ALEKS Math Placement Test: What to Expect, Plus 12 Practice Questions
How ALEKS PPL works, how the rules vary by college, how to use retakes, and 12 open-response practice questions solved step by step.
ALEKS PPL (Placement, Preparation, and Learning) is the math placement test many colleges use instead of the ACCUPLACER. It is adaptive, has up to 30 questions covering arithmetic through precalculus, and gives you a single score from 0 to 100. Your college decides which score places you into which course. There is no "passing" score.
Two things make ALEKS different from other placement tests, and both work in your favor if you know about them. First, most questions have no answer choices: you type the answer yourself. Second, between attempts you can work in a Prep and Learning Module and then retest, so your first score doesn't have to be your final one. Below is what to expect, how the rules differ from school to school, and 12 original practice questions in the ALEKS style.
The rules depend on your school
McGraw Hill builds ALEKS, but each college sets the time limit, the calculator policy, the number of retakes, and the scores it needs. A few real examples from college placement pages show how much this varies:
| College | Time limit | Calculator | Retakes |
|---|---|---|---|
| North Seattle College | 2 hours per attempt | Your own allowed | One, after 48 hours |
| Monmouth University | 2 hours 30 minutes | ALEKS calculator only | Set by the school |
| Catholic University of America | 3 hours (most finish in 60 to 90 minutes) | None | Up to 4 more, 48 hours apart, after 5 hours in the modules |
| Kennesaw State University | 48-hour window for the first attempt; 3 hours for proctored attempts | Set by the school | Prep module access for up to 6 months |
Before you start, find your own college's placement page and check these four things, plus whether the first attempt is proctored. Rules can change from year to year.
How to use the retakes to your advantage
- Take the first attempt honestly, without help. ALEKS places you based on what you actually know, and a falsely high score can put you in a course you are not ready for.
- Work the Prep and Learning Module on the topics it says you are missing. Many schools require a minimum amount of time in the module before you can retest.
- Retest when the module shows real progress, not just when the waiting period ends.
Practice questions in the ALEKS style
These questions go from arithmetic to trigonometry, roughly in the order ALEKS covers them. There are no answer choices: work out each answer, then open the solution.
Arithmetic and equations
1.Simplify: \(\left(\tfrac{3}{4} - \tfrac{1}{6}\right) \div \tfrac{5}{12}\)
Your answer: ________
Show solution
\[\begin{gathered}\tfrac{9}{12} - \tfrac{2}{12} = \tfrac{7}{12} \\ \tfrac{7}{12} \div \tfrac{5}{12} = \tfrac{7}{12} \times \tfrac{12}{5} = \tfrac{7}{5}\end{gathered}\]Common trap: Dividing before subtracting. The parentheses come first. Also, enter the fraction in simplest form; ALEKS usually expects exact answers, not rounded decimals.
Answer: \(\tfrac{7}{5}\)
2.Solve for \(x\): \(5 - 3(x - 2) = 2x + 1\)
Your answer: ________
Show solution
\[\begin{gathered}5 - 3x + 6 = 2x + 1 \\ \Rightarrow\; 11 - 3x = 2x + 1 \\ \Rightarrow\; 10 = 5x \\ \Rightarrow\; x = 2\end{gathered}\]Common trap: Writing \(-3(x - 2)\) as \(-3x - 6\). A negative times a negative is positive: \(-3 \times -2 = +6\).
Answer: \(x = 2\)
3.Solve the inequality: \(2x - 7 \gt 3x + 1\)
Your answer: ________
Show solution
\[\begin{gathered}2x - 3x \gt 1 + 7 \\ \Rightarrow\; -x \gt 8 \\ \Rightarrow\; x \lt -8\end{gathered}\]Common trap: Forgetting to flip the sign when dividing by \(-1\). Check with \(x = -10\): \(-27 \gt -29\) is true.
Answer: \(x \lt -8\)
4.Write the equation, in slope-intercept form, of the line through \((2, -1)\) that is parallel to \(2x + y = 5\).
Your answer: ________
Show solution
The given line is \(y = -2x + 5\), so the slope is \(-2\). Use the point to find \(b\):
\[\begin{gathered}-1 = -2(2) + b \\ \Rightarrow\; b = 3\end{gathered}\]Common trap: Using slope 2 because the equation shows \(2x\). Solve for \(y\) first: the slope is the coefficient of \(x\) only then.
Answer: \(y = -2x + 3\)
5.Solve the system: \(3x + 2y = 16\) and \(x - 2y = 0\). Give the answer as an ordered pair.
Your answer: ________
Show solution
Add the equations to eliminate \(y\).
\[\begin{gathered}4x = 16 \\ \Rightarrow\; x = 4 \\ 4 - 2y = 0 \\ \Rightarrow\; y = 2\end{gathered}\]Common trap: Entering only \(x = 4\). A system's solution is an ordered pair, and ALEKS will mark a single number wrong.
Answer: \((4, 2)\)
Polynomials, radicals, and rational expressions
6.Factor completely: \(6x^2 - 7x - 3\)
Your answer: ________
Show solution
\(ac = -18\). Two numbers that multiply to \(-18\) and add to \(-7\): \(-9\) and \(2\).
\[\begin{gathered}6x^2 - 9x + 2x - 3 \\ = 3x(2x - 3) + 1(2x - 3) \\ = (3x + 1)(2x - 3)\end{gathered}\]Common trap: Getting the factors right but the signs wrong. Multiply back: \((3x + 1)(2x - 3) = 6x^2 - 7x - 3\).
Answer: \((3x + 1)(2x - 3)\)
7.Simplify: \(\sqrt{50} + \sqrt{18}\)
Your answer: ________
Show solution
\[\begin{gathered}\sqrt{25 \cdot 2} + \sqrt{9 \cdot 2} \\ = 5\sqrt{2} + 3\sqrt{2} = 8\sqrt{2}\end{gathered}\]Common trap: Adding under one root, \(\sqrt{68}\). Square roots only combine after you simplify them to the same radical.
Answer: \(8\sqrt{2}\)
8.Simplify: \(\dfrac{x^2 - 4}{x^2 + 5x + 6}\)
Your answer: ________
Show solution
\[\frac{(x - 2)(x + 2)}{(x + 2)(x + 3)} = \frac{x - 2}{x + 3}\]Common trap: Canceling the \(x^2\) terms. Only common factors cancel, so factor the top and bottom first.
Answer: \(\dfrac{x - 2}{x + 3}\)
9.Solve: \(x^2 + 4x - 21 = 0\)
Your answer: ________
Show solution
\[\begin{gathered}(x + 7)(x - 3) = 0 \\ \Rightarrow\; x = -7 \text{ or } x = 3\end{gathered}\]Common trap: Entering only one solution. When ALEKS asks for all solutions, separate them with a comma.
Answer: \(x = -7\) or \(x = 3\)
Functions, exponents, and trigonometry
10.If \(f(x) = x^2 - 2x\), find and simplify \(f(a + 1)\).
Your answer: ________
Show solution
\[\begin{gathered}(a + 1)^2 - 2(a + 1) \\ = a^2 + 2a + 1 - 2a - 2 \\ = a^2 - 1\end{gathered}\]Common trap: Writing \((a + 1)^2\) as \(a^2 + 1\). Squaring a sum gives a middle term: \(a^2 + 2a + 1\).
Answer: \(a^2 - 1\)
11.Solve: \(3^{2x - 1} = 27\)
Your answer: ________
Show solution
\[\begin{gathered}27 = 3^3 \\ \Rightarrow\; 2x - 1 = 3 \\ \Rightarrow\; x = 2\end{gathered}\]Common trap: Setting \(2x - 1 = 27\). Rewrite both sides with the same base before comparing exponents.
Answer: \(x = 2\)
12.In a right triangle, \(\sin \theta = \tfrac{3}{5}\). Find \(\cos \theta\).
Your answer: ________
Show solution
Sine is opposite over hypotenuse, so the opposite side is 3 and the hypotenuse is 5. By the Pythagorean theorem, the adjacent side is \(\sqrt{25 - 9} = 4\).
\[\cos \theta = \tfrac{\text{adjacent}}{\text{hypotenuse}} = \tfrac{4}{5}\]Common trap: Answering \(\tfrac{5}{3}\) or \(\tfrac{3}{4}\). Cosine is adjacent over hypotenuse, and the hypotenuse is always the longest side.
Answer: \(\tfrac{4}{5}\)
Answer key
- 1 \(\tfrac{7}{5}\)
- 2 \(x = 2\)
- 3 \(x \lt -8\)
- 4 \(y = -2x + 3\)
- 5 \((4, 2)\)
- 6 \((3x + 1)(2x - 3)\)
- 7 \(8\sqrt{2}\)
- 8 \(\dfrac{x - 2}{x + 3}\)
- 9 \(x = -7\) or \(x = 3\)
- 10 \(a^2 - 1\)
- 11 \(x = 2\)
- 12 \(\tfrac{4}{5}\)
Missed several in the first group? Start with our Algebra 1 review. For factoring and rational expressions, see how to factor trinomials; for questions 11 and 12, the ACCUPLACER AAF practice test has more at the same level.
Teacher's note: Because ALEKS has no answer choices, there is nothing to check your work against, so build the check into your routine. Put every solution back into the original equation, and give answers in exact form, as fractions and radicals, unless the question asks you to round. Many students lose points not on the math but on entering \(1.4\) when ALEKS wanted \(\tfrac{7}{5}\).
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