Accuplacer Advanced Algebra and Functions (AAF) Practice Test 2024: Download our next-generation Accuplacer Advanced Algebra and Functions Placement Practice Test PDF. The Advanced Algebra and Functions Test includes the most sophisticated math found on the ACCUPLACER.

DIRECTIONS: This test contains items that measure your ability to do math at an introductory college level. Choose the best answer to each question. Feel free to use scrap paper. You may not use a calculator. However, with some problems with the computer-based ACCUPLACER, you may be given access to an on-screen calculator with limited functionality.

## Accuplacer Advanced Algebra and Functions Test

Name of the Test | Accuplacer Practice Test |

Administrated by | College Board |

Total Questions | 30 |

Question format | multiple-choice questions |

Test subjects | Advanced Algebra and Functions (AAF) |

**Q1**. If \frac1a + \frac{1}{2a} = b , what is the value of *a* in terms of *b*?

- (A) \frac{2}{3b}
- (B) \frac{3}{2b}
- (C) \frac{2b}{3}
- (D) \frac{3b}{2}

**Q2. **(2x – 3) (x² + 4x – 5) is equivalent to which of the following expressions?

- (A) 2x³ + 5x² + 2x + 15
- (B) 2x³ – 5x² – 2x + 15
- (C) 2x³ + 5x² – 22x + 15
- (D) 2x³ – 5x² + 22x + 15

**Q3**. In the following figure, lines *AB* and *CD* are parallel, with *AD* and* BC *intersecting at* E*. If the lengths of *AE, BE*, and *EC* are 2, 4, and 5 respectively, what is the length of *ED*?

- (A) 2.4
- (B) 2.5
- (C) 2.6
- (D) 2.8

**Q4.** If *f(x) = x² -4x* and g(x) = 3x + 6, what is the value of \frac{f(6)}{g(-4)} = ?

- (A) 2
- (B) 1
- (C) -1
- (D) -2

**Q5.** What is the equation of the line that is parallel to the following line and passes through the origin?

**Q6.** All of the following are functions EXCEPT

**Q7.** If *a* and *b* are the two solutions to the equation *2x² – 14x = -20*, which of the following is a possible value of *a-b*?

- (A) 3
- (B) 5
- (C) 7
- (D) 10

**Q8.**Which of the following equations is the function shown in this *xy* graph?

- (A) y= (x + 1)(x + 3)
- (B) y= (x + 1)(x – 3)
- (C) y= (x + 1)² -4
- (D) y= (x – 1)² -4

Q9. Points *A* and *B* are two points on the circle centered at *O*, shown here. If *OB= 4* and the measure of angle *AOB* is *40* degrees, what is the arc length *AB*?

- (A) \frac{2π}{9}
- (B) \frac{4π}{9}
- (C) \frac{8π}{9}
- (D) \frac{16π}{9}

**Q10**. Jonathan invested $2000 in a CD that paid 4% interest compounded annually. He used the equation* f(t)=2000(n) ^{t}* to calculate the amount his CD will be worth in t years. Which of the following values should he use for

*n*?

- (A) 0.04
- (B) 0.4
- (C) 1.04
- (D) 1.4

**Q11.** What is the value of x if \frac{x+2}{x-3} = \frac{x-5}{x-1} ?

- (A) \frac{13}{7}
- (B) \frac{13}{9}
- (C) \frac{17}{7}
- (D) \frac{17}{9}

**Q12.** Which value(s) are excluded from the domain of the function fx = \frac{1}{x² - 10x + 25} ?

- (A) 5
- (B) -5
- (C) 5 and -5
- (D) No values are excluded.

**Q13.** The equation \frac{x - 4}{4} = \frac{2}{x - 6} has two possible values for x. What is the sum of these two values?

- (A) 8
- (B) 10
- (C) 12
- (D) 16

**Q14.** If *log _{6}11x = 2*, then

*x*equals

- (A) \frac{11}{36}
- (B) \frac{11}{64}
- C) \frac{36}{11}
- (D) \frac{64}{11}

**Q15.** In triangle* XYZ,* angle *Y* is a right angle if sin *X=* \frac{7}{25} then *sin Z* =?

- (A) \frac{7}{24}
- (B) \frac{24}{25}
- C) \frac{24}{7}
- (D) \frac{25}{7}

**Q16.** Which of the following is the equation for this circle?

- (A) (x-2)² + y² =3
- (B) x² + (y+2)² =3
- (C) (x+2)² + y² =9
- (D) x² + (y-2)² =9

**Q17.** If *f(x)=x² – 4x*, what is the value of *2f(a-1)*?

- (A) 2a² + 8a – 6
- (B) 2a² – 12a – 6
- (C) 2a² – 8a + 10
- (D) 2a² – 12a + 10

**Q18.** \sqrt{x² -1}-2=x Solve for x.

- (A) \frac{4}{5}
- (B) \frac{5}{4}
- C) - \frac{4}{5}
- (D) - \frac{5}{4}

**Q19.** if 125 ^{x-1} = \sqrt{5}^{x+1}, what is the value of x?

- (A) \frac{5}{7}
- (B) \frac{7}{5}
- C) - \frac{5}{7}
- (D) - \frac{7}{5}

**Q20.** if* x-y = 3* and *x² – y² =15* then *x³ – y³ =?*

- (A) 27
- (B) 63
- (C) 75
- (D) 255

Q21. if *f(x) = x² – 7*, what is the value of *f(3)*?

- (A) 2
- (B) -2
- (C) 22
- (D) -22

**Q22.** Which of the following is true of the end behavior of polynomial* 3x ^{5} – 5x^{3} – 7x?*

- (A) It’s positive for both very large and very small values of x.
- (B) It’s negative for both very large and very small values of x.
- (C) It’s positive for very large values of x and negative for very small values of x.
- (D) It’s negative for very large values of x and positive for very small values of x.

**Q23.** Which of the following functions includes the point (0, -9) when graphed on the xy-plane?

- (A)
*y = x*^{3}– 5x^{2}-x + 9 - (B)
*y = -9x*^{3}+ 4x^{2}– 6x – 2 - (C)
*y = 6x*^{3}– 11x^{2}+ 8x – 9 - (D)
*y = 3x*^{3}+ 4x^{2}-x + 9x

**Q24.** Which of the following is a root of the function?

*y = (x+3)(x-1)(2x-5)*

- (A) \frac{2}{5}
- (B) \frac{5}{2}
- (C) - \frac{2}{5}
- (D) - \frac{5}{2}

**Q25.** What are the coordinates of the vertex of the quadratic function

*y= x ^{2} – 10x + 24?*

- (A) (5, -1)
- (B) (1, -5)
- (C) (5, -10)
- (D) (10, -5)

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