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Mixed skills
10 original practice questions · Untimed · Follow each question’s response instructions
1. Which of these numbers is greatest?
accuplacer-q0052. A shop charges a deposit equal to 15% of the total repair price. The deposit is $18. What is the total repair price?
accuplacer-q0043. A lab bottle contains 0.36 liter of a solution. A technician uses 0.75 of the amount in the bottle. How many liters does the technician use?
accuplacer-q0014. 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?
accuplacer-q0115. Adding the contents to an empty crate increases its weight by 4 pounds. Three identical full crates weigh 39 pounds altogether. What is the weight of one empty crate, in pounds?
accuplacer-q0136. Which option gives all real solutions of (x − 4)(x + 2) = 7?
accuplacer-q0207. Which option gives all real solutions of (x − 2)² = 25?
accuplacer-q0198. A line passes through the points (−4, 11) and (2, −1). What is its slope?
accuplacer-q0129. The graph of y = (x + 3)² − 4 has a lowest point. Which ordered pair gives that point?
accuplacer-q02110. The table shows receipts for repairs and rentals by time of day. A repair receipt is chosen uniformly at random. What is the probability that it came from the morning?
Answers & reasoning
1. 3/4 · Choice C
Convert each number to hundredths for a common comparison. The decimal gives 73, the percent gives 71, and seven tenths gives 70 hundredths. Three fourths equals 75 hundredths because each fourth contains 25 hundredths. The greatest count of hundredths is 75.
accuplacer-q0052. $120.00 · Choice B
Let P be the total repair price. The deposit is fifteen hundredths of P, so 0.15P = 18. Divide 18 by 0.15 to get 120 dollars. Checking in the original relationship, fifteen percent of $120 is exactly $18.
accuplacer-q0043. 0.27 · Choice C
Taking 0.75 of the amount means multiplying the whole amount by 0.75. Since 0.75 is between zero and one, the result must be smaller than 0.36 liter. Find three fourths of 0.36: one fourth is 0.09 liter, and three of those parts give 0.27 liter.
accuplacer-q0014. $8 · Choice A
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.
accuplacer-q0115. 9 · Choice A
Let x represent the empty weight. Each full crate weighs x + 4 pounds, so the combined weight is 3(x + 4) = 39. Divide by three to get x + 4 = 13, then subtract four. An empty crate weighs nine pounds. Three crates at 9 + 4 pounds apiece give 39 pounds.
accuplacer-q0136. x = −3 or x = 5 · Choice B
Expand the product to get x² − 2x − 8 = 7. Subtract seven from both sides so the equation has zero on the right. Factor x² − 2x − 15 as (x − 5)(x + 3). A zero product has a zero factor, so the solutions are five and negative three. In the original equation, each makes the product seven.
accuplacer-q0207. x = −3 or x = 7 · Choice A
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.
accuplacer-q0198. −2 · Choice B
Use the first point as the starting point for both differences. The vertical change is −1 − 11 = −12, and the horizontal change is 2 − (−4) = 6. Divide the vertical change by the horizontal change to get −2. The negative sign agrees with falling as you move right.
accuplacer-q0129. (−3, −4) · Choice C
A real square is always nonnegative, so the smallest possible value of the squared term is zero. That happens when x + 3 equals zero. Use x = −3 and substitute. The resulting output is −4, so the lowest point has coordinates (−3, −4).
accuplacer-q02110. 3/5 · Choice D
Start by restricting the sample space to repairs. There are 12 in the morning and 8 in the afternoon, giving twenty equally likely repair receipts. Twelve satisfy the morning condition, so the probability is 12/20 = 3/5. The rental row is useful for a question about all receipts.
accuplacer-q017Original selected foundation practice. Educator review is pending. Not an official exam paper.