Math Placement Test Units 3-5 Review

Sep 30, 2026

Upload by aboduw

Math Placement Test Sequence review for Units 3–5 in developmental mathematics at the College of Western Idaho. The test includes 15 questions covering proportions, unit rates, percent applications, right-triangle trigonometry via the Pythagorean Theorem, and linear graphs using ordered pairs, intercepts, slope, and line equations. It also practices polynomial operations, monomial degree and coefficients, and exponent rules for simplifying expressions and rational expressions. Scoring at 70% or higher allows moving to the next level with limits on attempts.

LanguageEnglish

CategoryExam

FormatPDF

Pages5

Reading Time13 min

AccessFree to download

Placement test rules

Scoring and retake limits

Sample problem topics

Proportions and proportions in applications

Unit rate problems

Percent problems

Percent problems using proportions

Right triangles and the Pythagorean Theorem

Graphing lines by ordered pairs

Intercepts and graphing equations

Slope and y-intercept

Equation of a line from two points

Subtracting polynomials

Monomial coefficients and exponents

Multiplying binomials (FOIL and distributive property)

Exponent rules for simplifying expressions

Simplifying rational expressions with exponent rules

Answer key

The Math Placement Test Sequence at the College of Western Idaho allows students to test out of Units in the developmental mathematics sequence. The Placement test for Units 3-5 has 15 questions. If you complete a level with a score of 70% or higher, you may attempt the next level in the sequence. You are limited to two attempts per level on the Placement Test. The two attempts must not be on the same day. Sample problems (and associated topics): 1. Solve 512 = 􀯬30 (Solve a proportion.) 2. Mary earned $4420 for 13 weeks of summer work. What was her unit rate in dollars per week? (Find a unit rate.) 3. A worker can complete the assembly of 16 cell phones in 5 hours. At this rate, how many can the worker complete in a 40-hour workweek? (Use a proportion in problem solving.) 4. Find the length of the missing side of the right triangle. (Use the Pythagorean Theorem.) 8 5. What is 35% of 105? (Solve percent problems.) 6. A salesperson’s commission rate is 5% . What is the commission from the sale of $300 worth of clothing? (Solve applications involving percent.) 7. 25.6 is what percent of 80? (Solve percent problems using proportions.) 8. 24 rail cars is what percent of 40 rail cars? (Solve applications involving percent.) 9. For the equation 􀝕 = − 23􀝔 + 4 , complete the ordered pairs (0, ) and ( , 2), then graph the line. (Graph a line by completing ordered pairs.) 10. Find the intercepts for the graph of the given equation ; write the answers as ordered pairs: 2􀝔 + 8􀝕 = −16 . (Find intercepts of a given equation.) 11. Write the equation of the line with slope of-3 and y-intercept (0, 4) . Write the equation of a line given its slope and y-intercept.) 12. Find the slope, if it exists. 5􀝔 − 4􀝕 = 16. (Find the slope of a given equation.) 13. Find the slope and y-intercept, then graph the equation: 􀝕 = 25 􀝔 − 1. Write the y-intercept as an ordered pair. (Using the slope and y-intercept of a given equation, graph the line.) 14. Find the equation of the line through the given pair of points: (4, 5) and (-2, 2) . (Write the equation of the line containing a given pair of points.) 15. Subtract: (−7􀝔2 + 8􀝔 − 12) − (􀝔2 − 5) . (Subtract polynomials.) 16. What is the coefficient and the exponent in the term m4. (Determine the degree and coefficient of a monomial.) 17. Multiply: (5􀝔 − 8)(10􀝔 + 4) . (Multiply two binomials by using FOIL.) 18. Multiply: (􀝔 + 4)(x − 4) . (Multiply the sum and difference of two terms.) 19. Multiply: 3􀝔(2􀝔 − 4)(5􀝔 − 3) . (Multiply two or more polynomials.) 20. Use the rules of exponents to simplify the expression. (Use the power-to-power rule and the product-to-power rule.) (m3 n 2 ) 3 (−m2 n 5 ) 2 21. Use the rules of exponents to simplify the rational expression. (Use rules of exponents.) (ab5 ) −6 a 10b −5 22. Use the rules of exponents to simplify the rational expression. (Use the quotient-topower rule and the negative power rule.) (34)−3 Answers: 1. y =252 or y = 12.5 2. $340 per week 3. 128 cell phones 4. x = 6 5. 36.75 6. $15 7. 32% 8. 60% 9. (0, 4) and (3, 2) 10. x-intercept (-8, 0), y-intercept (0, -2) 11. y = -3x + 4 12. slope = 54 13. slope = 25, y-intercept (0, -1) 14. 􀝕 = 12 􀝔 + 3 15. −8􀝔2 + 8􀝔 − 7 16. The coefficient of the term is 1 and the exponent is 4. 17. 50􀝔2 − 60􀝔 − 32 18. 􀝔 2 − 16 19. 30􀝔3 − 78􀝔2 + 36􀝔 20. m13n 16 21. a~~ ~~161b25~~ ~~22.6247 Some websites to help you practice are: IXL [https://www.ixl.com/math/algebra-1](https://www.ixl.com/math/algebra-1) S.O.S Math [http://www.sosmath.com/algebra/algebra.html](http://www.sosmath.com/algebra/algebra.html) Khan Academy [https://www.khanacademy.org/math/algebra?t=practice](https://www.khanacademy.org/math/algebra?t=practice) Purplemath [http://www.purplemath.com/](http://www.purplemath.com/)

FAQs

What are the scoring and retake rules for Units 3–5?

The Placement test for Units 3–5 has 15 questions. Completing a level with a score of 70% or higher lets you attempt the next level, and you can make two attempts per level, with the two attempts not on the same day.

Which math topics are covered in the sample problems?

Topics include solving proportions, finding unit rates, percent problems, percent using proportions, right-triangle side lengths with the Pythagorean Theorem, and graphing lines through ordered pairs, intercepts, slope, and line equations.

What kinds of algebra and exponent problems appear?

The review includes subtracting polynomials, identifying coefficients and exponents in monomials, multiplying polynomials (including FOIL), and simplifying expressions and rational expressions using exponent rules such as power-to-power, product-to-power, quotient-to-power, and negative power.

Sep 30, 2026

Upload by aboduw