Open Practice Tests

Pacing and deciding when to move on — Topic practice

5 exercises · 4 automatically checked · 1 written self-check · Untimed

Instructions and review guidance

4 questions · Shuffled order · Untimed practice

Try each question before choosing Check answer. Automatic checks assess your final numeric or choice answer only; compare your method, model and checks with the full explanation. Guide question labels stay the same when you shuffle the bank. 1 written response appears below the bank for self-review.

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.

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Practice explanations

Use these explanations to diagnose the first wrong decision, not only to compare final answers. Each solution appears with its question and links to a worked example with a transferable method. A different valid solution is welcome; compare its length, assumptions, and reliability.

The drill

Question 1

  • Guide question E6.1

If 6(3x − 2) = 54, what is 3x + 1?

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

Question 2

  • Guide question E6.2

The system 4x + y = 18, 2x − y = 6 is given. What is x?

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

Question 3

  • Guide question E6.3

A cylinder has radius r, height r + 5, and volume 144π, in consistent units. Which listed value is r?

Question 4

  • Guide question E6.4

Find the sum of all real k for which (k − 4)x2 + 2x + 1 = 0 has exactly one real solution in x.

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 E6.5

Four minutes remain, three questions are unanswered, and you reserve 45 seconds for a final scan. How much working time remains? What is the average available per unanswered question, and why is that not a fixed limit?

Show model answerHide model answer for question E6.5

195 seconds; 65 seconds on average

Four minutes is 240 seconds. Reserving 45 leaves 240 − 45 = 195 seconds for three unanswered questions, an average of 65 seconds each. This is a planning budget, not a rule to abandon every question at 65 seconds. Secure a clear answer promptly and reassess the remaining work after each question. The scenario’s reserve is an assumption, not an official testing rule. See Example 6.11.