Structure of Expressions and Modeling with Equations: Algebra 2 Math Test – PDF Download

Algebra 2 Expressions Equations Models Test: questions 1–5

Question 1: Interpret a model (2 points)

The value of a used car is \(V(t)=24000(0.85)^{t}\) dollars, where \(t\) is the number of years since it was bought.

1. Explain what 24000 and 0.85 mean in this situation. (1 point)
2. Find the value of the car after 3 years. (1 point)

Question 2: Factor completely (2 points)

1. Factor \(x^{4}-16y^{4}\) completely over the real numbers. (1 point)
2. Factor \(x^{2}+49\) over the complex numbers. (1 point)

Question 3: Binomial Theorem (3 points)

1. Expand \((x+3)^{4}\). (2 points)
2. Find the coefficient of \(x^{2}\) in the expansion of \((x-2)^{5}\). (1 point)

Question 4: Rearrange formulas (2 points)

1. Solve \(S=2\pi r^{2}+2\pi rh\) for \(h\). (1 point)
2. Solve \(y=\frac{2x+5}{x-1}\) for \(x\). (1 point)

Question 5: Where two graphs meet (3 points)

The graph shows \(f(x)=x^{2}-4x+1\) (solid) and \(g(x)=2x-4\) (dashed).

1. Use the graph to estimate the solutions of \(f(x)=g(x)\). (1 point)
2. Solve \(f(x)=g(x)\) algebraically to confirm. (2 points)

Algebra 2 Expressions Equations Models Test: questions 6–8

Question 6: Picture frame (3 points)

A rectangular photo measures 8 inches by 10 inches. Noah adds a frame of uniform width \(x\) inches. The photo and frame together have an area of 168 square inches.

1. Write an equation for \(x\). (1 point)
2. Solve it and state the width of the frame. Explain why one solution is rejected. (2 points)

Question 7: Savings account growth (3 points)

Jamal deposits $3,500 in an account that pays 6% interest compounded annually.

1. Write a function \(A(t)\) for the balance after \(t\) years. (1 point)
2. Write an equation that says the balance is $5,000. (1 point)
3. Find the least whole number of years after which the balance is at least $5,000. (1 point)

Question 8: Constraints (2 points)

At the school store, notebooks cost \$3 each (\(n\) of them) and binders cost \$5 each (\(b\) of them). Diego can spend at most $60 and needs at least 4 binders.

1. Write two inequalities that describe his purchase. (1 point)
2. Is buying 10 notebooks and 6 binders possible? Justify. (1 point)

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Take this algebra 2 expressions equations models test without notes, then grade it with the test answer key out of 20 points.

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