical Geometry 9 Trigoometry 10 Statistics

2 - - CAMI Eucatio like to CAPS: Grae 1 TOPIC 1. Patters, sequeces, series GRADE 1_Term 1 CONTENT 1. Number patters, icluig arithmetic a geometric sequeces a series.. Sigma otatio 3. Derivatio a applicatio of the formulae for the sum of arithmetic a geometric series: S = (a + ( 1) ) S = ( a + l) a( r 1) S = ; r 1 r 1 a S = ; 1 < r < 1; r 1 r 1 CAMI KEYS Fuctios 1. Defiitio of a fuctio.. Geeral cocept of the iverse of a fuctio a how the omai of the fuctio may ee to be restricte (i orer to obtai a oe-o-oe fuctio) to esure that the iverse is a fuctio. 3. Determie a sketch graphs of the iverses of the fuctios efie by: y = ax + q; y = ax x y = b ; b > 0; b 1 Focus o the followig characteristics: Domai a rage, itercepts with the axes, turig poits, miima, maxima, asymptotes (horizotal a vertical), shape a

3 - 3 - CAMI Eucatio like to CAPS: Grae Fuctios: Expoetial a Logarithmic 1.3 Fiace, growth a ecay symmetry, average graiet (average rate of chage), itervals o which the fuctio icreases/ ecreases. 1. Revisio of the expoetial fuctio a the expoetial laws a graph of the x fuctio efie by: y = b, for b > 0 e b 1.. Uersta the efiitio of a logarithm: y y = log x x = b, for b > 0 a b 1. b 3. The graph of the fuctio efie y = log x for both 0 < b < 1 a b > 1. b 1. Solve problems ivolvig preset a future value auities.. Make use of logarithms to calculate the value of, the time perio, i the equatios: A 1+ i) of A 1 i) 3. Critically aalyse ivestmet a loa optios a make iforme ecisios as to best optio(s) (icluig pyrami schemes) Trigoometry Compoue agle ietities:

4 - 4 - CAMI Eucatio like to CAPS: Grae Trigoometry cotiue 1.1 Fuctios: Polyomials cos( α ± β ) = cosα cos β m siα si β si( α ± β ) = siα cos β ± cosα si β si α = siα cosα cos α = cos α si α cos α = cos α 1 cos α = 1 si α GRADE 1_ Term 1. Solve problems i two a three imesios. Factorise thir egree polyomials. Apply the remaier a factor theorems to polyomials of egree at most three (o proofs require) Differetial calculus 1. A ituitive uerstaig of the limit cocept, i the cotext of approximatig the rate of chage or graiet of a fuctio at a poit.. Use limits to efie the erivative of a fuctio f at ay x : lim f ( x + h) f ( f '( = h 0 h Geeralize to fi the erivative of f at ay poit x i the omai of f, i.e. efie the erivative fuctio f '( of the

5 - 5 - CAMI Eucatio like to CAPS: Grae 1 fuctio f (. Uersta that f '( a) is the graiet of the taget to the graph of f at the poit with x -cooriate a. 3. Usig the efiitio, fi the erivative, f '( for a, b a c costats: f ( = ax f ( = ax + bx + c a f ( = ; x 0 x f ( = c Use the formula ax = ax 1 ( ) ; R x Together with the rules: [ f ( ± g( ] = [ f ( ± [ g( x x x [ kf ( ] = k [ f ( ]; k costat x x 5. Fi equatios of tagets to graphs of fuctios Itrouce the seco erivative f ''( = [ f '( ] va f ( x a how it etermies the cocavity of a fuctio. 7. Sketch the graphs of cubic polyomial fuctios usig ifferetiatio to etermie the cooriate of the statioary poits, a poits of iflectio (where cocavity chages). Also, etermie the x -itercepts of the graph usig the factor theorem a other

6 - 6 - CAMI Eucatio like to CAPS: Grae 1 techiques. 1.8 Aalytical Geometry 1.7 Eucliia Geometry 8. Solve practical problems cocerig optimizatio a rate of chage, icluig calculus of motio. 1. The equatio ( x a) + ( y b) = r efies a circle with raius r a cetre ( a ; b).. Determiatio of the equatio of a taget to a give circle. GRADE 1_Term 3 1. Revise earlier work o the ecessary a sufficiet coitios for polygos to be similar.. Prove (acceptig results establishe i earlier grae): that a lie raw parallel to oe sie of a triagle ivies the other two sies proportioally (a the mipoit theorem as a special case of this theorem). that equiagular triagles are similar. that triagles with sies i proportio are similar; a

7 - 7 - CAMI Eucatio like to CAPS: Grae Statistics (regressio a correlatio) Revisio Examiatio the Pythagorea Theorem by similar triagles. 1. Revise: epeat a iepeet evets; the prouct rule for iepeet evets: P ( AeB) P( B) the sum rule for mutually exclusive evets A a B : P ( AofB) + P( B) the ietity: P( AofB) B) P( AeB) the complemetary rule: P( ie = 1 P(. Probability problems usig Ve iagrams, trees, two-way cotigecy tables a other techiques (like the fuametal coutig priciple) to solve probability problems (where evets are ot ecessarily iepeet). 3. Apply the fuametal coutig priciple to solve probability problems. GRADE 1_Term

Mathematics 1 Outcome 1a. Pascall s Triangle and the Binomial Theorem (8 pers) Cumulative total = 8 periods. Lesson, Outline, Approach etc.

Mathematics 1 Outcome 1a. Pascall s Triangle and the Binomial Theorem (8 pers) Cumulative total = 8 periods. Lesson, Outline, Approach etc. prouce for by Tom Strag Pascall s Triagle a the Biomial Theorem (8 pers) Mathematics 1 Outcome 1a Lesso, Outlie, Approach etc. Nelso MIA - AH M1 1 Itrouctio to Pascal s Triagle via routes alog a set of