Ten multiple-choice questions check interpreting expressions, factoring with structure, the Binomial Theorem, rearranging formulas, graphical solutions and modeling. Exactly one option is correct in each question, and the explanation points out the usual mistake.
Algebra 2Common Core: A-SSE.A.1 · A-SSE.A.2 · A-CED.A.1 · A-CED.A.2 · A-CED.A.3 · A-CED.A.4 · A-REI.D.11 · A-APR.C.5 · N-CN.C.8 · N-CN.C.9
🎯 Structure of Expressions and Modeling with Equations – Algebra 2 math quiz
Question 1
In the model \(P(t)=250(1.08)^{t}\), what does the factor 1.08 tell you?
A
The population is multiplied by 1.08 each period, an 8% increase
B
The population grows by exactly 1.08 each period
C
The starting population is 1.08
D
The population decreases by 8% each period
Question 2
Factor \(x^{4}-1\) completely over the real numbers.
A
\((x^{2}+1)(x^{2}-1)\)
B
\((x+1)^{2}(x-1)^{2}\)
C
\((x^{2}+1)(x+1)(x-1)\)
D
\((x-1)^{4}\)
Question 3
Factor \(x^{2}+36\) over the complex numbers.
A
\((x+6)(x-6)\)
B
\((x+6i)(x-6i)\)
C
\((x+6i)^{2}\)
D
\((x+36i)(x-i)\)
Question 4
Use the first rows of Pascal’s triangle to find the coefficient of \(x^{2}y^{3}\) in \((x+y)^{5}\).
A
\(10\)
B
\(5\)
C
\(15\)
D
\(6\)
Question 5
Which expression equals \((x+2)^{3}\)?
A
\(x^{3}+8\)
B
\(x^{3}+2x^{2}+4x+8\)
C
\(x^{3}+3x^{2}+6x+8\)
D
\(x^{3}+6x^{2}+12x+8\)
Question 6
Solve \(V=\frac{1}{3}Bh\) for \(h\).
A
\(h=\frac{V}{3B}\)
B
\(h=\frac{3V}{B}\)
C
\(h=3VB\)
D
\(h=\frac{B}{3V}\)
Question 7
The graphs of \(f(x)=x^{2}-3\) and \(g(x)=x-1\) are shown. What are the solutions of \(f(x)=g(x)\)?
A
\(x=-2\) and \(x=1\)
B
\(y=-2\) and \(y=1\)
C
\(x=-1\) and \(x=2\)
D
\(x=-1\) only
Question 8
A rectangle is 4 feet longer than it is wide, and its area is 45 square feet. Which equation finds the width \(w\)?
A
\(w+(w+4)=45\)
B
\(w(w+4)=45\)
C
\(2w+2(w+4)=45\)
D
\(w^{2}+4=45\)
Question 9
Mei has $50. Ingredients cost $12 plus $1.75 per batch of cookies. What is the greatest whole number of batches she can make?
A
22
B
28
C
21
D
38
Question 10
What are the solutions of \(x^{2}-6x+13=0\)?
A
\(x=3\pm 4i\)
B
\(x=-3\pm 2i\)
C
\(x=3\pm 2\)
D
\(x=3\pm 2i\)
🎉 Quiz complete!
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Remember:
- Standards A-SSE.A.1, A-SSE.A.2, A-CED.A.1–4, A-REI.D.11, A-APR.C.5 and N-CN.C.8–9 on expressions and modeling.
- A difference of squares can hide inside higher powers: \(x^{4}-y^{4}=(x^{2}+y^{2})(x+y)(x-y)\).
- The solutions of \(f(x)=g(x)\) are the \(x\)-coordinates where the two graphs cross.
- Row \(n\) of Pascal’s triangle gives the coefficients of \((a+b)^{n}\).
- Over the complex numbers, \(x^{2}+4=(x+2i)(x-2i)\), and every quadratic has exactly two zeros.
See every chapter on the Algebra 2 math page.