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Build selected Arithmetic, QAS and AAF placement foundations. Selected foundations; check coverage for the full scope.
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8 original questionsSeparate explanationsBrowser print · Version 2026-11-04-r02
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Two machine bays charge constant rates per minute with no other charges. Bay A charges $7.50 for 30 minutes. Bay B charges $10.08 for 48 minutes. How much less does Bay B charge for 120 minutes?
$4.80
$0.04
$2.58
$25.20
Read the answer and explanation
Answer: $4.80
Find each charge in dollars per minute. Bay A charges 7.50 ÷ 30 = 0.25, while Bay B charges 10.08 ÷ 48 = 0.21.
The difference is $0.04 per minute. Over the same 120 minutes, Bay B saves 120 × $0.04 = $4.80. You can also compare the full charges of thirty dollars and twenty-five dollars and twenty cents.
Review the lesson QUESTION 3 · Factoring, quadratic equations, and graphs
Which option gives all real solutions of (x − 2)² = 25?
x = −3 or x = 7
x = 7 only
x = −7 or x = 3
x = −5 or x = 5
Read the answer and explanation
Answer: x = −3 or x = 7
The entire expression x − 2 is squared. Both 5 and −5 have square 25, so solve x − 2 = 5 and x − 2 = −5.
Adding 2 in each equation gives 7 and −3. Substitute to check: 7 − 2 = 5, and −3 − 2 = −5. Both squares equal 25. Keeping the negative inner value is necessary because squaring erases the sign.
A workshop charges a one-time setup fee plus the same price for each panel cut. An order of 3 panels costs $17 and an order of 8 panels costs $32. What is the setup fee?
$8
$3
$17
$14
Read the answer and explanation
Answer: $8
Subtract the total prices and the quantities to isolate the variable charge. Five more panels cost $15 more, so each panel costs $3.
The order of three panels contains $9 in variable charges. Subtract $9 from $17 to get the $8 setup fee. Checking the larger order gives 8 + 8 × 3 = 32.
Review the lesson QUESTION 5 · Function notation and domain restrictions
A function has rule f(t) = 2t + 4 when t < 3 and rule f(t) = t² − 2 when t ≥ 3. What is f(3)?
10
7
9
11
Read the answer and explanation
Answer: 7
The equality in t ≥ 3 includes the input three, so use the second rule. The first inequality is strict and does not include three.
Substitute the input into t² − 2. The square gives nine, and subtracting two gives seven.
Review the lesson QUESTION 6 · Data displays, summaries, and probability
Four attendance counts have a mean of 11. Three counts are 8, 10, and 12. What is the fourth count?
3
11
14
44
Read the answer and explanation
Answer: 14
The mean equals the total divided by the number of counts. With four counts and mean eleven, the total must be forty-four.
The known counts sum to thirty. Subtract that from forty-four to get fourteen. Verify the resulting four-count mean by dividing forty-four by four.
Review the lesson QUESTION 7 · Number sense, fractions, decimals, and percents
Two sections of a trail are 3/10 mile and 5/12 mile long. What is their total length in miles?
43/60
4/11
2/15
23/60
Read the answer and explanation
Answer: 43/60
The tenths and twelfths represent different-sized pieces. Rename both in sixtieths so they can be added.
Multiply the numerator and denominator of 3/10 by 6 to get 18/60. Multiply those of 5/12 by 5 to get 25/60. The total is 43/60 mile.
Review the lesson QUESTION 8 · Number sense, fractions, decimals, and percents
A coating machine uses 0.35 liter of finish for each square meter. How many square meters can it cover with 0.84 liter at that rate?
0.24
24
0.294
2.4
Read the answer and explanation
Answer: 2.4
Divide available liters by liters needed per square meter. The liters cancel, leaving square meters.
Multiply the dividend and divisor by 100 to get 84 ÷ 35 = 2.4. Check that 2.4 square meters at the given rate uses exactly 0.84 liter.
Selected Arithmetic, QAS, and AAF foundations for college math placement..
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