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? What is the work-rate formula?

• Distance = rate/time

• work done= overall rate (found by adding two rates) x time spent (W=rt)

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? When can you add and subtract inequalities?

The negative value switches the sign to the opposite direction

you can add inequalities if they have the same sign facing the same direction, but you cannever subtract an inequality

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)!

What are the special right triangles?

• 30-60-90 (1-square root of three-2)

• 45-45-90 (1-1-square root of 2)

What are the points of the unit circle?

(0,1) (root 3/2, 1/2) (root 2/2, root 2/2) (1/2, root 3/2) (0,1)

What do the graphs of sine, cosine, and tangent look like?

• Cosine: Starts with the amplitude up at ONE

• Sine: starts with the middle of the graph at 0

• Tangent: 0, 1/2, forever

What is amplitude and period?

Sine and cosine- period 2π, amplitude 1

Tangent- period 1, amplitude none

What are the trig identities?

Sin²+cos²=1

Tan²+1=sec²

Cot²+1=csc²

How do you complete the square?

• Bring C to the other side

• (B/2)²

• Add that to both sides

• Solve the quadratic on the left

What are the three forms of a parabola?

• Vertex form: y=a(x-h)²+k

• Standard form: y=ax²+bc+c

• Factored form: y=a(x-h)(y-k)

What is the rule of sines? Rule of cosines?

• SinA/a=SinB/b=SinC/c

• a=b²+c²-2bcCosA

What are the 2 most common Pythagorean triples?

• 3-4-5

• 5-12-13

• Any of their multiples

What does an equilateral triangle make cut in half? A square?

• A 30-60-90 triangle (x-x(root3)-2x)

• A 45-45-90 triangle (x-x-xroot2)

What are the formulas of a sine, cosine, tangent graph?

• y=A sine(bx-c)+D

• y=A cos(bx-c)+D

• y=A tan(bx-c)+D

• Amplitude is A

• 2π/|b| OR π/|b| is the period

• c/b is the HORIZONTAL SHIFT

How to find a parabolas vertex from the standard form equation?

-b/2a=x

C is the y intercept

What is the principal root?

The primary square root of a number, which is always positive. In other words, √x is POSITIVE, and √x cannot be a negative number in an equation

When does an equation have infinite solutions?

When both sides of the equation are equal

When does an equation have no solutions?

When both sides of the equation CANNOT be equal I.e ✓x=-3, 2=5, |x|=-3, x²=-3

And equation has no solutions when all the parts are equal EXCEPT the constants (ex. 3x+4=3x+5)

When wil

What is standard deviation?

How far away a dataset is from its MEAN

• ex. 0,0,10,10 and 3,5,7,9

• On average, the first set is farther away from five (the mean) than the second set is from six (also the mean)