The HiSET math cheat sheet on this page includes all of the formulas and conversions that you need for the HiSET test.
HiSET Math Cheat Sheet with Formulas
All of the formulas and conversions that you will need on the HiSET math test are included in the second half of this page.
You’ll be provided a formula sheet during the test. However, you will be able to answer the questions more competently and quickly if you know the formulas by heart.
You should also brush up on your algebra for the HiSET math test.
Algebra Practice
Question 1: (Solving for x)
If 5x – 2(x + 3) = 0, then x = ?
A. –2
B. –1
C. 1
D. 2
Answer 1:
The correct answer is D. To solve this type of problem, do the multiplication on the items in parentheses first.
5x – 2(x + 3) = 0
5x – 2x – 6 = 0
Then deal with the integers by putting them on one side of the equation as follows:
5x – 2x – 6 + 6 = 0 + 6
3x = 6
Then solve for x.
3x = 6
x = 6 ÷ 3
x = 2
Question 2: (FOIL Method and Polynomials)
Simplify the following equation: (x + 3y)2
A. 2(x – 3y)
B. 2x + 6y
C. x2 + 6xy + 9y2
D. x2 + 6xy – 9y2
Answer 2:
The correct answer is C. This type of algebraic expression is known as a polynomial. When multiplying polynomials, you should use the FOIL method. This means that you multiply the terms two at a time from each of the two parts of the equation in this order:
First – Outside – Inside – Last
(x + 3y)2 = (x + 3y)(x + 3y)
FIRST – Multiply the first term from the first set of parentheses with the first term from the second set of parentheses.
(x+ 3y)(x+ 3y)
x × x = x2
OUTSIDE – Multiply the first term from the first set of parentheses with the second term from the second set of parentheses.
(x + 3y)(x + 3y)
x × 3y = 3xy
INSIDE – Multiply the second term from the first set of parentheses with the first term from the second set of parentheses.
(x + 3y)(x + 3y)
3y × x = 3xy
LAST – Multiply the second term from the first set of parentheses with the second term from the second set of parentheses.
(x + 3y)(x + 3y)
3y × 3y = 9y2
Then we add all of the above products together to get the answer.
x2 + 3xy + 3xy + 9y2 =
x2 + 6xy + 9y2
Question 3: (Simplifying)
Simplify the following: (5x2 + 3x – 4) – (6x2 – 5x + 8)
A. –x2 – 2x + 4
B. –x2 – 2x – 12
C. –x2 + 8x + 4
D. –x2 + 8x – 12
Answer 3:
The correct answer is D. Remember to perform the operations on the parentheses first and to be careful with negatives.
(5x2 + 3x – 4) – (6x2 – 5x + 8) =
5x2 + 3x – 4 – 6x2 + 5x – 8
Then place the terms containing x and y together.
5x2 + 3x – 4 – 6x2 + 5x – 8 =
5x2 – 6x2 + 3x + 5x – 4 – 8
Finally add or subtract the terms to solve.
5x2 – 6x2 + 3x + 5x – 4 – 8 =
–x2 + 8x – 12
Question 4: (Substituting for x)
x2 + xy – y = 41 and x = 5. What is the value of y?
A. 2.6
B. 4
C. 6
D. –4
Answer 4:
The correct answer is B. Substitute 5 for the value of x to solve.
x2 + xy – y = 41
52 + 5y – y = 41
25 + 5y – y = 41
25 – 25 + 5y – y = 41 – 25
5y – y = 16
4y = 16
4y ÷ 4 = 16 ÷ 4
y = 4
Question 5: (Substituting for x and y)
Evaluate the expression 6x2 – xy + y2 if x = 5 and y = –1.
A. 36
B. 144
C. 146
D. 156
Answer 5:
The correct answer is D. “Evaluate” means to solve. So, to solve ASVAB math problems like this, put in the value of 5 for x and the value of –1 for y and multiply. Remember that two negatives together make a positive and to be careful when multiplying negative numbers.
6x2 – xy + y2 =
(6 × 52) – (5 × –1) + (–12) =
(6 × 5 × 5) – (–5) + 1 =
(6 × 25) + 5 + 1 =
150 + 5 + 1 = 156
HiSET Math Cheat Sheet
Weight
1 ounce ≈ 28.350 grams
1 pound = 16 ounces
1 pound ≈ 453.592 grams
1 milligram = 0.001 grams
1 kilogram = 1,000 grams
1 kilogram ≈ 2.2 pounds
1 ton = 2,000 pounds
Volume
1 cup = 8 fluid ounces
1 quart = 4 cups
1 gallon = 4 quarts
1 gallon = 231 cubic inches
1 liter ≈ 0.264 gallons
1 cubic foot = 1,728 cubic inches
1 cubic yard = 27 cubic feet
1 board foot = 1 inch by 12 inches by 12 inches
Distance
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5,280 feet
1 mile ≈ 1.61 kilometers
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 meter = 1,000 millimeters
1 meter = 100 centimeters
1 kilometer = 1,000 meters
1 kilometer ≈ 0.62 miles
Area
1 square foot = 144 square inches
1 square yard = 9 square feet
1 acre = 43,560 square feet
Circles
number of degrees in circle = 360°
circumference ≈ 3.14 × diameter
area ≈ 3.14 × (radius)2
Triangle
sum of angles = 180°
area = ½ (base × height)
Rectangles
perimeter = 2(length + width)
area = length × width
volume = length × width × height
Other shapes:
Cube
volume = (length of side)3
Cylinder
volume ≈ 3.14 × (radius)2 × height
Cone
volume ≈ (3.14 × radius2×height) ÷ 3
Sphere (Ball)
volume ≈ 4/3 × 3.14 × radius3
Temperature
°C = 0.56(°F – 32) or 5/9(°F – 32)
°F = 1.8(°C) + 32 or (9/5 × °C) + 32
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