- 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
- - 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 4.1.6.1 4.1.6. 4.1.6.3 4.1.6.4 4.1.6.5 4.1.6.6 4.1.6.7 4.1.6.8 4.1.6.9 4.1.7. 4.1.7.3 4.1.7.4 4.1.7.5 4.1.7.6 4.1.7.7 1.1 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 5.6..1 5.6.. 5.6..3 6.7.5
- 3 - CAMI Eucatio like to CAPS: Grae 1 1.1 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) 6.3.7.1 6.3.7. 6.7.6.1 6.7.6. 6.7.7 5.5.1.1 5.5.1. 5.5.1.3 5.5.1.4 5.5.1.5 5.5.1.6 5.5.1.7 5.5..1 5.5.. 5.5..3 5.5..4 10.7..5 10.7..6 10.7.3. 10.7.3.3 10.7.4. 1.9 Trigoometry Compoue agle ietities: 7.5.4.1 7.5.4. 7.5.4.3
- 4 - CAMI Eucatio like to CAPS: Grae 1 1.9 Trigoometry cotiue 1.1 Fuctios: Polyomials cos( α ± β ) = cosα cos β m siα si β 7.5.4.4 si( α ± β ) = siα cos β ± cosα si β 7.5.4.5 7.5.4.6 si α = siα cosα 7.5.4.7 cos α = cos α si α 7.5.4.9 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) 5.1.1.1 5.1.1. 5.1..1 5.1.. 5.1..3 5.1..4 5.1..5 4.6.3.3 4.6.3.4 4.6.3.5 4.6.4.1 4.6.4. 4.6.4.3 1.5 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 5.6.1.1 5.6.3.1 5.6.3. 5.6.3.3 5.6.3.4 5.6.4.1 5.6.4.
- 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 3 5.6.4.3 5.6.4.4 5.6.4.5 5.6.4.6 5.6.4.7 4. 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. 5.7.1.1 5.7.1. 6. 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 5.7..1 5.7.. 5.7.4.1 5.7.4.
- 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 5.7.3.1 5.7.3. 5.7.3.3 5.7.3.4 5.7.3.5 5.7.3.6 5.7.3.7 5.7.3.8 5.7.5.1 5.7.5. 5.7.6.1 5.7.6. 5.7.6.3 8.9.4.1 8.9.4. 8.9.5.1 8.9.5. 8.9.6.1 8.9.6.
- 7 - CAMI Eucatio like to CAPS: Grae 1 1.10 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 4 10..5 10..6