QU-Placer Math Sample Test - Section 1: Elementary Algebra - Answer the following questions

Q: What topics are covered in Section 1 of the sample test?

Section 1 focuses on elementary algebra skills such as evaluating expressions, solving equations and inequalities, working with polynomials, factoring, expanding binomials, and simplifying radicals.

Q: How do Section 2 questions use functions and graphs?

Section 2 includes questions that require interpreting graph information to solve inequalities, determine domains, and select the correct graph or solution set from multiple-choice options.

Q: What is the format of the answers in this test?

Most problems are multiple-choice, where you choose one option (A–D) corresponding to the correct result, equation form, solution set, or graph/domain choice.

Sep 29, 2026

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QU-Placer Math Sample Test No. 1 contains Elementary Algebra and Pre-Calculus question sets focused on foundational reasoning in real numbers, polynomials, inequalities, factoring, binomial expansion, and simplification of radicals. The test requires selecting correct multiple-choice options for definitions and properties (e.g., sum of negative numbers), solving equation and inequality solution sets, evaluating algebraic expressions, and interpreting function behavior from given graphs, including domains and graph-based solutions.

LanguageEnglish

CategoryExam

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Section 1: Elementary Algebra

Multiple-choice questions (1-30)

Section 2: Pre-Calculus

Multiple-choice questions (31-38)

| | | --- | | QU-Placer Math Sample Test No. 1
Section 1: Elementary Algebra
Answer the following questions:
1. The sum of two negative numbers is always a .
(A) Negative number
(B) Positive number
(C) Even number
(D) Odd number

2. Which subset of real numbers contains 3√2 + 1 ?
(A) Irrational Numbers
(B) Rational Numbers
(C) Integers
(D) Whole Numbers
3. Perform the indicated operations and write the answer in the simplest form:( − 􀜽1􀜾225 ÷ 122􀜽53~~ ~~􀜾~~ ~~ ) × − ~~ ~~745􀜾􀜽2 = 􀝓ℎ􀝁􀝎􀝁 􀜽 ≠ 0 , 􀜾 ≠ 0
(A) 5
16 􀜽 􀜾
(B) 􀜾 3 1125 􀜽 3
(C) 9􀜽5 􀜾
−
125 (D) 5 􀜽 2 􀜾 2
−
16 􀜽 3 􀜾 3 | 4. Evaluate 8 + 16 ÷ 4 × 5 − 3 (A) 31 (B) 27 (C) 25 (D) 16 | 5. | Evaluate 4 – 5 · [5 –(42 – 2)]
(A) 9
(B) 13
(C) 49
(D) 69 | | --- | --- | | 6. | The statement “81 is the product of a number and three times the same number” is expressed by which of the following equations?
(A) 81 = 􀝔 (􀝔 + 3)
(B) 81 = 􀝔 ∙ 3􀝔
(C) 81 = 3􀝔(􀝔 + 3)
(D) 81 = 3􀝔 ∙ 3􀝔 | | 7. | The solution of the equation 3 (􀝔 + 1) = 􀝔 + 2 is:(A) 2
(B) ~~ ~~12
(C) −2 (D) − 12 | | 8. Which of the following represents the graph of the solution to the inequality −12 ≤ 2􀝔 − 4 < 10 ?
(A)
(B)
(C)
(D)
| | 9. What is the leading coefficient in the polynomial 19 􀝔 3 − 32 􀝔 + 11 ?(A) − 32 (B) ~~ ~~19 (C) 3 (D) 11 | 10. | The quotient and the remainder of (􀝔5 + 􀝔 2 + 􀝔 + 1) ÷ (􀝔2 − 1) are:
(A) Quotient: 􀝔 3 − 􀝔 + 1 Remainder: 2
(B) Quotient: 􀝔 3 − 2 Remainder: 3
(C) Quotient: 􀝔 3 + 􀝔 + 1 Remainder: 2􀝔 + 2
(D) Quotient: 􀝔 3 + 2􀝔 Remainder: 3􀝔 + 1 | | --- | --- | | 11. | Expand the binomial (2􀝔 − 3)3 (A) 6􀝔3 − 36􀝔2 − 54􀝔 + 27 (B) 6􀝔3 − 18􀝔2 + 27􀝔 − 27 (C) 8􀝔3 − 36􀝔2 + 54􀝔 − 27 (D) 8􀝔3 − 6􀝔2 + 6􀝔 − 27 | | 12. | 􀝔 3 − 􀝔 2 + 􀝔 − 1 is equivalent to: ______________________.
(A) (1 − 􀝔)(􀝔2 − 1)
(B) (􀝔 − 1)(􀝔2 − 1)
(C) (1 − 􀝔)(􀝔2 + 1)
(D) (􀝔 − 1)(􀝔2 + 1) | | 13. | 2􀝔2 + 􀝔 − 3 =
(A) (2􀝔 + 1)(􀝔 − 3)
(B) (2􀝔 − 1)(􀝔 + 3)
(C) (2􀝔 + 3)(􀝔 − 1)
(D) (2􀝔 − 3)(􀝔 + 1) | 14. Factor completely (4􀝔2 − 2􀝔) (A) 􀝔 (4􀝔2 − 2) (B) 2 (2􀝔2 − 2􀝔) (C) 2􀝔(2􀝔 − 1) (D) 4􀝔(􀝔 − 1) | 15. | Given that 􀯫~~ ~~~~ ~~4 ÷ 􀜭 = 􀯫~~ ~~−2~~ ~~4 , which expression is equivalent to K ?
(A) 2􀝔
􀝔 2 − 16
(B) 􀝔 2 − 16 2􀝔
(C) 2􀝔2
􀝔 − 4
(D) 􀝔224 | | --- | --- | | 16. | 8􀯫+8􀯬 42
~~ ~~ · ~~ ~~ =
4 48􀯫+48􀯬
(A) 7 4 (􀝔 + 􀝕)
(B) 7 (􀝔 + 􀝕) 4
7
(C) ~~ ~~32 7
(D) ~~ ~~4 | | 17. | The LCM (Least Common Multiple) of the polynomials 8􀝔2 − 6􀝔 − 9 􀜽􀝊􀝀 16􀝔2 − 9 is:
(A) (2􀝔 − 3)(4􀝔 + 3)2 (4􀝔 − 3)
(B) (2􀝔 − 3)(4􀝔 + 3)(4􀝔 − 3)
(C) (2􀝔 − 3)(4􀝔 − 3)2
(D) (2􀝔 − 3)(4􀝔 + 3)2 | 18. Which of the following expressions is equivalent to (A) 4􀝔 + 4 9􀝔 − 4 (B) 4􀝔 9􀝔 − 4 (C) 6􀝔 + 4√􀝔 9􀝔 − 4 (D) 6􀝔 − 4√􀝔 9􀝔 − 4 2√􀯫 3√􀯫 −2 ? | 19. | 1 (32􀯫13􀯬 18)3
Simplify 1
(􀯫3􀯬 3 )3
(A) 2􀝔􀝕 3√2􀝔􀝕
(B) 2􀝔􀝕 3√2􀝔
(C) 2􀝔3􀝕 5 3√4􀝔􀝕
(D) 2􀝔3􀝕 5 3√4􀝔 | | --- | --- | | 20. | Simplify 5 √27 − 6 √3
(A) −√30
(B) −√24
(C) 9 √3
(D) 9 √6 | | 21. | What is the LCD (Least Common Denominator) of the equation 􀯫~~ ~~~~ ~~2~~ ~~ + 􀯫~~ ~~~~ ~~2~~ ~~ = 1􀯫02􀯫−−42 ?
(A) 􀝔 2 – 4
(B) 􀝔 2 − 16
(C) 10􀝔 − 2
(D) 12􀝔 − 2 | 22. The solution set of the inequality 2 ≤ 4􀝔 + 6 < 8 is: . 1 (A) [−5 −4] 2 , (B) [−4, 2] (C) [−4, 2) (D) [−1, 12) | 23. | Which of the following equations has 2 and −10 as solutions?
(A) 􀝔 2 − 40􀝔 − 20 = 0
(B) 􀝔 2 + 40􀝔 − 20 = 0
(C) 􀝔 2 + 8􀝔 − 20 = 0
(D) 􀝔 2 + 20 = 0 | | --- | --- | | 24. | For which value(s) of 􀜿 does the equation √√􀝔 + 4 − √􀜿 = 0 has a solution.
(A) 􀜿 = −4
(B) 􀜿 = 0
(C) 0 < 􀜿 < 4
(D) 􀜿 ≥ 4 | | 25. | The solution set of the equation x 4 − 2x3 − x 2 + 2x = 0 is
(A) {−1, 0, 1, − 3}
(B) {−1, 0, 1, − 2}
(C) {−1, 0, 1, 3}
(D) {−1, 0, 1, 2} | | 26. | The solution set of the equation 􀯫2 = 1 + 2 is .
(A) {−20, 10}
(B) {8, −10}
(C) {−8,

FAQs

What topics are covered in Section 1 of the sample test?

Section 1 focuses on elementary algebra skills such as evaluating expressions, solving equations and inequalities, working with polynomials, factoring, expanding binomials, and simplifying radicals.

How do Section 2 questions use functions and graphs?

Section 2 includes questions that require interpreting graph information to solve inequalities, determine domains, and select the correct graph or solution set from multiple-choice options.

What is the format of the answers in this test?

Most problems are multiple-choice, where you choose one option (A–D) corresponding to the correct result, equation form, solution set, or graph/domain choice.

Sep 29, 2026

Upload by Melati