GED Math Practice Test 2: Algebra, Geometry and Data
- Algebra, Geometry and Data
- 15 questions
- 22 minutes
These 15 questions practice the algebra, geometry and data skills that make up most of the GED Mathematical Reasoning test. The real test gives you a formula sheet, so the key skill is choosing the right formula and setting up the problem before you calculate.
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Question 1
Which inequality is equivalent to 5 − 2x ≤ 17?
Correct answer: B
Subtract 5 from both sides to get −2x ≤ 12, then divide by −2. Dividing by a negative number reverses the inequality sign, so x ≥ −6. The answer x ≤ −6 comes from forgetting to reverse the sign.
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Question 2
A theater charges $12 for an adult ticket and $8 for a child ticket. A family bought 9 tickets for a total of $92. How many adult tickets did the family buy?
Correct answer: C
Let a be the number of adult tickets, so 9 − a are child tickets: 12a + 8(9 − a) = 92. This gives 4a + 72 = 92, so a = 5. Check: 5 × $12 + 4 × $8 = $60 + $32 = $92. The answer 4 is the number of child tickets.
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Question 3
What are the solutions of the equation x2 + 2x − 15 = 0?
Correct answer: D
Factor the left side: x2 + 2x − 15 = (x + 5)(x − 3). Setting each factor equal to zero gives x = −5 or x = 3. The pair −3 and 5 has the signs reversed: (−3)2 + 2(−3) − 15 = −12, not 0.
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Question 4
A cylindrical water tank has a radius of 3 inches and a height of 10 inches. The volume of a cylinder is V = πr2h. What is the volume of the tank, to the nearest cubic inch?
Correct answer: C
V = π × 32 × 10 = 90π ≈ 282.7, which rounds to 283 cubic inches. The answer 188 is 2πrh, the area of the curved side, and 1,131 comes from using the diameter 6 in place of the radius.
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Question 5
Which equation describes the line that passes through the point (0, −3) and is parallel to the line y = 2x + 5?
Correct answer: A
Parallel lines have the same slope, so the new line also has slope 2. It crosses the y-axis at (0, −3), so its y-intercept is −3: y = 2x − 3. The slope −12 belongs to a line perpendicular to y = 2x + 5, not parallel to it.
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Question 6
A teacher collected data on how many hours students studied and their test scores. The line of best fit for the data is y = 4.5x + 52, where x is the number of hours studied and y is the test score. Based on this line, what score would be predicted for a student who studied 6 hours?
Correct answer: C
Substitute x = 6: y = 4.5(6) + 52 = 27 + 52 = 79. The answer 58 comes from adding 6 to 52 instead of multiplying 6 by the slope, and 261 comes from multiplying 4.5 by the sum 6 + 52.
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Question 7
The graph shows the amount of water left in a tank as it drains at a constant rate.
What is the slope of the line, and what does it mean in this situation?
Correct answer: A
The line falls from 40 gallons at 0 hours to 0 gallons at 8 hours, so the slope is (0 − 40) ÷ (8 − 0) = −5 gallons per hour. The value 40 is the y-intercept, not the slope, and −15 comes from dividing hours by gallons.
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Question 8
Dana's scores on her first three quizzes were 78, 85 and 92. What score does she need on the fourth quiz so that the mean of all four scores is 86?
Correct answer: D
A mean of 86 over four quizzes requires a total of 86 × 4 = 344 points. The first three scores add up to 78 + 85 + 92 = 255, so she needs 344 − 255 = 89. The answer 85 is the mean of the first three scores.
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Question 9
A rectangular backyard measures 20 feet by 12 feet. A square patio that is 6 feet on each side is built in one corner, and the rest of the yard is covered with grass. How many square feet of the yard are covered with grass?
Correct answer: A
The whole yard has an area of 20 × 12 = 240 square feet and the patio covers 6 × 6 = 36 square feet, so the grass covers 240 − 36 = 204 square feet. The answer 216 subtracts the patio's perimeter (24) instead of its area.
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Question 10
At the same time of day, a person who is 6 feet tall casts a shadow 4 feet long, and a tree casts a shadow 30 feet long. How tall is the tree?
Correct answer: C
The person and the tree form similar triangles, so height ÷ shadow is the same for both: 6 ÷ 4 = h ÷ 30, which gives h = 1.5 × 30 = 45 feet. The answer 20 comes from setting up the ratio upside down (30 × 4 ÷ 6).
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Question 11
Which expression is equivalent to (3x2y)(4x3y5)?
Correct answer: B
Multiply the coefficients (3 × 4 = 12) and add the exponents of each variable: x2 + 3 = x5 and y1 + 5 = y6. The answer 7x5y6 adds the coefficients instead of multiplying them.
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Question 12
A taxi company uses the equation C = 2.50m + 4 to find the cost C, in dollars, of a ride that is m miles long. What does the number 4 represent?
Correct answer: B
The 4 is the constant term: even a ride of 0 miles would cost $4, so it is a fixed fee added to every ride. The cost per mile is the coefficient 2.50, and a 4-mile ride would cost 2.50 × 4 + 4 = $14.
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Question 13
A fair coin is flipped and a standard number cube with faces 1 through 6 is rolled. What is the probability of getting heads and a number greater than 4?
Correct answer: A
The events are independent, so multiply: P(heads) = 12 and P(5 or 6) = 26 = 13, giving 12 × 13 = 16. The answer 56 comes from adding the two probabilities instead of multiplying.
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Question 14
A ball is thrown upward. Its height in feet after t seconds is h(t) = −16t2 + 64t + 5. The ball reaches its greatest height when t = 2. What is the greatest height of the ball?
Correct answer: D
Substitute t = 2: −16(4) + 64(2) + 5 = −64 + 128 + 5 = 69 feet. The answer 53 is the height after 1 second, and 65 is the height after 1.5 seconds, both before the ball reaches its peak.
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Question 15
A warehouse worker earns $15 per hour for the first 40 hours in a week. For each hour over 40, the worker earns 1.5 times the regular rate. How much does the worker earn in a week with 46 hours of work?
Correct answer: B
Regular pay is 40 × $15 = $600. The overtime rate is 1.5 × $15 = $22.50, and 6 overtime hours earn 6 × $22.50 = $135, for a total of $735. The answer $780 uses double pay ($30) for overtime, and $1,035 pays all 46 hours at the overtime rate.
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