ACT Practice: Algebra & Functions

Front

What is the distributive property in algebra?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Tags

CCSS.6.EE.A.3

Front

How do you simplify the expression (a - 6)(b + 4)?

Back

Use the distributive property: (a - 6)(b + 4) = ab + 4a - 6b - 24.

Tags

CCSS.HSA.APR.A.1

Front

What is the result of subtracting two polynomials, specifically (3x^2 - 5x + 1) - (3x^2 - 2x + 6)?

Back

The result is -3x - 5.

Tags

CCSS.HSA.APR.A.1

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How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Tags

CCSS.HSA.APR.B.2

Front

How do you find the value of x in the equation 4(x - 1) = 8(x - 2)?

Back

Distribute both sides: 4x - 4 = 8x - 16. Rearranging gives x = 3.

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of their variables.

Tags

CCSS.6.EE.A.4

Front

What is the process for factoring the quadratic expression x^2 - x - 12?

Back

To factor, find two numbers that multiply to -12 and add to -1. The factors are (x - 4)(x + 3).

Front

What is the solution to the equation 2x - y = -8 when y is expressed in terms of x?

Back

Rearranging gives y = 2x + 8.

Tags

CCSS.6.EE.C.9

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial function.