Question 1
If 7x − 9 = 40, what is x?
Why this answer
Answer: C / 7 Add 9 to get 7x
Linear equations / Foundation Review: Example 1.01.
Algebra — Topic practice
12 exercises · 12 automatically checked · Untimed
Instructions and review guidance
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.
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Question 2
The graph shows a line. What is its equation?
Why this answer
Answer: D / y
Lines and graphs / Foundation Review: Example 1.02.
Question 3
A line has equation 3x − 4y = 20. What is its slope?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 3/4 Isolate y: −4y
Linear equations in two variables / Standard Review: Example 6.01.
Question 4
If 2x + y = 17 and x − y = 4, what is x + y?
Why this answer
Answer: D / 10 Add the equations to get 3x
Systems of linear equations / Standard Review: Example 2.04.
Question 5
For which value of k does the system 4x + 6y = 15, 2x + ky = 8 have no solution?
Why this answer
Answer: B / 3 Parallel left sides require the second coefficients to be half the first, so k
Solution counts / Standard Review: Example 1.03.
Question 6
What is the greatest integer n satisfying 5n + 13 < 49?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 7 The inequality gives 5n < 36 and n < 7.2. The greatest integer is 7. Check: 48 is less than 49, but at 8 the left side is 53.
Integer inequalities / Standard Review: Example 3.07.
Question 7
A repair service charges $48 plus $35 per hour. A bill with no tax is $223. How many hours were charged?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 5 With h hours, 48 + 35h
Linear modeling / Standard Review: Example 1.04.
Question 8
For f(x) = 4x − 7, the function g is defined by g(x) = f(x + 3). What is g(2)?
Why this answer
Answer: A / 13 First compute the input to f : 2 + 3
Linear functions / Standard Review: Example 5.02.
Question 9
The equation C = 18 + rt gives cost C for time t, with t ≠ 0. Which expression equals r?
Why this answer
Answer: A / Subtract 18, then divide by nonzero t: C − 18
Rearranging equations / Standard Review: Example 6.02.
Question 10
A store sells pens for $2 and notebooks for $5. A buyer purchases 14 items for $49. How many notebooks were purchased?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 7 Let n be notebooks and 14 − n be pens. Then 5n + 2(14 − n)
Systems in context / Standard Review: Example 2.04.
Question 11
For every real x, a(3x − 2) = 12x + b. What is a + b?
Why this answer
Answer: B / −4 Equality for every x requires matching coefficients: 3a
Identities and constants / Standard Review: Example 1.03.
Question 12
The line through (3, −2) is perpendicular to y = x + 7. What is its y-intercept?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
Answer: 0 The perpendicular slope is −2/3. Write y
Perpendicular lines / Challenge Review: Example 6.01.
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