DOK 3 Practice

Justify systems reasoning and critique common mistakes.

These questions emphasize evidence, error analysis, model choice, and interpretation of systems and constraints.

How to use this set

For analysis items, state the reason: same slope, same line, false substitution, or all constraints satisfied.

Home Math 1 Home Strand Page

Set Focus

Systems analysis and justification

DOK 3 questions reward precise reasons, not just a computed answer.

Justification

Explain why intersections and equivalent systems work.

Error analysis

Correct ordered-pair and solution-type mistakes.

Constraints

Model limits and feasible choices in context.

Interpretation

Connect solution coordinates to real quantities.

Practice Questions

Analysis, Error Correction, and Modeling

Check your answer first, then reveal the explanation when you want the model.

Question 1

Error analysis

A student says the solution to y=2x+3 and y=-x+9 is (3,9). What is the best correction?

Question 2

Equivalent systems

Which system has infinitely many solutions?

Question 3

Constraint modeling

A club buys shirts for 8 dollars each and hats for 12 dollars each. The club can spend no more than 120 dollars. Which constraint is strongest?

Question 4

Feasible solution

Which point satisfies all constraints: x+y\le8, x\ge2, and y\ge1?

Question 5

Justify intersection

Why does an intersection point solve a system of two linear equations?

Question 6

Strategy selection

Which solving method is usually most efficient when one equation is already written as y=2x-4?

Question 7

No solution evidence

Which evidence shows that a linear system has no solution?

Question 8

Test a claim

A student claims (6,5) is a solution to x+y\le10. What is the best response?

Question 9

Context intersection

Car A has traveled 40+10t miles. Car B has traveled 20+15t miles. What does the solution t=4 mean?

Question 10

Optimize feasible choices

A feasible region includes (0,10), (4,6), and (10,0). If profit is P=3x+5y, which point gives the greatest profit?

Back to Systems & Inequalities Back to Math 1