Advanced Algebra: Concepts & Connections A

Question

Advanced Algebra: Concepts & Connections A

Q1 Benchmark
Fall 2023-2024
1. You had $320 dollars at the end of the summer, but you’ve been spending $5.65 on your
Starbucks coffee every morning. Which algebraic expression would describe this situation,
where d represents the number of days?
a) 5. 65𝑑 + 320
b) 320𝑑 − 5. 65
c) 320 − 5. 65𝑑
d) 5. 65 + 320𝑑
2. Is the following always, sometimes, or never true?
2(3𝑥 − 1) + 4 > 6𝑥 + 2
a) Always true
b) Sometimes true
c) Never true
3. Solve the following absolute value equation.
2|4𝑥 − 3| + 1 = 9
a) 𝑥 =−
7
4
,
1
4
b) 𝑥 =
7
4
c) 𝑥 = 2, −
1
2
d) 𝑥 =
7
4
, −
1
4
4. Write the equation in slope-intercept form and correctly list the slope and y-intercept.
5𝑥 − 2𝑦 = 12
a) 𝑦 = ; slope: ; y-intercept:
5
2
𝑥 − 6
5
2 − 6
b) 𝑦 = ; slope: ; y-intercept:
5
2
𝑥 − 6 − 6
5
2
c) 𝑦 =− ; slope: ; y-intercept:
5
2
𝑥 − 6 −
5
2 − 6
d) 𝑦 =− ; slope: ; y-intercept:
5
2
𝑥 + 6 −
5
2
6
5. Which of the following describes the graph of 𝑦 = |𝑥| after it has been reflected across the
x-axis, shifted vertically up 3 units, and shifted horizontally to the left 6 units?
a) 𝑦 = | − 𝑥 + 6| + 3
b) 𝑦 =− |𝑥 + 6| + 3
c) 𝑦 =− |𝑥 − 6| + 3
d) 𝑦 = |𝑥 − 6| + 3
6. Which of the following would be a solution to the inequality 3𝑥 + 2𝑦 ≥ 7?
a) (0, 0)
b) (− 1, 5)
c) (0, − 4)
d) (2, 0)
7. The Polar Express charges $69.50 per adult ticket and $48.50 per child’s ticket. A group of 11
people paid $538.50 for tickets. Which system of equations could be used to find x, the number
of adult tickets purchased, and y, the number of children's tickets purchased?
a) 48. 5𝑥 + 69. 5𝑦 = 538. 5
𝑥 + 𝑦 = 11
b) 48. 5𝑥 + 69. 5𝑦 = 11
𝑥 + 𝑦 = 538. 5
c) 69. 5𝑥 + 48. 5𝑦 = 538. 5
𝑥 + 𝑦 = 11
d) 69. 5𝑥 + 48. 5𝑦 = 11
𝑥 + 𝑦 = 538. 5
8. How many Solutions does the following system have?
a) Infinitely many solutions
b) Two Solutions
c) One Solution
d) No Solutions
9. Determine whether the variable y varies directly with x.
a) Yes, y does vary directly with x.
b) No, y does not vary directly with x.
10. Determine the correct domain for the function in the graph below.
a) D: {1, 3, 4, 5, 6}
b) D: {1, 2, 3, 4, 5, 6, 7}
c) D: {2, 3, 5, 7, 9}
d) D: All real numbers
11. Which of the following would NOT represent a function?
a) {(1, 3), (2, 5), (5, 3), (7, 10)}
b) {(-1, 4), (2, 4), (0, 4), (9, 4)}
c) {(-3, -2). (-1, 0), (3, 7), (6, 1)}
d) {(1, 12), (2, 8), (3, 1), (1, -4)}
12. An Uber driver in Metro Atlanta charges a $10 pick-up fee and then an additional $0.65 per
mile, m. Which of the following does NOT accurately represent the cost of a trip with this
driver?
a)
b) A slope of 10 and a y-intercept at (0, 0.65)
c)
d)
13. Evaluate the following function for the given value of x.
Find f(-4)
a) 39
b) -9
c) 71
d) 31
x 0 2 4 6
y 10 11.30 12.60 13.90
14. You are going to the fair with your friends. Tickets to enter the fair are $7 and each ride (x)
costs an additional $0.50. You can spend no more than the $20 you have in your pocket. Which
inequality would most accurately model your situation?
a)
b)
c)
d)
15. A jewelry company pays $100 for advertising and $5 per necklace they create. Each necklace
sells for $25. How many necklaces must the company sell in order for their expenses to equal
their revenue?
a) 125
b) 5
c) 150
d) 7

Answer 1

1. a) 5.65𝑑 + 320

2. b) Sometimes true
3. c) 𝑥 = 2, −1/2
4. b) 𝑦 = (5/2)𝑥 - 6; slope: 5/2; y-intercept: -6
5. c) 𝑦 = -|𝑥 - 6| + 3
6. b) (−1, 5)
7. c) 69.5𝑥 + 48.5𝑦 = 538.5; 𝑥 + 𝑦 = 11
8. c) One Solution
9. a) Yes, y does vary directly with x.
10. b) D: {1, 2, 3, 4, 5, 6, 7}
11. d) {(1, 12), (2, 8), (3, 1), (1, -4)}
12. c)
13. c) 71
14. a) 7 + 0.50𝑥 ≤ 20
15. c) 150

Answer 2

1. The algebraic expression that would describe this situation is c) 320 - 5.65d.

2. The statement 2(3x - 1) + 4 > 6x + 2 is sometimes true.

3. The solution to the absolute value equation 2|4x - 3| + 1 = 9 is d) x = 7/4, -1/4.

4. The equation 5x - 2y = 12 can be written in slope-intercept form as y = (5/2)x - 6. The slope is 5/2 and the y-intercept is -6.

5. The graph of y = |x| after being reflected across the x-axis, shifted vertically up 3 units, and shifted horizontally to the left 6 units can be described by the equation d) y = |x - 6| + 3.

6. The point (-1, 5) is a solution to the inequality 3x + 2y ≥ 7.

7. The system of equations that could be used to find the number of adult tickets purchased (x) and the number of children's tickets purchased (y) is a) 48.5x + 69.5y = 538.5 and x + y = 11.

8. The number of solutions to the system of equations is c) One Solution.

9. To determine if the variable y varies directly with x, more information is needed.

10. The correct domain for the function in the graph is b) D: {1, 2, 3, 4, 5, 6, 7}.

11. The set {(1, 12), (2, 8), (3, 1), (1, -4)} would NOT represent a function because there are two different y-values assigned to the x-value of 1.

12. The correct option that does NOT accurately represent the cost of a trip with the Uber driver is d).

13. To find f(-4), we look for the corresponding y-value when x = -4. From the given table, f(-4) = 13.90, so the answer is d) 31.

14. The inequality that would most accurately model your situation is c) 7 + 0.50x ≤ 20.

15. The number of necklaces the company must sell in order for their expenses to equal their revenue is a) 125.