SHSAT Math

Area of a Trapezoid (put a diagram)

(b1+b2/2)H

sum of interior angles for any shape

(number of sides-2)180

Area of a Cylinder

(pi r*2)h

Whole Numbers

0, 1, 2, 3. . . . (0 is included)

Natural Numbers/Counting Numbers

1,2,3. . . (0 is not included)

Algebra =

1. Get x on one side and the numbers on the other side 2. deal with what is stuck to the x (multiply or divide) 3. don't forget about negatives

How to deal with math multiple choice questions:

1. Read the question slowly and carefully 2. Create an equation 3. Solve the equation 4. If you are having trouble, use process of elimination (DON'T RUSH!!!)

Area of Right Triangle

1/2bh

Volume of a right triangular cone

1/3 area of base x height for a cone that is 1/3pi(r)squared(height)

Volume of a pyramid

1/3 area of base x height for a pyramid that is 1/3lwh

Area of a Pyramid

1/3 x area of base x height

1 centimeter = [ ] millimeters

10

1 meter = [ ] centimeters

100

1 kilometer = [. ] meters

1000

sum of all interior angles of an octagon

1080 degrees

1 foot = [. ] inches

12

Average number of degrees in an interior angle of a polygon

180 (n-2)/n where n = the number of sides

Three consecutive numbers contain at least one number that is divisible by ___ and at least one number that is divisible by ___

2, 3

Surface area of a box

2lw+2lh+2wh

Circumfrence of a circle

2πr or rd

Surface area of a cylinder

2πrh+2πr²

1 yard = [. ] feet

3

Right triangle angles

3, 4, 5; 5, 12, 13

What is the sum of all of the exterior angles of a triangle?

360 degrees

How many degrees in an exterior angle of a polygon?

360/n (where n equals the number of sides in the polygon)

Area of a Sphere Formula

4/3 pie(r)(squared)

Surface area of a cube

6s²

Rational number

A number that can be written as a fraction or repeating decimal

Whenever a problem says that when there is an amount x, there is an amount y, what kind of problem is it?

A ratio problem

Area of a circle

A=πr²

Area Of A Cone Formula

Area of the base of the cone: A = pie(r)squared, volume of the cone: V = 1/3 pie(r)squared(h)

When there is a problem with multiple units what do you do?

CONVERT FIRST!

In a problem where you have to find something in a unit where it isn't converted already what do you do

Convert first

How do you figure out the GCF of two numbers?

Do prime factorization of each and multiply their common prime factors. So, if the prime factorization of one number is 2*2*3*7 and the other is 2*3, the GCF is 2*3 or 6.

How do you figure out the LCM of two numbers?

Do prime factorization of each and then write out the prime factors of each number on top of one another. For each prime factor, see what the greatest number of that prime factor is for each and write that number down that many times. For example, to do the LCM of 42, 12; 42=7*2*3 and 12=2*2*3, so you multiply: 7*2*2*3. If both numbers have one of a prime factor, you enter that prime factor once. If only one of the numbers has a certain prime factor, you also only enter that number once. If one number has two of a given prime factor and the other number only has one of that prime factor, you enter that prime factor twice.

Divisible by 9

If the sum of the digits is divisible by 9

Even Numbers

Integers divisible by 2 (can be negative)

Prime Numbers

Integers greater than 1 and have exactly 2 factors (1 and themselves); 2 is only even prime number

Composite Numbers

Integers with more than 2 factors

Average of a set of consecutive numbers

Is the number in the middle of the set if odd number of terms or average of two middle terms if even number of terms.

Volume of a box formula

L x W x H

What do you do before writing down the answer to a math question?

Make sure you are answering exactly what the question is asking you to answer.

Median

Middle number in ordered set if odd number of elements. If even number, average of two middle numbers in the set.

Distinct Numbers

Numbers that are different from each other

Sum of two prime numbers is always even except when. . .

One of the numbers is 2

scale factor

Ratio of the dimensions of the object in the drawing to the dimensions of the actual object

Surface area of a cube formula

S = 6a(squared)

Steps for solving a percent increase or decrease:

Step 1: Find the number difference Step 2: Set up a proportion where #difference/original# = x/100 Step 3: Solve for x

When a question refers to a range of test scores, what does that mean?

The difference of the highest and lowest test score.

Divisible by 4

The last 2 digits are divisible by 4

Divisible by 5

The last digit is 0 or 5

Divisible by 2

The last digit is even (0,2,4,6,8)

Divisible by 10

The number ends in 0

Divisible by 6

The number is divisible by both 2 and 3

LCM (Least Common Multiple)

The smallest whole number greater than 0 that is a common multipl\e of each of two or more numbers. (24, 36, 60 = 360)

Divisible by 3

The sum of the digits is divisible by 3

what is the supplement of an angle?

Two angles that add up to 180 degrees

What are complimentary angles?

Two angles that add up to 90 degrees

How many numbers are between 33 and 111

Use mean/average

Volume of a cube formula

V = a(cubed)

Volume of a cylinder

V=πr²h

P(A or B) = PA + PB - P(A+B)

We wrote this down. Not sure what it means.

Integers

Whole numbers and their opposites (. . . -3, -2, -1, 0, 1, 2, 3. . .)

How do you evaluate A number with a negative exponent

Write the reciprocal of the number and then use a positive exponent

When you are multiplying exponents with the same base, what do you do?

You add the two exponents together

When you are dividing exponents, what do you do?

You find the difference of the two exponents

When you have to pick 2 things out of a bucket in probability, what do you do?

You multiply the two probabilities that you get.

What do you do first when you have to do the area of a trapezoid?

You see if you can use the Pythagorean Theorem.

What do you do when a question asks for the overall range of ______?

You use the range and the highest ______ to find the lowest _______ and then find all of the ranges for each thing and add them together.

For a right-angled triangle, formula for hypotenuse:

a squared + b squared = c squared (c = hypotenuse)

% up or down or relative error:

amount up or down or off by x/1000 (original amount or accurate measurement)

Pythagorean Theorem

a²+b²=c²

"is" means

equals

"Such as" means...

for example

Odd Numbers

integers not divisible by 2 (can be negative)

Volume of a circle

pie(r)squared(h)

Volume of a cube formula

side x side x side/side cubed

what is the formula for average or mean problems

sum of the test scores that you know divided by the number of numbers = the average of that group of numbers

GCF (Greatest Common Factor)

the largest common factor of two or more given numbers (24, 36, 60 = 12)

What is the answer of the greatest of 5 consecutive integers + the least of 5 consecutive integers

the middle of those 5 consecutive integers

"of" means

times

slope =

up/down over side to side

"what" means

x

START WITH FORMULA AND THEN PLUG IN WHAT YOU KNOW AND PUT X FOR UNKNOWN

you just wrote this not sure what it is

when a question is asking you to answer how many ____ numbers are in between ___ and ___, what do you do?

you write down three blank lines as three digits and under the lines, write down each possible digit that the line could hold. Then, multiply the number of possibilities in each of the three digits.