12 exercises · 12 automatically checked · Untimed
12 questions · Shuffled order · Untimed practice
Work each question before choosing Check answer. Record confidence and help used. Automatic checks assess the final answer; compare your method and checks with the full explanation.
Guide question labels stay the same when the order changes. Check answers when you are ready to review.
Difficulty appears when a solution is opened. Written responses are self-review exercises.
Saved on this browser and device; clearing browser data removes progress.
Your practice is saved on this device.
Which expression is equivalent to x2 + 9x + 20?
Answer: B / (x + 4)(x + 5) The constant terms must multiply to 20 and add to 9. The pair 4 and 5 works. Expanding verifies x2 + 5x + 4x + 20.
Equivalent expressions / Foundation Review: Example 1.05.
For x > 0, simplify (x3/4)8.
Answer: D / x6 For a positive base, multiply the exponents: (3/4)(8)
Exponents / Standard Review: Example 6.07.
What is the value of 813/4?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 27 The fourth root of 81 is 3, and 33
Rational exponents / Standard Review: Example 1.06.
What is the larger solution to x2 − 11x + 24 = 0?
Answer: A / 8 Factor as (x − 3)(x − 8)
Quadratic equations / Standard Review: Example 6.04.
For f(x) = 3(x + 2)2 + 5, what is the minimum value of f ?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 5 The squared term is nonnegative and becomes zero at x
Quadratic features / Standard Review: Example 1.07.
For what value of c does x2 + 10x + c = 0 have exactly one distinct real solution?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 25 The leading coefficient is 1, so set the discriminant to zero: 100 − 4c
Discriminants / Standard Review: Example 6.05.
Solve = x − 2 over the real numbers.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 6 The right side requires x ≥ 2. Squaring gives x + 10
Radical equations / Challenge Review: Example 1.08.
For x ≠ −4, which expression is equivalent to ?
Answer: C / x − 2 Factor the numerator as (x + 4)(x − 2) and cancel x + 4, preserving x ≠ −4.
Rational expressions / Standard Review: Example 5.04.
What is the sum of the solutions to |2x − 3| = 9?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3 Solve 2x − 3
Absolute-value equations / Standard Review: Advanced Math reference.
A quantity is modeled by Q(t) = 700(0.85)t. By what percent does it decrease when t increases by 1?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 15 The multiplier 0.85 retains 85% of the prior value. The decrease is 100 − 85
Exponential interpretation / Standard Review: Example 1.09.
If f(x) = (x − 3)2 and g(x) = f(x) + 4, what is the vertex of the graph of g?
Answer: C / (3, 4) Adding 4 shifts every output up by 4 while leaving the vertex input 3 unchanged. Thus g(x)
Function transformations / Standard Review: Example 4.06.
The graphs y = x2 and y = 3x + 10 intersect. What is the sum of the x-coordinates of their intersections?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 3 Equating outputs gives x2 − 3x − 10
Nonlinear systems / Challenge Review: Example 3.04.
Review Practice, Review and Reference Materials