Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Later problems use the rational and irrational number rules from N-RN.B.3, and the final six are multi-step situations with compound growth, geometry and plans to compare.
Standards: A-SSE.A.1a, A-SSE.A.1b, N-RN.B.3 · Level: Grade 9 Algebra 1
Problem 1 Count the terms ★★★
List the terms of 6x2 − 4x + 9, and state how many there are.
Problem 2 Coefficients and constant ★★★
In 8a − 5b + 2, find the coefficient of each variable term and the constant term.
Problem 3 Factors of a term ★★★
List all the factors of the term 7xy.
Problem 4 Classify points on a line ★★★
Points A, B and C on the number line are 1/2, √2 and π. Which are irrational? Explain.
Problem 5 Factors of a product ★★★
How many factors does 2(x + 5)(x − 1) have? Name them.
Problem 6 Gym membership ★★★
The monthly cost of a gym is C = 35m + 20, where m is the number of months. What do 35 and 20 represent?
Problem 7 Interpret an exponential ★★★
A savings account holds A = 1200(1.05)t dollars after t years. Interpret 1200 and 1.05.
Problem 8 Factored view ★★★
A club buys 4 tickets for each of n + 3 people at a fair. The total number of tickets is 4(n + 3). Explain what the factor (n + 3) stands for, and what 4 stands for.
Problem 9 Rational plus irrational ★★★
Is 5 + √3 rational or irrational? Explain your reasoning.
Problem 10 Rational times irrational ★★★
Is (2/3)·√5 rational or irrational? Explain.
Problem 11 Two irrationals, rational sum ★★★
Show that the sum of two irrational numbers can be rational by using √7 and 3 − √7.
Problem 12 Product of two roots ★★★
Is √2 · √8 rational? Simplify to decide.
Problem 13 Draining tank ★★★
A tank holds 80 gallons and drains 6 gallons each minute. The amount left after t minutes is 80 − 6t. Interpret each term, then find the amount left when t = 5.
Problem 14 Evaluate a growth expression ★★★
Evaluate 800(1.03)2 and interpret the result as dollars in an account that earns 3% per year.
Problem 15 Savings account ★★★
Use A = P(1 + r)n with P = 2,500, r = 0.04 and n = 3. Find A to the nearest cent and name the growth factor.
Problem 16 Bike rental plans ★★★
Shop A charges 15 + 6h dollars and Shop B charges 3 + 8h dollars for h hours. (a) Which shop has the higher fixed fee? (b) Which charges more per hour? (c) Find the cost at each shop for 4 hours.
Problem 17 Garden perimeter ★★★
A garden has width w feet and length w + 8 feet. Write the perimeter as 2(w + w + 8), simplify it, and interpret 4w and 16. Then find the perimeter when w = 6.
Problem 18 Circular pond ★★★
A pond has radius 2.5 meters. The circumference is 2π(2.5) and the area is π(2.5)². Rewrite each as a multiple of π, decide whether each is rational, and give approximations to the nearest hundredth.
Problem 19 Car value ★★★
A car’s value is V = 24,000(0.85)t dollars after t years. (a) What percent does the value lose each year? (b) Find the value after 3 years.
Problem 20 Compare two accounts ★★★
Account A pays 1.5% every six months, so A = 1,000(1.015)8 after 4 years. Account B pays 3% each year, so B = 1,000(1.03)4 after 4 years. Find both amounts to the nearest cent and say which is larger and by how much.
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