Accuplacer Advanced Algebra and Functions Practice Test

For the functions f₂(x) below, x and y are integers greater than 1. If f₁(x) = x², which of the functions below has the greatest value for f₁(f₂(x))?

f₂(x) = x/y
f₂(x) = y/x
f₂(x) = xy
f₂(x) = x – y

In the xy plane, line B passes through the origin and is perpendicular to line A. Line A passes through the points (2, –5) and (6, 3). The equation of line B could be which one of the following?

y = –¹/₂x + 0
y = ¹/₂x + 0
y = 2x + 0
y = –2x + 0

The rectagular solid below has a length of 10 centimeters (cm) a height of 4 cm and a depth of 4 cm. What is the surface area of the rectangular solid?

Accuplacer Advanced Algebra and Functions Surface area of rectangular box

Accuplacer Advanced Algebra and Functions Surface area of rectangular box

16cm²
40cm²
160cm²
192cm²

Which expression is equivalent to the following? $Algebraic fraction 1$

$Algebraic fraction 2$
$Algebraic fraction 3$
$Algebraic fraction 4$
$Algebraic fraction 5$

The graph below shows the relationship between the total number of hamburgers a restaurant sells and the total sales in dollars for the hamburgers. The cost of shakes, where c is the cost and s is the number of shakes, is represented by the following equation: c = ⁹/₄ × s

Accuplacer Advanced Algebra and Functions Graph of cost of hamburgers

Accuplacer Advanced Algebra and Functions Graph of cost of hamburgers

Which of the following best estimates difference between the cost of one hamburger and the cost of one shake?

$2.25
$4.25
$6.25
$8.20

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The graph below illustrates which of the following functions?

Accuplacer Advanced Algebra and Functions Function graph question image 1

Which of the following is equivalent to the expression 2(x + 2)(x – 3) for all values of x?

2x² – 2x – 12
2x² – 10x – 6
2x² + 2x – 12
2x² + 10x – 6

2 inches on a scale drawing represents F feet. Which of the following equations represents F + 1 feet on the drawing?

^{2(F + 1)}/_F
^{(F + 1)}/_F
²/_{F + 1}
^2F/_{F + 1}

Consider the quadratic function (x) = ax² + bx + c. In this problem, f(x) = y. If m is a constant, how many solutions exist for the equation ax² + bx + c = mx?

0
1
2
Cannot be determined

What is the value of f₁(2) where f₁(x) = 5^x?

2⁵
10
25
25²

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Which of the following best describes the range of y = x² + 36?

All real numbers.
All real positive numbers greater than or equal to 36.
All real negative numbers less than or equal to –36.
All real numbers greater than or equal to 36.

What are two possible values of x for the following equation? x² + 6x + 8 = 0

1 and 2
2 and 4
6 and 8
–2 and –4

If f(x) = x ÷ (1 + x) and g(x) = 1 ÷ x, what is the domain of the function f + g?

{ –1, 0}
All real numbers.
All real numbers except 0.
All real numbers except 0 and –1.

Find the value of x: Accuplacer Advanced Algebra and Functions Radical question 1

4
16

Perform the operation: (5ab – 6a)(3ab³ – 4b² – 3a)

15a²b⁴ – 20ab³ – 15a²b – 18a²b³ – 24ab² – 18a²
15a²b⁴ – 20ab³ – 15a²b – 18a²b³ + 24ab² + 18a²
15a²b⁴ – 20ab³ – 15a²b – 18a²b³ – 24ab² + 18a²
15ab⁴ – 20ab³ – 15a²b – 18a²b³ + 24ab² + 18a²

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The central angle in a circle is 90° and is subtended by an arc which is 8π centimeters in length. How many centimeters long is the radius of this circle?

32
16
8π
8

In the function f(x) = a(x + 1)(x + 2), a is an integer constant. The end behaviour of the graph of y = f(x) is positive for large negative and large positive values of x. Which of the following statements is true with respect to the leading coefficient?

The leading coefficient is negative.
The leading coefficient is positive.
The leading coefficient is an odd number.
The leading coefficient is an even number.

Express the following as a logarithmic function and solve for x: 4^2x = 64

2x = log₄64; x = 3
2x = log₄64; x = 1.5
4 = log_2x64; x = 3
4 = log_2x64; x = 1.5

If x and y are positive integers, the expression Accuplacer Advanced Algebra and Functions Positive integer question 1

is equivalent to which of the following?

If cos A = 0.30902 and sin A = 0.95106, then tan A = ?

3.07767
0.307767
0.32492
0.04894

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