Topic 1 Simultaneous Equations

• Topic 1-1 substitution work each time
• Topic 1-2 poof the bottom
• Topic 1-3 applications

Topic 2 Identities

• Topic 2-1 highest power to lowest power - hp2low
• Topic 2-2 simultaneous equations - simis

Topic 3 Remainder Theorem

• Topic 3-1 linear divisor
• Topic 3-2 quadratic divisor
• Topic 3-3 simis
• Topic 3-4 special treat

Topic 4 Factor Theorem

• Topic 4-1 linear divisor
• Topic 4-2 quadratic divisor
• Topic 4-3 simis
• Topic 4-4 special treat

Topic 5 Cubic Factorisation

• Topic 5-1 three factors given
• Topic 5-2 two factors given
• Topic 5-3 one factor given
• Topic 5-4 no factor given
• Topic 5-5 substitution
• Topic 5-6 special treat

Topic 6 Partial Fractions

• Topic 6-1 linear denominators
• Topic 6-2 repeated denominators
• Topic 6-3 quadratic denominator
• Topic 6-4 linear denom + repeated denom
• Topic 6-5 linear denom + quadratic denom
• Topic 6-6 special treat

Topic 7 Quadratic Roots

• Topic 7-1 $\alpha^1,\beta^1$
• Topic 7-2 $\alpha^2,\beta^2$
• Topic 7-3 $\alpha-\beta$
• Topic 7-4 $\alpha^3,\beta^3$
• Topic 7-5 $\alpha^4,\beta^4$
• Topic 7-6 substitution
• Topic 7-7 special treat

Topic 8 Quadratic Inequality

• Topic 8-1 the cheeks or lower lip
• Topic 8-2 reverse it
• Topic 8-3 AND means OVERLAP
• Topic 8-4 graphical inequalities
• Topic 8-5 applications
• Topic 8-6 identify the positive part
• Topic 8-7 fractions

Topic 9 Discriminant

• Topic 9-1 no real roots $b^2-4ac < 0$
• Topic 9-2 one real root $b^2-4ac=0$
• Topic 9-3 two distinct roots $b^2-4ac > 0$
• Topic 9-4 certainly real roots $b^2-4ac\geqslant0$
• Topic 9-5 new quadratic equation from simis
• Topic 9-6 special treat

Topic 10 Exp & Log Graphs

• Topic 10-1 up and down
• Topic 10-2 left and right
• Topic 10-3 reflect at x-axis
• Topic 10-4 reflect at y-axis
• Topic 10-5 gluttony & starvation
• Topic 10-6 too much calcium & too little calcium
• Topic 10-7 test yourself
• Topic 10-8 exam questions!

Topic 11 Modulus

• Topic 11-1 what is modulus?
• Topic 11-2 equations with one modulus
• Topic 11-3 equations with two moduli
• Topic 11-4 simis
• Topic 11-5 inequalities
• Topic 11-6 straight line graphs
• Topic 11-7 quadratic graphs

Topic 12 Indices

• Topic 12-1 divide me
• Topic 12-2 power left equals to power right
• Topic 12-3 synonyms
• Topic 12-4 merge them up
• Topic 12-5 cancel top and bottom
• Topic 12-6 special treat

Topic 13 Exponential Equations

• Topic 13-1 quadratic & log
• Topic 13-2 simis
• Topic 13-3 short problems
• Topic 13-4 cubic substitution

Topic 14 Surds

• Topic 14-1 purely rationalize
• Topic 14-2 $\sqrt{10}=\sqrt{2}\times\sqrt{5}$
• Topic 14-3 synonyms
• Topic 14-4 squaring
• Topic 14-5 volume & surface areas - vas
• Topic 14-6 special treat

Topic 15 Logarithms - same base

• Topic 15-1 simplify logs
• Topic 15-2 taking log
• Topic 15-3 antilog
• Topic 15-4 merge & antilog
• Topic 15-5 simis
• Topic 15-6 synonyms
• Topic 15-7 substitute, quadratic & log
• Topic 15-8 log as power

Topic 16 Logarithms - change of base

• Topic 16-1 simplify logs
• Topic 16-2 antilog
• Topic 16-3 merge & antilog
• Topic 16-4 simis
• Topic 16-5 log as power
• Topic 16-6 synonyms

Topic 17 Binomial Expansion

• Topic 17-1 using formula
• Topic 17-2 find r
• Topic 17-3 take what you need
• Topic 17-4 n is missing
• Topic 17-5 estimating exponent of decimals
• Topic 17-6 binomials of same power can combine
• Topic 17-7 use binomial expansion to find trinomial expansion
• Topic 17-8 special treat

Topic 18 Coordinate Geometry

• Topic 18-1 midpoint, bisector, length
• Topic 18-2 area of polygon
• Topic 18-3 $gradient,m=tan\theta$

Topic 19 Linear Law

• Topic 19-1 make a straight line
• Topic 19-2 find original curve given $Y=MX+C$
• Topic 19-3 find original curve given points on $x-y$ axes
• Topic 19-4 equation of new line is a constant
• Topic 19-5 equation of new line is a straight line
• Topic 19-6 incorrect values
• Topic 19-7 find gradient without plotting

Topic 20 Matrices

• Topic 20-1 singular matrix & identity matrix
• Topic 20-2 finding inverse matrix
• Topic 20-3 simis

Topic 21 Trigonometry - basic angles

• Topic 21-1 the two ratios,$sin\:30^{\circ}=\frac{1}{2}\:$ $tan\:45^{\circ}=\frac{1}{1}$
• Topic 21-2 the 4 triangles
• Topic 21-3 locate then arc
• Topic 21-4 factorize, locate then arc
• Topic 21-5 $sin\:\theta,\:cos\:\theta,\:tan\:\theta,\:cosec\:\theta,\:sec\:\theta,\:cot\:\theta$

Topic 22 Trigonometry - graphs

• Topic 22-1 $y=sin\:x$
• Topic 22-2 $y=cos\:x$
• Topic 22-3 $y=tan\:x$

Topic 23 Trigonometry - fundamental identities

• Topic 23-1 $sin^2\:\theta+cos^2\:\theta=1$
• Topic 23-2 $tan^2\:+1=sec^2\:\theta$
• Topic 23-3 $cot^2\:+1=cosec^2\:\theta$

Topic 24 Trigonometry - addition formula

• Topic 24-1 identify the expanded form
• Topic 24-2 pieces of a puzzle
• Topic 24-3 24-3 locate then draw triangles
• Topic 24-4 rearrange for $tan\:\theta$
• Topic 24-5 solve equations
• Topic 24-6 simis
• Topic 24-7 special treat

Topic 25 Trigonometry - double-angle formula

• Topic 25-1 $sin\:2\theta$
• Topic 25-2 $cos\:2\theta$
• Topic 25-3 $tan\:2\theta$

Topic 26 Trigonometry - factor formula

• Topic 26-1 (i)combine $sin\:3\theta$ and $sin\:\theta$ (ii)combine $cos\:3\theta$ and $cos\:\theta$
• Topic 26-2 solving equations

Topic 27 Trigonometry - r-formula

• Topic 27-1 basics
• Topic 27-2 max & min values
• Topic 27-3 solving equations

Topic 28 Trigonometry - proving of identities

• Topic 28-1 using every formula

Topic 29 Equation of Circles

• Topic 29-1 given radius and center
• Topic 29-2 find radius and center
• Topic 29-3 given perpendicular bisector and chord
• Topic 29-4 given tangent
• Topic 29-5 given two points
• Topic 29-6 inside, outside or on the circle
• Topic 29-7 equation of diameter
• Topic 29-8 discriminant
• Topic 29-9 center on a straight line
• Topic 29-10 longest and shortest distance
• Topic 29-11 reflection
• Topic 29-12 given three points
• Topic 29-13 special treat

Topic 30 Differentiation - power rule & chain rule

• Topic 30-1 bring down power, power minus one
• Topic 30-2 diff outside, diff inside - dodi
• Topic 30-3 prepare before diff
• Topic 30-4 applications

Topic 31 Differentiation - product rule & quotient rule

• Topic 31-1 diff first, keep second - dfks
• Topic 31-2 turning point
• Topic 31-3 proving

Topic 32 Differentiation - exponential functions

• Topic 32-1 diff first, keep second - dfks
• Topic 32-2 turning point
• Topic 32-3 proving

Topic 33 Differentiation - logarithmic functions

• Topic 33-1 diff first, keep second - dfks
• Topic 33-2 turning point
• Topic 33-3 proving

Topic 34 Differentiation - trigonometric functions

• Topic 34-1 diff first, keep second - dfks
• Topic 34-2 turning point
• Topic 34-3 proving

Topic 35 Equation of tangent & normal

• Topic 35-1 tangent
• Topic 35-2 normal
• Topic 35-3 simis

Topic 36 Max & Min Values

• Topic 36-1 volume
• Topic 36-2 surface areas & shaded regions
• Topic 36-3 length & perimeter
• Topic 36-4 special treat

Topic 37 Related Rates

• Topic 37-1 basics
• Topic 37-2 $\frac{dV}{dt}$
• Topic 37-3 $\frac{dA}{dt}$
• Topic 37-4 $\frac{dx}{dt}$
• Topic 37-5 coordinate geometry
• Topic 37-6 approximate change
• Topic 37-7 special treat

Topic 38 Integration - indefinite

• Topic 38-1 power + 1, put to denom

Topic 39 Integration - definite

• Topic 39-1 power + 1, put to denom
• Topic 39-2 the multiples
• Topic 39-3 the reverse
• Topic 39-4 find the unknown
• Topic 39-5 combination
• Topic 39-6 adjust the range

Topic 40 Integration - exponential functions

• Topic 40-1 diff power, put to denom
• Topic 40-2 convert into integrate-able form

Topic 41 Integration - trigonometric functions

• Topic 41-1 can integrate right away
• Topic 41-2 convert into integrate-able form

Topic 42 Integration - integrate $\frac{1}{x+2}$ to $log_{e}(x+2)$

• Topic 42-1 denom put into log, diff denom and put to bottom
• Topic 42-2 first partial fractions then repeat

Topic 43 Finding Area

• Topic 43-1 between curve and $x$-axis
• Topic 43-2 between two curves
• Topic 43-3 between curve and $y$-axis

Topic 44 Finding Equation of Curve

• Topic 44-1 $\frac{dy}{dx}$ to $y$
• Topic 44-2 $\frac{d^2y}{dx^2}\:\overrightarrow{integrate}\:\frac{dy}{dx}\:\overrightarrow{integrate}\:\underline{y}$

Topic 45 Reverse Integration

• Topic 45-1 diff first, then integrate

Topic 46 Kinematics

• Topic 46-1 $ {\color{red}{\textbf{given displacement,s}}}\:\overrightarrow{differentiate\:s,\:\frac{ds}{dt}}\:{\color{green}{velocity,v}}\:\overrightarrow{differentiate\:v,\:\frac{dv}{dt}}\:{\color{blue}{acceleration,a}} $
• Topic 46-2 $ {\color{red}{displacement,s}}\:\overleftarrow{integrate\:s,\:\frac{ds}{dt}}\:{\color{green}{\textbf{given velocity,v}}}\:\overrightarrow{differentiate\:v,\:\frac{dv}{dt}}\:{\color{blue}{acceleration,a}} $
• Topic 46-3 $ {\color{red}{displacement,s}}\:\overleftarrow{integrate\:s,\:\frac{ds}{dt}}\:{\color{green}{velocity,v}}\:\overleftarrow{integrate\:v,\:\frac{dv}{dt}}\:{\color{blue}{\textbf{given acceleration,a}}} $