Open Practice Tests

Algebraic language and notation — Topic practice

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

Instructions and review guidance

2 questions · Shuffled order · Untimed practice

Work through the set before checking solutions. Guide question labels match the source lesson references. 3 written responses appear below the question bank, with model answers for self-review; these are not automatically graded.

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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The drill

Question 2

  • Guide question E3.2

Evaluate −2a2 + 5a when a = −3.

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

Question 5

  • Guide question E3.5

If 4(x + 1) = 20, what is the value of (x + 1)2 − 3?

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

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Written self-checks

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

Guide question E3.1

In −7x2 + x − 3, what is the coefficient of x and what is the constant term?

Show model answerHide model answer for question E3.1

Coefficient of x: 1; constant term: −3. In −7x2 + x − 3, the term x means 1x. The coefficient −7 belongs to x2, not to x. The term independent of x is −3, including its sign. Repair: Example 3.01.

Guide question E3.3

Simplify 3(2x − 5) − 2(x + 4).

Show model answerHide model answer for question E3.3

4x − 23.

Distribute both signed multipliers:

3(2x − 5) − 2(x + 4) = 6x − 15 − 2x − 8 = 4x − 23.

The second constant is −8, not +8. At x = 0, both the original expression and the simplified expression equal −23, a useful check on the constants. Repair: Example 3.05.

Guide question E3.4

Simplify x2−25x−5, and state the original restriction on x.

Show model answerHide model answer for question E3.4

x + 5, for x ≠ 5. Factor x2 − 25 = (x − 5)(x + 5), then divide out x − 5 only when it is nonzero. The original expression remains undefined at x = 5 even though the simpler formula x + 5 is defined there. Equivalent values must be compared on the original domain. Repair: Example 3.08.

After the exit check

If the final answer is wrong, mark the first step that failed: identifying the coefficient, substituting a signed value, distributing through a group, canceling a factor, or recognizing the requested expression. Repair that step on a new problem before adding more complexity.

Section 3 readiness

You should recognize signed coefficients, substitute into powers accurately, distribute to every term, distinguish an expression from an equation, and preserve domain restrictions when canceling a factor. One matching numerical test does not prove an identity.