Open Practice Tests

Choosing between algebra, graphing, and mental calculation — Topic practice

5 exercises · 2 automatically checked · 3 written self-checks · Untimed

Instructions and review guidance

2 questions · Shuffled order · Untimed practice

Try each question before choosing Check answer. Guide question labels stay the same when you shuffle the bank. 3 written responses appear below the bank, with model answers for self-review; these are not automatically graded. Follow any rounding instruction in the question.

Guide question labels stay the same when the order changes. Check answers when you are ready to review.

Written self-checks are below the question bank and are excluded from the automatic score.

Written responses are self-review exercises.

Saved on this browser and device; clearing browser data removes progress.

Compare the reasoning as well as the answer. Equivalent valid methods are welcome. A referenced example provides a targeted repair route.

The drill

Question 1

  • Guide question E5.1

If 8x + 12 = 44, find 2x + 3 without first finding x.

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question 4

  • Guide question E5.4

For nonnegative integers n, let Q(n) = 300(1.1)n. What is the least n for which Q(n) > 450?

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Question navigator and options
  • Answered
  • Correct
  • Incorrect
  • Revealed, not answered
  • Current

Written self-checks

Write your complete response before opening the model answer. Compare both your answer and your reasoning.

Guide question E5.2

If 4x + y = 19 and x + 4y = 16, what is x + y? Explain a method that avoids a graph.

Show model answerHide model answer for question E5.2

7.

Add the equations: 5x + 5y = 35, so x + y = 7. The individual values x = 4 and y = 3 verify the sum and both original equations. The efficient method depends on the target; a different requested expression might favor another combination. Review Example 5.03.

Guide question E5.3

For which real values of a does ax2 + 4x + 4 = 0 have exactly one distinct real solution?

Show model answerHide model answer for question E5.3

a = 0 or a = 1.

When a ≠ 0, the equation is quadratic and the discriminant must be zero: 16 − 16a = 0, giving a = 1. When a = 0, the equation becomes 4x + 4 = 0 and has the single root −1. Both cases are valid; do not apply the quadratic test to a linear equation. Review Example 5.06.

Guide question E5.5

Workflow drill. A question is marked for review, but its answer field is blank. The calculator contains a correct result. Has a response been recorded? What should the final audit check?

Show model answerHide model answer for question E5.5

No; the answer must be selected or entered in the question.

A mark is a navigation flag, not an answer. A calculator entry is working space, not the response field. Return to the question, confirm the requested quantity, type or select the intended answer, and inspect the question menu for any remaining blanks. Do this before leaving the active module. Review Example 5.13.