Yaer 10 Term 1 Math

how to solve binomial expansion (a+b)(c+d)

ac + ad + bc + bd

how to solve a²- b²

(a+b)(a-b)

x²-9

x²-3²

(x+3)(x-3)

how to solve (a+b)² or (a-b)²

a²+2ab+b² or a²-2ab+b²

how to solve non-monic quadratics

find 2 numbers (lets say x &y) which multiply to c and add to b
format as (a+/-x)(a+/-y)

how to solve non-monic quadratics

find 2 numbers (lets say x & y) which multiply to c x coefficient of a and add up to b

then divide whole thing by coefficient of a, factorise one of the parts and cancel out

how to add, subtract, divide and multiply surds

to add and subtract the surd has to be the same and then you can do like algebra,, you cant divide, you can multiply by multiplying number then surd

how to simplify surds

type number in calculator and collect all perfect squares, multiply it together to get outside number, divide whole number with outside number to get inside number

how to get a rational denominator

multiply top and bottom with the surd is only 1 term in denominator or multiply conjugate of denominator to top and bottom

how to multiply and divide indices

multiply numbers and add indices, divide numbers and subtract indices

anything to the power of 0 = ?

1

How to express fractional indices as a surd

make the denominator the nth root and make the numerator the indice for the number inside the root

what is normal, time and a half and double time

1 x hr rate, 1.5 x hr rate, 2 x hr rate

what is gross income, tax deductions, taxable income, medicare levy and net income

income before deductions, amount allowed that is tax free, income with deducted tax, additional 2% of taxable income, same as taxable income

formula for simple interest

I = Prn

how to find P/r/n

make them x and isolate it

formula for compound interest

A = P(1+r)^n

when doing compound interest, r and n are?

in the same time period and to find n if r is p.a is multiply amount of times it compounds per year multiplied by amount of years

how to find leave loading or minus leave loading

multiply by 1.175, divide my 117.5 and multiply by 100 to get percentage

Pythagorous Theorem

a² + b² = c²

how to find unknown side/angle from θ and 1 side in right angle triangle

use SOH CAH TOA to identify to use sin, cos or tan. and then do sin/cos/tan(θ) = O/H, A/H or O/A
and then isolate x

sine rule

sin A/a = sin B/b = sin C/c

cosine rule

c = a² + b² - 2abcosC (SAS)
C = cos^-1(a² + b² - c²/2ab) (SSS)

(C is inbetween a & b)

Area rule

½absinC

what is compass and true bearings

true bearing are always 3 digits and measure clockwise form north

compass bearings are always 2 digits and measure between 2 cardinal points formatted as N/S(θ)E/W