Q1. Evaluate the expression for , .

Background

Topic: Evaluating Algebraic Expressions

This question tests your ability to substitute given values into an algebraic expression and simplify.

Key Terms and Formulas

• Substitution: Replacing variables with their given values.

• Simplification: Performing arithmetic operations to reduce the expression.

Step-by-Step Guidance

1. Substitute and into the expression:

2. Calculate the numerator and denominator separately:

   Numerator: ,

   Denominator:

3. Subtract in the numerator:

Try solving on your own before revealing the answer!

Q2. Use an associative property to complete the statement:

Background

Topic: Properties of Addition

This question tests your understanding of the associative property, which allows grouping of terms in addition.

Key Terms and Formulas

• Associative Property:

Step-by-Step Guidance

1. Identify the original grouping:

2. Apply the associative property by regrouping:

Try solving on your own before revealing the answer!

Q3. Use a commutative property to complete the statement:

Background

Topic: Properties of Addition

This question tests your understanding of the commutative property, which allows changing the order of terms in addition.

Key Terms and Formulas

• Commutative Property:

Step-by-Step Guidance

1. Identify the original expression:

2. Apply the commutative property:

Try solving on your own before revealing the answer!

Q4. Solve the equation:

Background

Topic: Solving Linear Equations

This question tests your ability to combine like terms and solve for in a linear equation.

Key Terms and Formulas

• Linear Equation: An equation of the form

• Combine like terms: Add or subtract terms with the same variable.

Step-by-Step Guidance

1. Combine like terms for and constants:

2. Rewrite the equation:

3. Subtract 9 from both sides:

Try solving on your own before revealing the answer!

Q5. Solve the equation:

Background

Topic: Solving Linear Equations

This question tests your ability to simplify expressions and solve for .

Key Terms and Formulas

• Distributive Property:

• Combine like terms: Add or subtract terms with the same variable.

Step-by-Step Guidance

1. Expand the expression: becomes

2. Combine like terms: ,

3. Set the simplified expression equal to :

Try solving on your own before revealing the answer!

Q6. Solve the equation:

Background

Topic: Solving Linear Equations with Fractions

This question tests your ability to solve for when it is multiplied by a fraction.

Key Terms and Formulas

• Multiplicative Inverse: To solve , divide both sides by .

Step-by-Step Guidance

1. Multiply both sides by to eliminate the fraction:

2. Simplify:

Try solving on your own before revealing the answer!

Q7. Solve the equation:

Background

Topic: Solving Linear Equations with Fractions

This question tests your ability to clear fractions and solve for .

Key Terms and Formulas

• Clear fractions by multiplying both sides by the denominator.

• Combine like terms and solve for the variable.

Step-by-Step Guidance

1. Multiply both sides by 5 to clear the fraction:

2. Expand both sides:

3. Move all terms to one side and constants to the other:

Try solving on your own before revealing the answer!

Q8. Solve:

Background

Topic: Solving Linear Equations

This question tests your ability to expand and simplify both sides of an equation.

Key Terms and Formulas

• Distributive Property:

• Combine like terms.

Step-by-Step Guidance

1. Expand the left side:

2. Compare both sides:

3. Recognize that this equation is true for all values of .

Try solving on your own before revealing the answer!

Q9. Solve:

Background

Topic: Solving Linear Equations

This question tests your ability to isolate the variable.

Key Terms and Formulas

• Subtracting from both sides to isolate the variable.

Step-by-Step Guidance

1. Subtract 4 from both sides:

Try solving on your own before revealing the answer!

Q10. Ted drove 294 miles in 8 hours. How fast was Ted driving?

Background

Topic: Rate, Distance, and Time

This question tests your ability to use the formula for speed: .

Key Terms and Formulas

• Speed:

• Distance: 294 miles

• Time: 8 hours

Step-by-Step Guidance

1. Write the formula:

2. Plug in the values:

Try solving on your own before revealing the answer!

Q11. The sum of three consecutive integers is 570. Find the numbers.

Background

Topic: Solving Word Problems with Consecutive Integers

This question tests your ability to set up and solve equations involving consecutive numbers.

Key Terms and Formulas

• Let the first integer be , then the next two are and .

• Sum:

Step-by-Step Guidance

1. Set up the equation:

2. Combine like terms:

3. Subtract 3 from both sides:

Try solving on your own before revealing the answer!

Q12. The manager mixes 70 pounds of cashews () with peanuts () to get a mixture selling for . How many pounds of peanuts should be used?

Background

Topic: Mixture Word Problems

This question tests your ability to set up and solve a mixture equation.

Key Terms and Formulas

• Let = pounds of peanuts.

• Total pounds:

• Value equation:

Step-by-Step Guidance

1. Set up the equation:

2. Expand:

3. Move all terms to one side and constants to the other:

Try solving on your own before revealing the answer!

Q13. Evaluate:

Background

Topic: Order of Operations and Exponents

This question tests your understanding of how to evaluate negative numbers raised to a power.

Key Terms and Formulas

• Exponent: means multiplied by itself times.

• Order of operations: Exponents before multiplication by negative sign.

Step-by-Step Guidance

1. Evaluate first:

2. Apply the negative sign:

Try solving on your own before revealing the answer!

Q14. Simplify:

Background

Topic: Order of Operations

This question tests your ability to follow the correct order of operations (PEMDAS).

Key Terms and Formulas

• PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction

Step-by-Step Guidance

1. Evaluate innermost parentheses:

   So

2. Evaluate , then

3. Now substitute:

Try solving on your own before revealing the answer!

Q15. Remove parentheses and simplify:

Background

Topic: Simplifying Expressions

This question tests your ability to distribute and combine like terms.

Key Terms and Formulas

• Distributive Property:

• Combine like terms.

Step-by-Step Guidance

1. Distribute to each term inside the parentheses:

2. Rewrite the expression:

3. Combine like terms: , ,

Try solving on your own before revealing the answer!

Q16. Subtract:

Background

Topic: Basic Arithmetic

This question tests your ability to subtract numbers.

Key Terms and Formulas

• Subtraction:

Step-by-Step Guidance

1. Subtract 11 from 10:

Try solving on your own before revealing the answer!

Q17. Solve for :

Background

Topic: Solving Formulas for a Variable

This question tests your ability to rearrange a formula to solve for a specific variable.

Key Terms and Formulas

• Isolate in the formula.

Step-by-Step Guidance

1. Subtract 32 from both sides:

2. Multiply both sides by to isolate :

Try solving on your own before revealing the answer!

Q18. Add:

Background

Topic: Adding Integers

This question tests your ability to add a positive and a negative integer.

Key Terms and Formulas

• Addition of integers:

Step-by-Step Guidance

1. Rewrite as

Try solving on your own before revealing the answer!

Q19. Divide:

Background

Topic: Dividing Fractions

This question tests your ability to divide fractions and handle negative signs.

Key Terms and Formulas

• Division of fractions:

• Negative divided by negative is positive.

Step-by-Step Guidance

1. Rewrite division as multiplication by the reciprocal:

2. Multiply numerators and denominators:

Try solving on your own before revealing the answer!

Q20. Solve the inequality:

Background

Topic: Solving Linear Inequalities

This question tests your ability to solve inequalities and understand solution sets.

Key Terms and Formulas

• Distributive Property:

• Solving inequalities: Similar to equations, but pay attention to direction when multiplying/dividing by negatives.

Step-by-Step Guidance

1. Expand the right side:

2. Rewrite the inequality:

3. Move all terms to one side and constants to the other:

Try solving on your own before revealing the answer!