Short ACT Math Book Notes + Math Test Corrections Tips

Sum of n terms of arithmetic progression

[n(n+1)]/2

How to find unknown length of larger triangle with given ratio?

Set equation to known length and multiply ratio by unknown side/hypotenuse

SOHCAHTOA

SIN (Opposite/Hypotenuse) COS (Adjacent/Hypotenuse) TAN (Opposite/Adjacent)

How can any linear relationship be represented?

y=mx+b

How to find probability of independent events?

multiply the probability of all events together; represents probability of all events occurring

mean =

sum/num of items

sum =

mean(num of items)

Difference between measurements in a protractor

angle

Finding price with tax

price(1 + x)

Removing tax from price

price/(1 + x)

Finding grade weight

(sum of weights x grades)/(sum of weights); (w1 x g1 + w2 x g2…) / (w1 + w2…)

Finding final grade

Required = (Goal − Current Grade × (1 − Final Weight)) / Final Weight

distance formula

square root of (x2-x1)^2 + (y2-y1)^2

When not to use the distance formula

Right triangle with known sides, can relate shape to right triangle, shape has vertical or horizontal lines

Pythagorean theorem

a²+b²=c²

How to find length of hypotenuse when length of both legs are known

c= √a^2 + b^2

To predict next point on coordinate plane with slope

add coordinates by slope/rate of change

area of square

s²

perimeter of square

4s

perimeter of rectangle

2l+2w

area of triangle

1/2bh

area of circle

πr²

circumference of circle

2πr