Act Algebra Review

Evaluate 10 to the 0 power

• 1

• 10

• 0

• 100

Answer explanation

10⁰ is equivalent to 1 because any non-zero number raised to the power of 0 equals 1. Therefore, the correct answer is 1.

Tags

CCSS.8.EE.A.1

Aria is trying to find out between which two whole numbers the square root of 277 lies. Can you help her?

• 15 and 16

• 16 and 17

• 18 and 19

• 14 and 15

Answer explanation

The square root of 277 is approximately 16.64. Since 16^2 = 256 and 17^2 = 289, the square root lies between 16 and 17. Thus, the correct answer is 16 and 17.

Tags

CCSS.8.NS.A.2

Grace is trying to simplify the expression ∛54 for her math homework. What is the simplest form of this expression?

• 3∛6

• 9∛2

• 3∛2

• 3∛3

Answer explanation

To simplify ∛54i, we can express 54 as 27 * 2. Thus, ∛54i = ∛(27 * 2)i = ∛27 * ∛2 * i = 3∛2 * i. The simplest form is 3∛2.

Michael is trying to solve a puzzle where he needs to find two numbers. The first number is twice the second number, and their sum is -15. What are the numbers?

Let the first number be y and the second number be x.

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Answer explanation

Substituting x = 3y into 2y + x = -15 gives 2y + 3y = -15. This simplifies to 5y = -15, so y = -3. Then, x = 3(-3) = -9. The solution is (-9, -3).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Charlotte and Anika are comparing their savings. Charlotte says her savings are equal to Anika's savings.
Anika says her savings are twice Charlotte's savings minus 1 dollar.
Find the amount of savings each has.

Answer explanation

Substituting y=x into y=2x-1 gives x=1. Then, y=1. The solution is (1,1), which matches the correct answer.

Tags

CCSS.8.EE.C.8C

• (14,4) 

• (4,14)

• (4, 0)

• (0,4)

Answer explanation

To solve the system, substitute y from the first equation into the second: 5x - 6 = 4x - 2. Solving gives x = 4. Substitute x back to find y: y = 5(4) - 6 = 14. Thus, the solution is (4, 14).

Tags

CCSS.8.EE.C.8C

Evelyn is trying to balance her budget. She realizes that she needs to adjust her expenses by adding $12 to both sides of her budget equation to solve for x . Which equation is she working with?

Answer explanation

To isolate x in the equation 13 = 5y - 12, you would add 12 to both sides, resulting in 25 = 5y. This step is necessary to eliminate the -12 from the right side.

Tags

CCSS.HSA.REI.A.1

Noah has 10 apples. He gives away m apples to his friends. Write an algebraic expression for the number of apples Noah has left.

• 10 = m

• 10 + m

• 10 x m

• 10 - m

Answer explanation

The phrase '10 decreased by m' indicates subtraction. Therefore, the correct algebraic expression is 10 - m, which represents taking m away from 10.

Tags

CCSS.HSA-SSE.A.1A

Michael is buying packs of pencils. Each pack contains 2 pencils. Write an algebraic expression for the total number of pencils Michael buys if he buys q packs.

• 2 x q

• 2 + q

• q - 2

Answer explanation

The question asks for the product of 2 and q, which means we need to multiply them. The correct algebraic expression for this is 2 x q, as it represents multiplication. The other options do not represent a product.

Tags

CCSS.HSA-SSE.A.1A

Mia has 8 more apples than Oliver. If Oliver has 36 apples, how many apples does Mia have?

• 28

• 36

• 44

• 40

Answer explanation

To evaluate w + 8 when w = 36, substitute 36 for w: 36 + 8 = 44. Therefore, the correct answer is 44.

Tags

CCSS.1.OA.A.1