A plumber charges $65 for a visit plus $48 for each hour of work. One bill came to $257. Which equation gives the hours worked, h?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
A school sold 150 tickets to a play for $1,400 in all. Adult tickets cost $12 and student tickets cost $7. How many adult tickets were sold?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
How many solutions does the system 2x − 6y = 10 and x − 3y = 4 have?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
Solve 4(2x − 3) − 5 = 3(x + 6) + 2x − 2.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
Solve A = (1/2)h(b + c) for b.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
Solve the inequality 3 − 2(x + 4) ≥ 7.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
Which pair (x, y) solves the system 2x + 3y = 12 and 4x − 3y = 6?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear equations" (10–15% of the test)
Show all 60 questions (53 more)
Linear applications and graphs 7
A candle is 20 cm tall and burns down 1.5 cm each hour. After how many hours is it 8 cm tall?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
At what point do the lines y = 2x + 1 and y = −x + 7 cross?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
The cost C, in dollars, of renting a truck and driving it m miles is C = 0.75m + 30. What does 0.75 stand for?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
Line p passes through (0, 4) and is parallel to the line 2x − y = 3. Where does line p cross the x-axis?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
Which equation is the line through (2, −1) and (6, 7)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
Which line passes through (3, 1) and is perpendicular to 3x + 4y = 8?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
Which point is in the solution region of both y ≤ 2x + 1 and y > −x + 2?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Linear applications and graphs" (10–15% of the test)
Factoring 4
Factor 2x³ − 18x completely.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Factoring" (5–10% of the test)
Factor 6x² − 7x − 20.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Factoring" (5–10% of the test)
Factor x³ + 2x² − 9x − 18 completely.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Factoring" (5–10% of the test)
Factor x³ − 27.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Factoring" (5–10% of the test)
Quadratics 7
A ball is thrown upward. Its height in feet after t seconds is h = −16t² + 64t + 80. What is its greatest height?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
How many real solutions does 3x² + 2x + 5 = 0 have?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
Solve 2x² − 4x − 3 = 0.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
Solve the inequality x² − x − 12 < 0.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
Solve x² − 5x − 14 = 0.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
What is the vertex of the parabola y = x² − 6x + 11?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
Where do the graphs of y = x² − 3 and y = 2x meet?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Quadratics" (10–15% of the test)
Functions 7
A shop finds that making n shirts costs C(n) = 4.5n + 120 dollars. What does C(40) = 300 say?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
The graph of y = f(x) is moved 3 units right and 2 units up. Which equation is the new graph?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
If f(x) = 2x − 5 and g(x) = x² + 1, what is f(g(3))?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
If f(x) = 2x² − x, which expression is f(a + 1)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
If f(x) = 3x² − 2x + 4, what is f(−2)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
What is the average rate of change of f(x) = x² + 1 from x = 1 to x = 4?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
What is the inverse of f(x) = (2x − 7)/3?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Functions" (10–20% of the test)
Radical and rational equations 6
The graph of y = (x + 1)/(x − 5) has a vertical asymptote atCollege Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
Simplify (x² − 9)/(x² + x − 6).College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
Solve 3/(x − 2) = 5/(x + 2).College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
Solve √(2x + 3) = x.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
What is the domain of f(x) = √(x − 4)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
Which single fraction equals 2/x + 3/(x + 1)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Radical and rational equations" (5–15% of the test)
Polynomial equations 5
How does the graph of f(x) = −3x⁴ + 5x² − 1 behave far to the left and far to the right?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Polynomial equations" (5–15% of the test)
Multiply (x² − 2x + 3)(x + 4).College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Polynomial equations" (5–15% of the test)
What are all the real solutions of x⁴ − 5x² + 4 = 0?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Polynomial equations" (5–15% of the test)
What are all the zeros of p(x) = x³ − 4x² − 5x?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Polynomial equations" (5–15% of the test)
What is the remainder when x³ − 2x² + 4x − 5 is divided by x − 2?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Polynomial equations" (5–15% of the test)
Exponential and logarithmic equations 6
A car's value in dollars after t years is V = 24,000(0.85)^t. What does the 0.85 say?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
A pond has 40 lily pads, and the number doubles every 6 days. Which function gives the number N after t days?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
Solve 2^(x + 1) = 32.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
Solve log₅(2x − 1) = 2.College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
What is log 8 + log 125, where log is the base-10 logarithm?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
What is log₃(1/9)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Exponential and logarithmic equations" (5–15% of the test)
Geometry concepts for Algebra 1 3
A triangle has a base of 2x and a height of x + 5. Which expression is its area?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 1" (5–10% of the test)
The point (2, −5) is rotated 90° counterclockwise about the origin. What are the coordinates of its image?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 1" (5–10% of the test)
What is the distance between the points (−2, 3) and (4, −5)?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 1" (5–10% of the test)
Geometry concepts for Algebra 2 3
A cone has a radius of 3 and a height of 8. What is its volume?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 2" (5–10% of the test)
Triangles ABC and DEF are similar, with AB matching DE and BC matching EF. If AB = 6, BC = 9 and DE = 10, how long is EF?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 2" (5–10% of the test)
Which equation is the circle with center (2, −3) and radius 5?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Geometry concepts for Algebra 2" (5–10% of the test)
Trigonometry 5
A circle has a radius of 6. How long is the arc cut off by a central angle of 2π/3 radians?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Trigonometry" (5–15% of the test)
In a 30°-60°-90° triangle the hypotenuse is 10. How long is the side opposite the 60° angle?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Trigonometry" (5–15% of the test)
In a right triangle, the leg opposite angle A is 5 and the hypotenuse is 13. What is cos A?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Trigonometry" (5–15% of the test)
Two sides of a triangle are 5 and 8, and the angle between them is 60°. How long is the third side?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Trigonometry" (5–15% of the test)
What is 150° in radians?College Board, Next-Generation ACCUPLACER Test Specifications, Advanced Algebra and Functions placement test: content area "Trigonometry" (5–15% of the test)
How this list was compiled: Our own questions, written to the eleven content areas of the Advanced Algebra and Functions placement test in College Board's Next-Generation ACCUPLACER Test Specifications, Version 2.0 (https://accuplacer.collegeboard.org/accuplacer/pdf/next-generation-test-specifications-manual.pdf, read 2026-10-07), with the share of the test the specifications give each: linear equations 10–15%, linear applications and graphs 10–15%, factoring 5–10%, quadratics 10–15%, functions 10–20%, radical and rational equations 5–15%, polynomial equations 5–15%, exponential and logarithmic equations 5–15%, geometry concepts for Algebra 1 5–10%, geometry concepts for Algebra 2 5–10%, trigonometry 5–15%. The bank holds 7, 7, 4, 7, 7, 6, 5, 6, 3, 3 and 5. Every answer was worked out a second time from the numbers the question prints. Licence: Questions, choices and explanations are original work of this site.
How it works
This Accuplacer AAF practice test has 60 questions of our own in the eleven content areas College Board lists for Advanced Algebra and Functions, from linear equations to trigonometry. It is unofficial and not affiliated with, endorsed by or sponsored by College Board.
Read the full guide
What the AAF test covers
College Board's test specifications, read October 7, 2026, list eleven content areas. Functions is the largest, 10 to 20 percent. Linear equations, linear applications and graphs, and quadratics take 10 to 15 percent each. Radical and rational equations, polynomial equations, exponential and logarithmic equations, and trigonometry take 5 to 15; factoring and two geometry areas 5 to 10.
College algebra and college math
The specifications list College-Level Math among five older Accuplacer tests that the redesigned tests replace. AAF is the redesigned test with the most advanced algebra, so this page serves as an Accuplacer college algebra practice test and an Accuplacer college math practice test.
Reading the notation
Powers are written x²; other exponents use a caret, as in 2^(x + 1). log₃ is a base-3 logarithm.
Check each answer to a radical equation in the original: squaring can add a solution that does not work.
Factor a rational expression fully, then cancel whole factors only.
Know the side ratios of 30°-60°-90° and 45°-45°-90° triangles; the specifications name special triangles.
Questions and answers
What is the Accuplacer AAF test?
Advanced Algebra and Functions is the Accuplacer math test that the specifications describe as suited to students entering STEM fields and other fields that need some advanced math. It has 20 multiple-choice questions, no time limit, and adapts to your answers.
Is trigonometry on the Accuplacer AAF test?
Yes. Trigonometry is one of the eleven content areas: right triangles, special triangles, radian measure, arc length, and the laws of sines and cosines. Five of the 60 questions here are trigonometry, and three more cover circles, cones and similar triangles.
Can you use a calculator on the Accuplacer AAF?
A handheld calculator may not be used on any Accuplacer math test, College Board's test-day page says, except as an approved accommodation. Some questions show a calculator icon and open one on screen. Every question on this page can be worked by hand.
What AAF score places you into college-level math?
That depends on the college. AAF reports a score from 200 to 300, and College Board recommends no placement scores: each college sets its own. Ask your college for the score its math courses require before you test.