SY25 Algebra Exit Exam - Practice Test 2

• c = 0.75p

• c = 30.75p

• c = 30 + 0.75p

• c = 30p + 0.75

Answer explanation

Elizabeth's total cost includes a fixed rental fee of $30 and a variable cost of $0.75 for each bag of popcorn. Thus, the equation is c = 30 + 0.75p, which accounts for both costs.

Tags

CCSS.HSF-BF.A.1A

Jerod makes a mistake in solving an equation. His work is shown below: -6(x - 7) = 2(x + 1) step 1 -6x + 42 = 2x + 2 step 2 -6x - 2x = 2 - 42 step 3 -4x = -40 step 4 x = 10 step 5 Where did Jerod make a mathematical mistake?

• Going from step 1 to step 2

• Going from step 2 to step 3

• Going from step 3 to step 4

• Going from step 4 to step 5

Answer explanation

Jerod made a mistake going from step 2 to step 3. He incorrectly combined the terms. The correct operation should be -6x - 2x = 2 - 42, leading to -8x = -40, not -4x = -40.

Tags

CCSS.HSA.REI.A.1

• (x - 7)

• (x + 7)

• (x - 3)

• (x + 3)

Answer explanation

To factor the quadratic 3x^2 + 2x - 21, we look for two numbers that multiply to -63 (3 * -21) and add to 2. The numbers 9 and -7 work, leading to (3x + 9)(x - 7). Thus, (x - 7) is a factor.

What is the mode of the data?

• approximately 48

• approximately 40

• approximately 31

• approximately 22

Answer explanation

The mode is the value that appears most frequently in a data set. In this case, approximately 31 occurs more often than the other values, making it the mode.

Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

Gita deposited d dollars into her account on January 1, 2000. The amount of the money in her account doubled each year until Gita had 640 dollars on January 1, 2005. Which of the following graphs represents this situation?

• A. [Graph A]

• B. [Graph B]

• C. [Graph C]

• D. [Graph D]

Answer explanation

Gita's deposit doubles each year: d, 2d, 4d, 8d. By 2005, she has 640 dollars, meaning d = 80. The graph should show exponential growth, which is represented by Graph C, as it reflects the doubling pattern over the years.

Which of the following quadratic equations is a parabola with a vertex of (6, 4) when graphed?

• y = (x - 6)(x - 4)

Answer explanation

The correct choice is y = (x - 6)^2 + 4, which is in vertex form. The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex. Here, (6, 4) matches the vertex.

Tags

CCSS.HSF-IF.C.7A

Marianna wants to buy tickets to a baseball game from an online ticket service. The ticket service charges a one-time fee for processing the purchase of the tickets. The equation P = 25t + 15 represents the total amount, P, Marianna will pay for t tickets. Which of the following best describes the meaning of 15 in this equation?

• A. The number of tickets she buys

• B. The price of each ticket

• C. The total amount she spends

• D. The processing fee

Answer explanation

In the equation P = 25t + 15, the 15 represents a one-time processing fee that Marianna must pay regardless of the number of tickets (t) she buys. Therefore, the correct choice is D, the processing fee.

Tags

CCSS.HSF.LE.B.5

• (-13, -4)

• (-8, -4)

• (5, -4)

• (7, -4)

Answer explanation

The equation y = (x - 5)^2 + k is symmetric about x = 5. Since (3, -4) is on the graph, the point (7, -4) is also on the graph. However, the point (-8, -4) is also valid as it reflects across x = 5, confirming it must lie on the graph.

Tags

CCSS.HSF-IF.C.7A

• -20

• 6

• -15

• 8

Answer explanation

To find the coefficient of x^3 in the expansion of (3x^3 + 4x)(2x^2 - 5), we consider the terms: 3x^3 * -5 = -15 and 4x * 2x^2 = 8x^3. Adding these gives -15 + 8 = -7. The correct coefficient is from the first term, which is -20.

Tags

CCSS.HSA.APR.C.5

Which of the following could represent a function?

• { (-2, 5), (1, 7), (4, 5), (4, 7) }

• [Graph image]

• [Table: x | y; -3 | 9; 0 | 0; 3 | 9; 6 | 36]

Answer explanation

The table represents a function because each x-value corresponds to exactly one y-value. The other options either have repeated x-values with different y-values or do not define a function.