ACT Math Formulas

What are the exponent rules?

• a^b x a^c = a^(b+c)

• a^b/a^b = a^(b-c)

• (a^b)^c = a^bc

• (ab)^c = a^c x b^c

• a^(-b) = 1/(a^b)

What are the rules of scientific notation?

• You can add or subtract scientific notation if the numbers have the SAME power of 10

• If they don't, change them until they do

• Multiply or divide scientific notation with exponent rules

What are the radical rules?

• Square root of A/B = Square root of A/ Square root of B

• Square root of AB = Square root for A times Square root of B

• (a^b) To the root of c = a^(b/c)

• any number squared is ALWAYS + or -

• Square root of any number is ALWAYS+

• Cube roots of negative numbers are negative

• Multiply a fraction with a radical in the denominator, multiply by it's CONJUGATE (or opposite)

• When numbers are taken out of the square root, they should be smaller than inside

What are the equations for sequences?

Geometric sequence: a(n) = a(1) x r^(n-1)

Arithmetic sequence: a(n) = a(1) + d(n-1)

What is the cycle of i?

I, -1, -i, 1

How do you add or subtract matrices?

• You have to have the same number of rows and columns

• You add the numbers in the same spots to each other

What is the equation for a determinant?

AD-BC

How do you multiply matrices?

• make sure that one has the the same amount of rows as the other has columns

• Will be R1 x C1 and R2 x C2, C1 MUST equal C2, and R1 x C2 will be final dimensions

• Go left to right, up to down

• To practice, write it on a notepad

What is the rate formula?

• Distance = rate/time

What is true about adding percentages?

You can only do it if it's out of the same whole

Cancelling ratios rule

(a/b)(b/c)=a/c

What is the midpoint formula

((X1+x2)/2, (y1+y2)/2))

What are the forms of a line?

• ax²+bc+c=0

• y=mx+b

• y2-y1=m(x2-x1)

What is the sum of the roots? The product

b/a, -c/a

What happens when you have absolute value in an inequality?

The negative value switches the sign to the opposite direction

Where do you shade the graph for an inequality?

• y>mx+b, then shade ABOVE

• y<mx+b, then shade BELOW

What is the discriminant? What does it tell you?

• b²-4ac

• If it's negative, no solutions

• If it's positive, two solutions

• If it's 0, one solution

What are common quadratic formulas?

• a²+b²+2ab = (a+b)²

• a²+b²-2ab = (a-b)²

• a²-b² = (a+b)(a-b)

What are expected values?

The weighted average of a specific data set.

• The amount or value of something x the probability of that thing happening x how many times it is attempted

What is probability?

• Desired outcomes/total outcomes

How do you find either or probabilities? How about combined (and) probabilities?

• Either or- add your probabilities (should be BIGGER than og prob)

• And- multiply (should be SMALLER than og prob)

How do you find the total amount of outcomes of 2 events?

Multiply! If event A had x outcomes and event B has y, then xy is the total amount of outcomes.

• P(A)

• P(A’)

• P(A upside down u B)

• P(A U B)

• P(A l B)

• P(n above r)

• Probability of A

• Complement probability of A

• Probability of A and B

• Probability of A or B

• Probability of A given B already happened

• Number of ways to choose r from a set of n items when order does not matter

What are permutations and combinations? What are the formulas?

Permutations- order matters

• (Number of objects)!/Combinations! (Objects - combinations)!

Combinations- order does not matter

• (Number of objects)!/(Objects - combinations)!