Praxis Math (Algebra)

At a craft fair, Tony bought 3 items, Isabella bought 1 item, and Tanisha bought 5 times as many items as Tony and Isabella did combined. Which of the following represents the number of items Tanisha bought?

(3+1) x 5

What is equivalent to 7x + 1

5(x + 1) + 2(x - 2)

For x=4 and y= -3, what is the value of 2x + 3y

-1

How to check whether a more complex expression is equivalent to a simpler expression

1. Distribute any coefficients: a(bx±c)=abx±ac 2. Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants 3. Arrange the terms in the same order, usually x-term before constants 4. If all of the terms in the two expressions are identical, then the two expressions are equivalent.

To translate verbal descriptions of mathematical operations:

1. Identify any key words or phrases that indicate an operation. 2. Combine the individual operations into an expression or equation. Make sure to preserve the order of operations.

If x^2=9, which of the following could be the value of x?

3

6x + 3 is equivalent to...

3(2x + 1)

Which of the following equations matches the description above? Choose 1 answer

3(x+1) = 6

If 5 times the square of a certain number is 80, which of the following could be that number? (Written as 5x² = 80)

4

If 3x+5y=9, what is the value of 15x+25y?

45

If 2x^2 = 50, which of the following could be the value of x?

5

The first term in a recursive sequence is 1. Each subsequent term in the sequence is calculated by multiplying the previous term by 3 and subtracting 1 from the result. Which of the following are terms in the sequence?

5

If the product of a certain number and 4 is 64, which of the following equations, when solved, would give us the value of the number?

64

49x - 35 is equivalent to...

7(7x- 5)

Venn Diagram

A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.

Which of the following sequence of steps, when completed, will solve the equation 6x-7=8? Solve for x

Add 7 to both sides of the equation, then divide both sides by 6

What are quadratic equations?

An equation with at least one variable to the second power as its highest power term and one or more constants.

What is an inverse operation?

For numbers ≥ 0, squaring and taking the square root. (Result would be the original number)

What is a square of a number?

It is a number equal to the number multiplied by itself.

Verbal procedures and flowcharts

Lets us trace our steps from the end of a procedure to the beginning

Solution Procedures

Sequence of steps that, when taken, solves an equation

Flowchart

Visual representation of a sequence of operations

The sum of a and b

a+b

Algebraic word problems

are questions that require translating sentences to equations, then solving those equations.

The equations we need to write will only involve

basic arithmetic operations and a single variable.

distributive law

deals with the combination of addition and multiplication. When a sum is multiplied by value, the value is distributed to each part of the sum

What are formula?

equations that contain 2 or more variables

What are equivalent expressions?

expressions that work the same even though they look different

Algebraic expressions and equations

follow the same set of rules as numerical expressions and equations.

associative law

tells us that in addition or multiplication, we can associate the terms or factors as we please

commutative law

tells us we can reorder the terms when performing addition or multiplication

Instead of having a definitive value for an expression,

we need to evaluate an algebraic expressions for specific values of the variables, observe how the value of the expression changes as the values of the variables change, and determine statements that are true for all values of the variables.

Which of the following statements are true for all real numbers

x(y-z)=xy-xz