ACT Math

midpoint formula

(x₁+x₂)/2, (y₁+y₂)/2

Plus, added to, and, some, combined, total, increased by

+

Minus, subtracted from, smaller than, less than, fewer, decreased by, difference between

-

mindset

- the end justifies the means - take time to save time - when in doubt, shake it up

Divided by, Per , out of, each, ratio

/

story problem steps

1. understand the problem 2. determine essential information 3. make a plan 4. follow the plan 5. check the answer

right angle

90 degrees

To remember where to shade...

< looks like L so shade to the left wbu chi is negative

Equals two, is, equivalent to, was, will be, has, costs, adds up to, the same as, as much as

=

Ratio

A comparison of one quantity to another

factor-label method

A method of conversion using the multiplication of fractions

vertex

A point where two or more straight lines meet.

Percent

A ratio that compares a number to 100

To solve an equation you must......

To get a variable alone.

find the objective

circle, underline and do something to the objective, it helps when you get stuck

how to find the range

max-min

your eyes don't tell you what you need to know about the figure

you have to do the math

try eyeballing

you wont be able to get specifics without doing the math, sometimes, but you will be able to rule out some answers and get a better idea of what you're looking for

Times, of, multiplied by, product of, twice, double, by

•

Parallel

2 lines that never intersect

(picking numbers tip) very rarely would you need to pick more than...

2 sets of numbers to find the right answer

Rational number

A number that can be written as a fraction

Coordinate plane

A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.

Midpoint

A point that divides a segment into two congruent segments

Prime number

A positive integer that is divisible without a reminder by only one and itself. The number two is the smallest prime number and the only even prime number; one is not considered prime

how to find the mean

Add #s together and then divide by the total number of figures.

Factor

An integer is any number that divides precisely into that integer with no remainder

Multiple

An integer that is an integer times any number. In other words, factor • factor = multiple

Irrational number

Any real number which cant be expressed as a fraction of two integers

remainders

Are integers left over when dividing. I have a question asks for the remainder 115÷2, don't say "15÷2 is 7.5 so the remainder is .5" what you should say is "15÷2 is seven with the remainder of one"

part-to-part ratio

Compares different parts of a group to each other

part-to-whole ratio

Compares one part of a group to the whole group

Dirt

Distance is rate times time

Convert fraction to decimal

Divide numerator by denominator

prime numbers

Do not include one. The technical definition of a prime number is a positive energy with exactly 2 distinct positive energy factors. Two is prime because it has exactly 2 positive factors: one and two. It's the smallest, and the only even, prime number. Four is not prime because it has three positive factors (1, 2 and 4) - too many! And what is not prime because it has only one positive factor (2) - too few!

Nonzero number raised to the zero power

Equals 1

All number are both ____________ & ___________

Factors and multiples

Combine ratio

If you have two ratios, eight: B & B:C, you can drive a call and see by finding a common multiple of the b terms

integers

Include a zero and negative whole numbers. If a question says "X and why are integers," it's not ruling out numbers like zero and -1

even and odds

Include zero and negative whole numbers. Zero and -2 are even numbers; negativeone is an odd number

Finding a common denominator

Involves multiplying one or more of the fractions by numbers that denominators will be the same

Rate

Is any "something per something" example: days per week, miles per hour

Proportion

Is two ratios that equal to each other

When you work with fractions...

It will always be put into the lowest term

Compare fractions

Manipulate them so they have a common denominator

Multiply fractions

Multiply numerators and denominators

Square

Multiply the number by itself.

Convert mixed numbers

Multiply the whole number part by the denominator then add the numerator

Line

Never stops

Average rate

Not the average of two rates, but the average of the total amounts

Solving an Inequality Example

Only when you multiply or divide an inequality by a negative or swap the position of the elements (example from x > 5 to 5 < x), you are allowed to switch the sign of the inequality)

PEMDAS

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Three-part percent formula

Part = percent • whole

percent increase/decrease formula

Percent change = (amount of change/original amount) • 100

Plot points

Points on a plot

how to find the median

Put all the numbers in numerical order. If there is an odd number of results, the median is the middle number. If there is an even number of results, the median will be the mean of the two central numbers.

how to find the mode

Put the numbers in order and then look for the most common number: Ex...Find the most common number: 1, 2, 5, 8, 90, 91, 91, 99, 100, 101, 102, 102, 102, 103, 104, 105, 110, 110, 121.

Exponent

Refers to the number of times a base is multiplied by itself

the √ symbol

Represents the positive square root only. Equation X squared equals nine has two solutions: three and -3 when you see square root nine it means only positive three

Y coordínate

Second number in an ordered pair

Original whole before a percent increase or decrease

Set up an equation with a variable in place of the original number

To evaluate a negative exponent

Take the reciprocal of the base and change the sign of the exponent

picking numbers

Technique to use when there are variables in all of the answer choices - don't pick 0, 1 or negative numbers.

Absolute value

The distance from zero on the number line, which is why absolute values are always positive

Reciprocal of a fraction

The inverse of that fraction

Distance

The length of a path between two points

LCM (Least Common Multiple)

The smallest whole number greater than 0 that is a common multiple of each of two or more numbers.

Adding and Subtracting Fractions

To add or subtract fractions, first find a common denominator and then add or subtract the numerators.

Evaluating an expression

To evaluate an algebraic expression, plug in the given values for the unknowns and calculate according to PEMDAS

supplementary angles

Two angles whose sum is 180 degrees

Relative primes

Two integers are relative primes if they share no prime factors. To determine whether two integers are relative primes, break them both down to the prime factorization's.

If an expression has parentheses...

Work from the innermost out

3 > X can also be written as

X < 3

A number, how much, how many, what

X, n, etc.

Use pick a number strategy when

You must simply imagine expression or equation to a scenario

cubed

a number raised to the third power

integer exponent

a small number written above the base that is an integer or zero

backsolving strategy

always start with the middle choice because if your middle choice comes out too big, you can eliminate the bigger numbers ALWAYS START WITH C!!!

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

straightforward math

do you know how to answer the questions using your math skills? go for it!

remove the disguise

find out what the question is really asking - it might not be obvious at first glance

rational exponent

fraction exponent

when the choice "cannot be determined" comes up...

it is almost always a trap question

Divide fractions

keep first numbers, change the second numbers to be flipped and then multiply

acute angle

less than 90 degrees

diagram question steps

let the diagram tell you what you need to know

obtuse angle

more than 90 degrees

To increase a number by x%

multiply by 1+x% i.e. 100 x (1+50%)=100x1.5=150

To raise a power to another power

multiply the exponents

step one - locate the end goal....

objective and circle it

Line segment

part of a line with two endpoints

backsolving

start with choice (B) or (D) use whenever you can manageably plug an answer choice into the question stem. after doing so, you merely confirm whether that value is consistent with the other values given in the stem.

Picking Numbers Strategy

step 1: easy to use numbers step 2: solve the question using numbers you've picked step 3: test each answer choice using the numbers you've picked, eliminate the ones that give you a result that is different from the one youre looking for step 4: if more than one choice remains, pick a different set of numbers and repeat steps 1-3

X Coordinate

the first number in an ordered pair

GCF (Greatest Common Factor)

the greatest number that is a factor of two or more numbers

congruent triangles

triangles that have their corresponding parts congruent

restate

try looking at the question from a different angle

guess strategically

try to eliminate as many incorrect answers before choosing

Angle

two rays with a common endpoint

concept question steps

understand the concept and jargon being used