Complete this quiz after finishing Modules 2.2–2.6 (Algebra). You should be able to answer every question without referring back to the modules. If you get stuck, reread that section.

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Part A

Multiple Choice

This section tests your understanding of linear equations, systems of equations, inequalities, and linear models.

1A student sees "If 2x + 1 = 5, what is the value of 8x + 4?" and immediately solves for x first. What is the faster method?*

A) Use Desmos to solve for x B) Substitute x = 2 into 8x + 4 C) Multiply the entire original equation by 4 D) Set up a second equation

Please select an answer.

2In the system ax + by = c and dx + ey = f, what ratio tells you the two lines are parallel (no solution)?*

A) a/d = e/b B) a/d = b/e ≠ c/f C) a/d = b/e = c/f D) a/b = d/e

Please select an answer.

3A student flips the inequality sign when multiplying both sides by −3. Why is this correct?*

A) Negative numbers always reverse inequalities B) The sign only flips when dividing, not multiplying C) The sign flips only for strict inequalities D) Multiplication by a negative number reverses the inequality direction

Please select an answer.

4A linear model problem says: "A club charges a $45 registration fee and $22 per month. After how many months does the total equal $177?" Which equation is correct?*

A) 45m + 22 = 177 B) 22(m + 45) = 177 C) 22m + 45 = 177 D) 45 + 22 = 177m

Please select an answer.

5When is Desmos the faster move for a system of equations?*

A) Always — Desmos is faster than algebra for all systems B) When the numbers are messy or elimination is not obvious C) Only when the system has no solution D) Never — always use elimination or substitution

Please select an answer.

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Part B

Short Answer

Respond in your own words.

6Explain the difference between "no solution" and "infinitely many solutions" for a system of equations. How does each case show up in the SAT's ax + by = c form?*

Please answer this question.

7A student struggles to identify the slope in the equation 3x − 2y = 6. Walk through how you explain it.*

Please answer this question.

8Describe a word problem that naturally leads to a system of equations rather than a single equation. What is the key signal in the problem?*

Please answer this question.

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Part C

Teaching Scenario

This puts you in a tutoring session. Respond in your own words.

9A student consistently makes the right setup but makes arithmetic errors solving systems. What drill or habit would you introduce? How do you frame it without making the student feel like they are being punished for careless mistakes?*

Please answer this question.

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What Comes Next

Teach-Back and Check-In

Nice work finishing Algebra (Modules 2.2–2.6). You've covered linear equations, systems of equations, inequalities, and linear models, the core toolkit you'll lean on in most Algebra lessons. Before moving into the next module, you'll walk a trainer through a couple of these concepts the way you'd walk a student through it. Pick who you're meeting with below, and they'll reach out to find a time.

Pick the trainer that you'll meet for the teach-back lesson*

Please pick a trainer.

Any comments or questions before the meeting?

Algebra Tutor Assessment

Multiple Choice

Short Answer

Teaching Scenario

Teach-Back and Check-In

You're all set