GED Math Worksheets: Free, With Answer Keys, New Every Time

1.40 feet

1. Write the formula. The formula sheet gives the perimeter of a rectangle.P = 2l + 2w
2. Substitute the measurements. Both pairs of sides count: there are two lengths and two widths.P = 2(12) + 2(8) = 24 + 16
3. Add. This is the total distance around the outside.P = 40
4. Check the units. Perimeter is a distance, so the answer is 40 feet, not square feet, which would be area.

2.B. 32 millimeters

1. Add every value. The mean starts with the total of all the numbers in the table.32 + 33 + 30 + 34 + 34 + 29 = 192
2. Count the values. The table has 6 rows, so there are 6 values.
3. Divide the total by the count. Sharing the total equally among the values gives the mean.192 ÷ 6 = 32
4. Check that it is reasonable. A mean of 32 sits between the smallest value (29) and the largest (34), which is what an average should do.

3.C. $1,980.00

1. Write down the formula. The formula sheet lists simple interest as I = Prt, where P is the principal, r is the yearly rate and t is the time in years.I = P × r × t
2. Turn the rate into a decimal. The rate is a percent, so divide it by 100 before it goes into the formula.4% = 0.04
3. Substitute and multiply. Multiply the principal by the decimal rate, then by the number of years. Because the interest is simple, every year earns the same amount.I = 1500 × 0.04 × 8 = 480
4. Add the principal back. I is only the interest. The amount owed is the original money plus the interest.1500 + 480 = 1980

4.D. t + 21

1. Group the like terms. Terms with t can be combined with each other, and plain numbers can be combined with each other. Keep each sign attached to the term in front of it.(9t − 8t) + (10 + 11)
2. Combine the t-terms. Add the numbers in front of t, signs included.9 − 8 = 1, so the t-terms give t
3. Combine the plain numbers. Do the same with the terms that have no variable.10 + 11 = 21
4. Check with a value. Substituting t = 1 into the original gives 22, and the simplified expression gives the same.9 + 10 − 8 + 11 = 22

5.7 dollars

1. Decide on the operation. The same total is shared equally, so divide the total cost by the number of bottles of water.
2. Divide. Split the total into equal parts.84 ÷ 12 = 7
3. Check by multiplying back. A unit rate should rebuild the total.7 × 12 = 84

6.C. w = 3 or w = 5

1. Find the factor pair. Look for two numbers that multiply to the constant term 15 and add to the middle coefficient −8.−5 × −3 = 15 and −5 − 3 = −8
2. Write the factored equation. Each number goes into its own set of parentheses with the variable.(w − 5)(w − 3) = 0
3. Set each factor equal to zero. If two things multiply to zero, at least one of them must be zero. Solving each small equation gives a solution.w − 5 = 0 gives w = 5; w − 3 = 0 gives w = 3
4. Check both solutions. Substituting each solution back into the original equation should give zero.(3)² − 8(3) + 15 = 0 ✓ and (5)² − 8(5) + 15 = 0 ✓

7.D. y = 9x + 75

1. Find the part that happens only once. The $75 call-out fee is charged a single time, no matter how many hours there are. In y = mx + b that is b, the y-intercept.b = 75
2. Find the part that repeats. The $9 happens for every hour, so it gets multiplied by x. That is the slope.m = 9
3. Put the two numbers into y = mx + b. The slope multiplies x; the one-time amount is added on the end.y = 9x + 75
4. Test the equation. After 5 hours the equation should match what you get by counting: 5 × $9 plus the $75 call-out fee.y = 9(5) + 75 = 45 + 75 = 120

8.A. 17

1. Work inside the parentheses. Add the two numbers grouped by the parentheses.2 + 16 = 18
2. Divide. Division comes before addition, so divide the sum before adding the last number.18 ÷ 3 = 6
3. Add last. Add the final number to the quotient.6 + 11 = 17
4. Check the order. Parentheses, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

9.B. 2n − 3

1. Translate "2 times a number n". A number multiplied by 2 is written with the number in front of the letter.2 × n = 2n
2. Translate "3 less than". "3 less than" something means that something comes first and 3 is taken away from it.2n − 3
3. Test it with a number. Try n = 10. 2 times 10 is 20, and 3 less than that is 17, which is what the expression gives.2(10) − 3 = 17

10.A. 3/2

1. Name the rule. Slope measures steepness as rise over run: how far the line goes up or down, divided by how far it goes across.m = rise ÷ run
2. Pick two points the line passes through exactly. Use the two marked points, where the line crosses corners of the grid.(2, 1) and (4, 4)
3. Count the rise and the run. From the first point to the second the line goes 3 squares up and 2 squares right.rise = 4 − 1 = 3; run = 4 − 2 = 2
4. Divide and simplify. The fraction is already in lowest terms.m = 3 ÷ 2 = 3/2