Structure of Expressions and Modeling Test – Algebra 2 Math (Printable PDF)

Question 1 Factor completely (2 points)

Write x⁴ − 256 as a product of as many real factors as possible.

Question 2 Rearrange formulas (2 points)

1. Solve C = (5/9)(F − 32) for F. (1 point)
2. Solve v² = u² + 2as for a. (1 point)

Question 3 Binomial expansion (3 points)

Use Pascal’s triangle to expand (x − 2)⁴.

Question 4 Complex factoring (2 points)

1. Factor x² + 49 over the complex numbers. (1 point)
2. Find the zeros of x² − 6x + 25. (1 point)

Question 5 Intersection of two graphs (3 points)

The graph shows f(x) = x² − 4 (solid) and g(x) = x + 2 (dashed).

1. Estimate the x-coordinates where f(x) = g(x). (1 point)
2. Solve f(x) = g(x) algebraically. (2 points)

Question 6 Scooter depreciation (3 points)

A scooter bought for $1,800 loses 15% of its value each year.

1. Write a function V(t) for its value after t years. (1 point)
2. Find the value after 3 years. (1 point)
3. When is it worth $900, to the nearest tenth of a year? (1 point)

Question 7 Ticket system (2 points)

A concert sold 120 tickets for $780. Adult tickets cost $9 and child tickets cost $5. How many of each were sold?

Question 8 Pen with a minimum area (2 points)

A rectangular pen is built with 40 feet of fencing and must enclose at least 91 square feet. If the width is w, write an inequality and find the possible widths.

Question 9 Check an identity (1 point)

Verify (x² + y²)² = (x² − y²)² + (2xy)² for x = 5 and y = 2.