Algebra Review Test
Quarter 1 Interim Prep
Algebra I Review Test
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Target Time: 60 Minutes • 22 Questions
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Student Test Directions
This review mirrors your real Interim Assessment. For Questions 1–18, select the single best multiple choice answer. For Questions 19–22, write out all steps in the organized workspace and circle your final answer.
1 Check each step twice
2 Use the strategy toolkit
3 Box every final value
Algebra Reference & Strategy Tools
Solving Equations Checklist Core Skill
- Simplify: Distribute parenthesis \(a(b+c)\) & combine like terms.
- Group Variables: Move variable terms to one side (+ or −).
- Isolate \(x\): Undo addition/subtraction, then multiply/divide.
💡 Golden Rule: Whatever you do to one side of the =, do to the other side!
Order of Operations (PEMDAS) Rule
P( )
E\(x^2\)
MDLeft→Right
ASLeft→Right
Work top of fraction completely, then bottom, then divide last!
Functions & Graphs Reminders Key Terms
- Input/Output: \(f(x) = y\). Inside is \(x\), answer is \(y\).
- Domain: All \(x\)-values from Left to Right.
- Range: All \(y\)-values from Bottom to Top.
- Circles: Closed [ ] includes value. Open ( ) does not.
Special Lines & Solutions Checklist
- \(y = \text{number}\): Flat HORIZONTAL line across the \(y\)-axis.
- \(x = \text{number}\): Straight VERTICAL line through \(x\)-axis.
- Infinite Solutions: Left Side = Right Side (e.g., \(2x+4 = 2x+4\)).
- No Solution: Same variable, different numbers (e.g., \(2x+1 = 2x+5\)).
Personal Goal: Show work step-by-step and attempt all 22 questions.
Confidence: 🙂 😐 🤔
Quarter 1 SPED Algebra I Practice Assessment Page 1 of 8
Part 1: Multiple Choice
Equations & Expressions (Questions 1–4)
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1
What is the value of \(x\) in the equation below?
Hint: Distribute 3 first
\(2x - 5 = 3(x + 1)\)
(A) \(x = -8\)
(B) \(x = -2\)
(C) \(x = 4\)
(D) \(x = 8\)
2
What is the solution to the equation below?
Hint: Multiply by reciprocal \(\frac{4}{3}\)
\(\frac{3}{4}(x - 2) = 6\)
(A) \(x = 6\)
(B) \(x = 8\)
(C) \(x = 10\)
(D) \(x = 12\)
3
Which expression is equivalent to \(4x + 9 - 2x + 3\)?
Combine like terms
Group the \(x\)-terms together and group the constant numbers together.
(A) \(6x + 12\)
(B) \(2x + 6\)
(C) \(2x + 12\)
(D) \(6x + 6\)
4
A function \(S(d)\) represents the number of students who bought cafeteria lunch on day \(d\). What does the inequality \(S(4) < S(1) + S(2)\) mean?
(A) There were fewer students who bought lunch on day 4 than the combined total on days 1 and 2.
(B) The number of days students bought lunch was less than 4 on days 1 and 2.
(C) There were 4 fewer students on day 1 than on day 2.
(D) The price of lunch on day 4 was less than the combined price on days 1 and 2.
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Part 1: Multiple Choice
Word Problems, Formulas & Functions (Questions 5–8)
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5
A dog walker earns \(\$12\) per hour. If they walk all dogs safely and return on time, they receive an additional \(\$5\) bonus tip, regardless of the number of hours worked. Which expression represents the total amount earned for any number of hours?
(A) \(12h + 5\), where \(h\) is hours
(B) \(5h + 12\), where \(h\) is hours
(C) \(12(h + 5)\), where \(h\) is hours
(D) \(17h\), where \(h\) is hours
6
The formula \(d = rt\) calculates the distance \(d\) an object travels at a constant rate \(r\) over time \(t\). Based on this formula, what is the rate, \(r\), in terms of \(d\) and \(t\)?
Divide by \(t\)
(A) \(r = \frac{d}{t}\)
(B) \(r = dt\)
(C) \(r = \frac{t}{d}\)
(D) \(r = d - t\)
7
Simplify the following expression completely:
Inner \(-\) distributes: \(-(5 - x) = -5 + x\)
\(-2[3x - (5 - x)]\)
(A) \(-8x + 10\)
(B) \(-4x + 10\)
(C) \(-8x - 10\)
(D) \(-6x + 10\)
8
Let \(f(x) = 3x^2 + 2x - 5\). What is the value of \(f(2)\)?
Plug in \(x = 2\)
Remember: Calculate \((2)^2 = 4\) first before multiplying by 3.
(A) \(f(2) = 11\)
(B) \(f(2) = 15\)
(C) \(f(2) = 9\)
(D) \(f(2) = 7\)
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Part 1: Multiple Choice
Equations & Expressions (Questions 9–12)
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9
An electrician charges a flat \(\$45\) service visit fee plus \(\$35\) for every hour of work. Which function best represents the total cost \(C(h)\) for \(h\) hours of work?
(A) \(C(h) = 45h + 35\)
(B) \(C(h) = 35h + 45\)
(C) \(C(h) = 80h\)
(D) \(C(h) = 45 + 80h\)
10
Evaluate the expression below following order of operations:
PEMDAS
\[\frac{6^2 \div 4 \cdot 2^3}{3 + 3^2}\]
(A) \(6\)
(B) \(12\)
(C) \(72\)
(D) \(2\)
11
What value of \(x\) satisfies the proportion equation below?
Cross-multiply: \(3(2x+1) = 5(x+2)\)
\[\frac{3}{x + 2} = \frac{5}{2x + 1}\]
(A) \(x = 3\)
(B) \(x = 5\)
(C) \(x = 7\)
(D) \(x = 9\)
12
If \(15 = \frac{m}{4} - 3\), what is the value of \(m\)?
Add 3 first, then multiply by 4
Step 1: Isolate the fraction term. Step 2: Clear the denominator.
(A) \(m = 48\)
(B) \(m = 72\)
(C) \(m = 60\)
(D) \(m = 18\)
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Part 1: Multiple Choice
Coordinate Graphs, Domain & Range (Questions 13–16)
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Use the graph of \(f(x)\) below to answer Questions 13 and 14.
0 2 4 6 8 x 2 4 6 8 y f(x)
13
What is the value of \(f(2)\)?
(A) 2
(B) 4
(C) 6
(D) 8
14
For what value of \(x\) is \(f(x) = 4\)?
(A) 2
(B) 4
(C) 6
(D) 0
15
What is the domain and range of the function graphed below?
Domain: left→right | Range: bottom→top
-4 -2 2 x -3 2 y
(A) Domain: \([-4, 2]\) | Range: \([-3, 2]\)
(B) Domain: \((-4, 2)\) | Range: \((-3, 2)\)
(C) Domain: \((-4, 2]\) | Range: \([-3, 2]\)
(D) Domain: \([-4, 2)\) | Range: \((-3, 2]\)
16
Which of the following graphs represents the function \(y = -3\)?
(A)
(B)
(C)
(D)
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Part 1 & Part 2
Expressions & Constructed Response (Questions 17–19)
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17
Simplify the following polynomial expression completely:
Distribute 3 first
\(3(x^2 - 2x) + 4x - 2x^2\)
(A) \(x^2 - 2x\)
(B) \(x^2 + 2x\)
(C) \(5x^2 - 2x\)
(D) \(x^2 - 10x\)
18
Which of the following equations have the same solution as \(5x + 15 = 0\)? Select all that apply.
Solution is \(x = -3\)
(A) \(x + 3 = 0\)
(B) \(-(x + 3) = 0\)
(C) \(2x + 6 = 0\)
(D) \(5x - 15 = 0\)
19
Open-Ended: What value of \(x\) is the solution to the equation below? Show all steps. (3 points)
Show Work
\[\frac{1}{2}(16 - 4x) = 2 - \frac{1}{2}x\]
Step 1: Distribute \(\frac{1}{2}\) to each term on the left side:
Step 2: Collect all \(x\) terms on one side of the equation:
Step 3: Isolate \(x\) and find your final solution:
Box Final Answer: \(x = \)
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Part 2: Constructed Response
Equations & Modeling (Questions 20–21)
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20
In the equation below, \(k\) is a constant number. For what value of \(k\) does the equation have an infinite number of solutions? Show all steps. (2 points)
2 Points
\[18x + 24 = 6(3x + k)\]
💡 Remember: For infinite solutions, the left side and right side must be completely identical!
Show your work here:
Box Final Answer: \(k = \)
21
Suppose Marcus has already saved \(\$40\) toward a new tablet. He plans to save \(\$8\) more each week from his allowance.
4 Points Total
Part A: Write an equation that models the total amount \(T\) Marcus will have \(w\) weeks from now. (1 point)
Equation: \(T = \) _________________________________________________
Part B: How many weeks will it take Marcus to save \(\$96\)? Show your algebraic steps and write a final complete sentence with units. (3 points)
Show algebraic solving steps:
Final Sentence with Units: It will take Marcus ________________ weeks to save \(\$96\).
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Part 2: Constructed Response
Dual Function Graph Analysis (Question 22)
8 Points Total
22
Use the graph of \(y = f(x)\) and \(y = g(x)\) below to answer Parts A through D. Show all work to receive full credit.
\(f(x)\) \(g(x)\)
0 1 2 3 4 5 6 7 8 x 1 3 5 7 y g(x) f(x)
Part A: Evaluate both \(f(2)\) and \(g(2)\). Write your answers using function notation. (2 points)
\(f(2) = \) ________
\(g(2) = \) ________
Part B: Evaluate \(\left[3 \cdot f(0) + \frac{g(2)}{5}\right]\). Show the steps that lead to your final answer. (2 points)
Steps: Find \(f(0)\) and \(g(2)\) on graph, then substitute and simplify
Answer:
Part C: Determine the value of \(x\) for which \(f(x) = g(x)\). Provide visual evidence from the graph. (2 points)
\(x\)-value where graphs intersect: \(x = \) ________
Evidence / Coordinate point: _________________________________________
Part D: Provide an integer value of \(x\) for which \(f(x) > g(x)\). Explain why using graph coordinates. (2 points)
Value of \(x\): \(x = \) ________
Because at this \(x\), \(f(x) =\) _____ which is greater than \(g(x) =\) _____
CONGRATULATIONS! YOU HAVE COMPLETED THE REVIEW ASSESSMENT.
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