15 exercises · 15 automatically checked · Untimed
15 questions · Shuffled order · Untimed practice
Covers multiple Math domains.
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The roots of 2x2 − 7x + 3 = 0 are r and s. What is r2 + s2?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 37/4 The root sum is 7/2 and product is 3/2. Use r2 + s2 = (r + s)2 − 2rs = 49/4 − 3 = 37/4.
Root relationships / Challenge Review: Example 6.15.
A 30-liter drink mixture is 20% concentrate by volume. Water is added until it is 12% concentrate by volume. Assuming the volumes add, how many liters of water are added?
Answer: A / 20 The concentrate amount remains 0.20(30)
Percent mixtures / Standard Review: Example 2.06.
For positive x, x1/2 = 5. What is x3/2?
Answer: D / 125 x3/2 = (x1/2)3 = 53 = 125. Finding x
Exponent structure / Standard Review: Example 6.07.
The shaded region in the graph includes its boundary. Which inequality describes it?
Answer: B / y ≥ −x + 3 The solid boundary is the line through (0, 3) and (3, 0), so its equation is y
Graphing inequalities / Standard Review: Example 1.04.
A rectangular prism has dimensions 4, 6, and 9. A similar prism has longest dimension 15. What is its volume?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Answer: 1000 The length factor is 15/9
Similar-solid volume / Challenge Review: Example 4.11.
If f(x) = 2x2 − 8x + 3, what is the minimum value of f ?
Answer: B / −5 Complete the square: f(x)
Quadratic minimum / Standard Review: Example 6.06.
A store must earn at least $420 after a fixed fee of $36 is subtracted from revenue. Each item sells for $19. What is the least number of items it must sell?
Answer: C / 24 The net is 19n − 36 ≥ 420. Thus 19n ≥ 456 and n ≥ 24. Twenty-four gives exactly 420; 23 gives less.
Integer modeling / Standard Review: Example 4.14.
A circle has equation x2 + y2 + 4x − 10y = 7. What is its radius?
Answer: C / 6 Completing squares gives (x + 2)2 + (y − 5)2 = 7 + 4 + 25 = 36. The radius is 6, not 36.
Circle equations / Standard Review: Example 1.15.
For the linear function f, f(4) − f(1) = 15. What is f(9) − f(5)?
Answer: B / 20 The slope is 15/(4 − 1)
Linear rate / Standard Review: Example 2.01.
The frequency table gives a data set. What is its mean?
Value | 2 | 4 | 8 |
|---|---|---|---|
Frequency | 2 | 3 | 1 |
Answer: D / 4 The total frequency is 2 + 3 + 1
Frequency-table mean / Standard Review: Example 1.10.
For what value of k does x2 − 8x + k = 0 have a root of 3?
Answer: C / 15 Substitute the known root: 9 − 24 + k
Unknown constants / Standard Review: Example 5.05.
The system y = x2 + 1, y = 6x − 8 has exactly one intersection. What is its x-coordinate?
Answer: A / 3 Substitution gives x2 − 6x + 9 = (x − 3)2 = 0. The unique input is 3, and the corresponding output is 10.
Tangency and systems / Standard Review: Example 2.14.
A pump moves 2.5 liters per second. How many cubic meters does it move in 8 minutes? Use 1000 liters = 1 m3.
Answer: A / 1.2 Eight minutes is 480 seconds. Volume is 2.5(480)
Unit conversion / Standard Review: Example 2.13.
If = x − 1, what is the solution?
Answer: C / 3 Require x ≥ 1. Squaring gives x + 1
Extraneous solutions / Standard Review: Example 4.08.
Positive numbers a and b satisfy a + b = 12 and ab = 20. What is (a − b)2?
Answer: A / 64 Use (a − b)2 = (a + b)2 − 4ab = 144 − 80 = 64. The actual numbers 2 and 10 verify the result, but need not be found.
Algebraic identities / Challenge Review: Example 6.15.
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