Accuplacer Advanced Algebra and Functions
The Accuplacer exam includes advanced algebra and functions problems.
Try the free sample questions below. Then have a look at our great video!
1) Express the following in scientific notation: (9.51 × 10–2) ÷ (4.9 × 10–8)
2) f(x) = 3x2 + 2x. What is the algebraic expression for 2f(x – 1)?
3) f(x) = 2x + 3. Find the value of f(5).
4) f1(x) = (x + 5) and f2(x) = (x – 3)(x + 4). What is f2(f1(x)) when x = 5?
5) What is the domain of the following: y = 63 ÷ x2
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Answers
1) 1.940816327 × 106
2) 6x2 – 8x + 2
3) 13
4) 98
5) All real numbers except 0.
Solutions to the Accuplacer Advanced Algebra & Functions Questions
Solution 1:
1) You will probably see at least one question on scientific notation on the real Accuplacer advanced algebra and functions exam.
When dividing two numbers that are expressed in scientific notation, you have to divide the numbers in front of the times signs and subtract the exponents.
Your result needs to be expressed as a number between 1 and 10, multiplied by 10 to an exponential power.
(9.51 × 10-2) ÷ (4.9 × 10-8) =
(9.51 ÷ 4.9) × (10-2 ÷ 10-8) =
(9.51 ÷ 4.9) × 10-2 – -8 =
(9.51 ÷ 4.9) × 10-2 + 8 =
(9.51 ÷ 4.9) × 106 =
1.940816327 × 106
Solution 2:
2) Step 1 – Substitute x – 1 for x and multiply all of the terms by 2.
f(x) = 3x2 + 2x
f(x – 1) = 2 × {[3 × (x – 1)(x – 1)] + 2(x – 1)} =
2 × {[3 × (x2 – 2x + 1)] + 2x – 2} =
2 × {(3x2 – 6x + 3) + 2x – 2}
Step 2 – Then group similar terms together and simplify.
2 × {(3x2 – 6x + 3) + 2x – 2} =
2 × (3x2 – 6x + 3 + 2x – 2) =
2 × (3x2 – 6x + 2x + 3 – 2) =
2 × (3x2 – 4x + 1)
Step 3 – Solve by multiplying the entire result times 2.
2 × (3x2 – 4x + 1) =
(2 × 3x2) + (2 × –4x) + (2 × 1) =
6x2 – 8x + 2
Solution 3:
3) Be sure that you understand all aspects of functions for the Accuplacer advanced algebra and functions exam.
Substitute 5 for the value of x to solve for f(x) = 2x + 3.
Find the value of f(5) as follows:
f(5) = 2x + 3 = (2 × 5) + 3 = 10 + 3 = 13
Solution 4:
4) Solve for f1(x):
f1(x) = (x + 5) = (5 + 5) = 10
Then use the value of 10 in the second function to solve:
f2(x) = (x – 3)(x + 4)
f2(x) = (10 – 3)(10 + 4) = 7 × 14 = 98
Solution 5:
5) You will also need to understand the domain and range of functions to answer Accuplacer advanced algebra and functions questions.
The domain of a function or equation is all possible “inputs” or x values.
You have to avoid values of x that result in imaginary numbers.
Imaginary numbers would occur when you divide by zero or have find the square root of a negative number, for example.
Here, we have to avoid dividing by zero.
So the domain is all real numbers except 0.
If you are asked about the range of a function, remember that the range is the “outputs” or results of the function.
More Exam Practice
Advanced Algebra and Functions Practice Tests
What on the Advanced Algebra & Functions Test?
The Accuplacer advanced algebra and functions exam includes questions on the following skills:
- Linear equations, applications and graphs
- Quadratics
- Factoring
- Functions
- Radical and rational equations
- Exponential and logarithmic equations
- Advanced geometry
- Trigonometry
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