Mathematics

1: Pythagoras

a² + b² = c²

that's all

2: Trigonometry

sin, cos and tan.

SOH, CAH, TOA

hypotenuse: longest line

3: GST (%)

to add GST: x1.15

to remove GST: /1.15

note: / is divide

4: Exchange Rates

To convert from your currency into another: times the amount of money from your currency by the exchange rate

To convert back into your currency from another: divide the foreign currency amount by the exchange rate

examples!

If 1 NZD = 10.38 ZAR

1 ZAR = 0.096 NZD

to convert 150NZD to ZAR

150 NZD x 10.38 (exchange rate) = 1559 ZAR

to convert back the 1559 ZAR

1559 / 10.38 = 150

or 1559 x 0.096 = 150

numbers rounded cause cause

5: volume / surface area / area / perimeter

most of these will be given in the formula sheet

area is base x height

perimeter is the sides added up

note: GET THE BRACKETS RIGHT. DONT INSERT THEM WRONG.

6: geometry (angles in shapes)

not sure what that note means but I assume its some combination of trig and the area/perimeter/volume stuff

7: similar shapes (i got the numbering mixed up for 6 and 7 but shhh)

just remember how ratios work or something you'll probably be fine.

8: finding the equation of a line or parabola

NONONONONONONONONONO

Parabolas

the ways parabolas can be written

normal

y = ax² + bx + c

useful solving equations and number patterns

root form

y = a(x-r₁)(x-r₂)

used when you have the roots of the parabola (x intercepts)

vertex form

y = a(x-p)²+q

how to use

check the points you have available

do you have the roots (x intercepts)?

do you have the vertex (bottom point)?

any other points?

If you have the vertex and another point, then you'll use the vertex form

If you have the roots and another point, then you'll the root form

If you have something else you did it wrong, check again

roots

y = a(x-r₁)(x-r₂)

1. substitute the roots

2. substitue the x and y with the other point.

3. simplify and calculate what a is (if you can't, you suck. try again

4. reform the equation so it looks normal without the x and y substituted

vertex

y = a(x-p)²+q

1. subtitue the p and q for the x and y points of the vertex. (p = x, q = y)

2. substitue the x and y points from the equation with the x and y points from the other point

3. simplify to find a

4. go back and reqrite the equation with substituting x and y

lines

1. Find 2 points

2. calculate the gradient using m = ^y₂-y₁ / _x2-x1

3. substitue m (the gradient) into y-y₁ = m(x-x₁)

4. simplify y = ______

9: drawing graphs

use this chart to graph out each point individually

10: Number Patterns (quadratics)

expand fully and remember the 3 steps

2a =

3a + b =

a + b + c =

I'm probably the only person who will understand this lmao but it works

then just put the a b and c into the ax² + bx + c

if it asks you to find the n^th term then substitue x for n

10: Number Patterns (quadratics)

expand fully and remember the 3 steps

2a =

3a + b =

a + b + c =

I'm probably the only person who will understand this lmao but it works

then just put the a b and c into the ax² + bx + c

if it asks you to find the n^th term then substitue x for n

11: factorising

if you have a lovely quadratic equation, for example

x² + 5x -24

you will want to expand it. this is how.

1. list all facts of the constant (in this case 24)

2. select the pair that would add or subtract to be the coeefficient (5x)

3. in this case the factors are 3 and 8 and you can put them together by tying a neat little bow around them like this.

(x-3)(x+5)

4. check if you want by expanding

12: expanding

its not that hard

13 and 14 are easy

15. simulataneous fucking equations

the bane of my existance

here are the steps apparantly (i could neither confirm nor deny the accuracy of these

1. write both equations in the same order

2. look for a variable with matching coefficiants

3. If not coefficients match, multiply an equation so they do

4. Decide if you will add or subtract

5. solve for the remaining variable

6. substitue it to find the other variable

check