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.

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.

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).

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.

• (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).

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.

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.

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.

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.