One of the best ways to study for the GED Mathematical Reasoning test is to practice with questions that are similar to the real thing. Here are some questions to give you GED math practice in several different topics. Answers with full explanations are at the end of the post, along with some links to resources to help you if you need more review.

## GED Math Practice Questions

1. Which choice is the following expression simplified?

4(8−3)^{2}÷10−2(3)+5

A. 9

B. 19

C. 29

D.39

2. What are the values of x and y, given the system of equations below?

x+4y=3

3x+2y=49

A. x=−4; y=19

B. x=19; y=−4

C. x=4; y=−19

D. x=−19; y=4

3. Solve the following inequality.

7-2x>21

A. x>7

B. x−7

C. x>−7

D. x<−7

4. Which choice shows how to factor the following trinomial?

8x^{2}−14x−15

A. (2x−5)(4x+3)

B. (8x−14)(5x−3)

C. (4x−7)(x+15)

D. (2x+3)(2x−5)

5. Burke is buying a new sofa. The sofa is listed for $1,699 dollars. The store is having a sale, and the sofa is 20% off. She pays 10% sales tax on the sale price of the sofa. How much money did Burke spend on the sofa?

A. $1,224.00

B. $1,359.20

C. $1,495.12

D. $1,529.10

6. The ratio of cats to dogs that a veterinary office treats is 3 to 7. On Monday, the office sees 21 dogs. How many cats and dogs does the office see in total on that day?

A. 9

B. 24

C. 28

D. 30

7. What are the odds of flipping a coin five times and landing on heads each of those times?

A. 1 out of 2

B. 1 out of 5

C. 1 out of 32

D. 1 out of 36

8. Wyatt is putting new wood paneling on his dining room floor. If his dining room is 14 by 11 feet, how many square feet of paneling does he need to buy?

A. 25 square feet

B. 50 square feet

C. 121 square feet

D. 154 square feet.

9. Which set of numbers has a mean and a median of 22?

A. 18, 20, 22, 24, 26

B. 22, 22, 24, 26, 28

C. 17, 18, 22, 24, 25

D. 13, 22, 24, 25, 26

10. Which equation describes a line with a slope of 3 that passes through the point (−1, 2)?

A. 2 = −1x + 3

B. y = 3x + 5

C. 3 = 2x + b

D. y = 5x + 3

### Answer Key

##### 1. A

When simplifying this expression, remember to use the order of operations. Use the acronym PEMDAS to help you remember the order:

- P = parentheses
- E = exponents
- M = multiplication
- D = division
- A = addition
- S = subtraction

Note: If an expression does not include any of these operations, simply skip it and move on to the next operation.

**P**EMDAS: Begin with the calculation in parentheses:

4(8−3)^{2}÷10−2(3)+5

4(5)^{2}÷10−2(3)+5

P**E**MDAS: Next, simplify the exponential expression:

4(5)^{2}÷10−2(3)+5

4(25)÷10−2(3)+5

PE**MD**AS: Now complete multiplication and division, left-to-right:

4(25)÷10−2(3)+5

100÷10−2(3)+5

10−2(3)+5

10−6+5

PEMD**AS**: Finally, complete addition and subtraction, left-to-right.

10−6+5

4+5=9

##### 2. B

To solve a system of equations using substitution, there are three steps:

- Isolate the x variable in the first equation.
- Substitute the expression of x into the second equation and solve for y.
- Substitute the value of y into any equation and solve for x.

Step 1: Isolate the x variable in the first equation:

x+4y=3

x=3−4y

Step 2: Now you have an expression describing x. Substitute this expression for x in the second equation. Find the value of y.

3x+2y=49

3(3−4y)+2y=49

9−12y+2y=49

9−10y=49

−10y=40

y=−4

Step 3: Now that you know the value of y, you can substitute this value into any equation in the system and solve for x.

x=3−4y

x=3−4(−4)

x=3+16

x=19

##### 3. D

Solve inequalities the same way that you solve equations: by isolating the variable on either side of the greater than or less than symbol. However, when working with inequalities, you need to remember to flip the direction of the sign if you multiply or divide by a negative number.

7−2x>21

−2x>14

x**<**−7

##### 4. A

This is a multiple choice question, so use that to your advantage. You know the answer is one of those four choices— work backwards and see which one works! You can work backwards using the FOIL method to multiply the two binomials in each answer choice until you find the pair whose product is equal to the trinomial.

The FOIL acronym can help you remember the order in which you should multiply the terms in the binomials. FOIL stands for first, outside, inside, and last.

**F**OIL: The first thing you need to do is multiply the first terms in the binomials.

(**2x**−5)(**4x**+3)

(2x)(4x)=8x^{2}

F**O**IL: Next multiply the outside terms in the binomials: the first term in the first binomial, and the last term in the second binomial.

(**2x**−5)(4x+**3**)

(2x)(3)=6x

FO**I**L: Next multiply the inside terms in the binomials: the second term of the first binomial, and the first term of the second binomial.

(2x**−5**)(**4x**+3)

(−5)(4x)=−20x

FOI**L**: Finally, multiply the last terms in each binomial.

(2x**−5**)(4x+**3**)

(−5)(3)=−15

Now combine the four new terms into a new polynomial:

8x^{2}+6x−20x−15

Combine like terms to simplify:

8x^{2}+6x−20x−15

8x^{2}−14x−15

##### 5. C

To find the discount price of an item, you need to follow two steps:

- Multiply the listed price by the percent off to find the discounted amount.
- Subtract the discounted amount from the listed price to find the sales price.

This problem also includes the tax Burke paid on the sales price of the sofa. So, this problem requires two additional steps:

- Multiply the sales price by the tax percentage to find the amount of tax.
- Add the amount of tax to the sales price.

Step 1: The listed price is $1,699. The sofa is 20% off. Before you multiply, you need to change the percent to a decimal. 20% is the same as the decimal .20:

1699(.20)=339.80

Step 2: The amount discounted from the listed price is $339.80. Subtract this amount from the listed price:

1699−339.80=1359.20

Step 3: The sales price is $1,359.20. The tax is 10%. 10% is the same as the decimal .10:

1359.20(.10)=135.92

Step 4: The tax is $135.92. The final step is to add the tax to the sales price.

1359.20+135.92=1495.12

##### 6. D

To solve, set up two ratios and set them equal to each other: the ratio of cats to dogs, and the ratio of cats to dogs treated on Monday. Since you don’t know the number of cats seen on Monday, use a variable to stand for the unknown amount and cross-multiply to solve.

The office treated 9 cats on Monday.

The question, however, asks how many cats and dogs were seen in total. So, you need to add the number of dogs and cats: 21 + 9 = 30.

##### 7. C

This is a matter of compound probability, since multiple independent events need to happen. To find the probability, you need to multiply the probabilities of each independent event together. Since there are five events (getting a heads 5 times), and the probability of each event is 1 out of 2 (since a coin has two sides), to find the probability of tossing 5 heads in a row you would calculate:

½×½×½×½×½=^{1}⁄_{32}

##### 8. D

Since Wyatt is covering a 2-dimensional space, a floor, this is a matter of area. To find the area of a rectangle, you need to multiply the length times the width:

14(11)=154

##### 9. A

Calculate the mean by adding all numbers in the set, and then dividing by the number of numbers in the set. For this particular set, there are 5 numbers, so you would calculate:

18+20+22+24+26=110

110÷5=22

So the mean is 22.

The median is the middle number in a set of numbers ordered numerically. For a set with an odd number of numbers, it is simply the number that has the same amount of numbers before and after it. Since this set has five numbers, the median is the number with two numbers below it and two numbers above it. That’s also 22:

18, 20, **22**, 24, 26

##### 10. B

The slope-intercept form of a line states that y=mx+b, where (x,y) equals any point on the line, *m* equals the slope of the line, and *b* equals the y-intercept. Choice B is the only equation that correctly substitutes the slope (3) for m in the slope-intercept form. You can also use the given point to calculate that the y-intercept is 5:

y=mx+b

2=(3)(−1)+b

2=−3+b

5=b

So the line has a slope of 4, and a y-intercept of 5, giving you the equation y=3x+5.

## Need More Practice?

If any of these had you stumped, you might need a little more topical review. Check out these other helpful math posts for more GED math practice:

- What’s on the GED Math Test?
- Probability
- Converting Units of Measurement
- Geometry Formulas
- Data Analysis