GED® Practice Exam 1 Mathematical Reasoning
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- Question 1 of 46
1. Question
Answer without using a calculator
A ticket to see a movie costs $8.50 at the local theatre. Samuel goes and buys tickets for himself and his two friends. In addition, he buys a large popcorn for $6.75 and three sodas that each cost $3.00. If Samuel pays with a $50 gift card, how much money is the remaining balance?
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2. Question
Answer without using a calculator
Perform the operation.
\( \left( -3x^{2}-2xy+4y^{2} \right) + \left( 5x^{2}+3xy-3y^{2} \right) \)
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3. Question
Answer without using a calculator
What is 96 ÷ 12?
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4. Question
Answer without using a calculator
Multiply.
\( \left( 5x-3 \right) \left( 5x+3 \right) \)
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5. Question
Answer without using a calculator
A small landscaping company mows lawns and has three 5.4–gallon gas cans. One day, the landscapers empty the gas cans three times. How many gallons of gas did they use?
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6. Question
If 17 widgets failed but the other 1,273 worked properly, what is the failure rate of that widget?
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7. Question
Which is different from the others?
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8. Question
How many prime numbers are less than 20 but greater than 0?
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9. Question
Which number will appear farthest right on a standard number line?
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10. Question
Evaluate the expression. 15 x (-15)
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11. Question
A regular hexagon has a side length of 5 inches and an apothem of 2 inches.
Find the area in square inches. (Note: A = ½ ap).
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12. Question
If the term of a mobile-phone contract is in multiples of a year, which duration can a customer choose?
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13. Question
Find the median for the data set:
34, 31, 37, 35, 38, 33, 39, 32, 36, 35, 37, 33
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14. Question
A wedge of cheese is in the shape of a right triangular prism. The area of the base is 30 square inches.
What is the height in inches of the cheese if the volume is 150 cubic inches?
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15. Question
A rectangular pyramid has a length of 10 inches, a width of 11 inches, and a height of 12 inches. Find the volume in cubic inches.
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16. Question
What is the intersection of two walls in a room?
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17. Question
A circle has an area of 12 square feet. Find the diameter to the nearest tenth of a foot. Use 3.14 for π.
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18. Question
Solve the equation by any method.
\({2x}^2-70=2\)
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19. Question
Which decimal is the least?
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20. Question
There is an election at a school where 5 candidates out of 10 will be elected. Which object and results are the most appropriate for a simulation?
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21. Question
Convert 2.5 miles to feet.
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22. Question
The histogram below shows the amount a family spent on groceries during the year. Which statement is true for the histogram?
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23. Question
Simplify.
\( \left( \frac{x^{3}y^{-2}}{x^{-2}y^{3}} \right) ^{5}\)
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24. Question
Solve the system of equations.
\(-2x+2y=28\\3x+y=-22\)
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25. Question
Solve the equation by completing the square.
\(x^2-2x-37=0\)
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26. Question
If a letter is chosen at random from the word SUBSTITUTE, what is the probability that the letter chosen is “S” or “T”?
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27. Question
What is the order of rotational symmetry for a parallelogram?
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28. Question
A spinner contains numbers 1–20. What is the probability of spinning a multiple of 3 or a multiple of 5?
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29. Question
A basketball has a diameter of 10 inches. What is the volume in cubic inches inside the ball? Use 3.14 for \( \pi \).
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30. Question
Find the values from the box plot.
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31. Question
Solve the equation for the unknown.
\(\frac{x}{2}+5=8\)
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32. Question
Find the range for the data set:
34, 45, 27, 29, 36, 60, 52, 48, 41, 65, 44, 50, 64, 58, 47, 31
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33. Question
One athlete had a salary of about 3 x 10⁷ dollars per year and another athlete had a salary of about 2 x 10⁶ dollars per year. How many times larger is the salary of the first athlete?
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34. Question
A group is conducting a survey at a mall asking shoppers their opinion of the mall. What type of sampling is used?
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35. Question
Solve the equation by factoring.
\(x^2-5x-50=0\)
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36. Question
Find the area in square centimeters of a circle with a diameter of 16 centimeters. Use 3.14 for π.
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37. Question
The area of a half circle is 48 square centimeters. Find the circumference of the curved portion of the half circle to the nearest tenth of a centimeter. Use 3.14 for π.
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38. Question
Find the mode for the data set:
42, 45, 44, 44, 45, 42, 45, 44, 45, 46, 42, 44, 41, 48, 47, 46, 45, 42, 42, 44
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39. Question
A person has $250 in a checking account and writes checks for $70, $85, $60, and $100. There is also a fee of $20. What is the balance of the account?
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40. Question
Change 0.375 to a fraction. Simplify completely.
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41. Question
A box in the shape of a right rectangular prism has dimensions of 6 centimeters by 7 centimeters by 8 centimeters. What is the volume in cubic centimeters?
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42. Question
A doctor wants to study the effects of a low–fat diet in patients. What would be needed to create an observational study?
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43. Question
Solve the system of equations by graphing.
\(y=\frac{1}{3} x+2\\y=\frac{2}{3} x+5\)
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44. Question
Apply the polynomial identity to rewrite \(x^2+20x+100\).
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45. Question
Solve the inequality for the unknown.
\(\frac{1}{2} \left( 4x+3 \right) <\frac{3}{4}x+2\)
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46. Question
A pair of jeans with tax costs $39.97, and a shirt with tax costs $18.49. What is the amount of change for a pair of jeans and two shirts if playing with a $100 bill?
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