Tips for a Successful Algebra 1 Midterm Review

Midterm Review Overview

• Recap of topics covered during the midterm review.

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Problem 1: Equivalent Expressions

• Common Mistakes: Students often multiply only first and last terms incorrectly.

• Correct Method: Use the box method to group and multiply correctly.

  • Example: For the expression, break it into parts:

    • 3x, -8 (grouped with each other)

    • 4x, 2 (also grouped with each other)

• Final Expansion: Apply distribution:

  • Result: 12x² - 32x + 6x - 16

  • Combine like terms: -32x + 6x = -26x

• Final Answer: 12x² - 26x - 16 (Answer choice D).

• Key Point: Equivalent means having the same value; ensure correct grouping.

Problem 2: Solving Inequalities with Fractions

• Understanding Inequalities: Solutions are a range, not a single number.

• First Steps:

  • Subtract 13: -23x >= 14.

  • Multiply by 3 to eliminate fractions: -2x >= -42.

• Dividing by a Negative: When dividing by a negative, flip the inequality sign:

  • Result: x <= 21.

• Solution Set: Include all numbers less than or equal to 21.

  • Circle choices A, B, C (all less than or equal to 21).

• Key Tips: Remember to flip the inequality when dividing by a negative.

Problem 3: Properties of Exponents

• Given Expression: -4x^(-3)y^(5), asked to square it.

• Square the Constant: -4^2 = 16 (positive, not mistaken for negative values).

• Exponent Rules:

  • x^(-3) squared = x^(-6)

  • y^5 squared = y^(10)

• Narrowing Choices:

  • Possible answers now known to be positive 16.

• Final Answer Choice: D.

Problem 4: Rearranging Formulas

• Formula to Rearrange: V = 1/3 * B * H (solve for B).

• Steps to Isolate B:

  • Multiply both sides by 3: 3V = B * H.

  • Divide by H: B = 3V / H.

• Result: Answer choice C.

Problem 5: Properties of Equality

• Understanding Steps in the Equation: Identify properties used during the transition between steps.

• First Step: Typically given (provide the equation).

• Distributive Property: Use to explain how multiplication occurred in the equation.

• Next Steps: Identify that the subtraction property was used to isolate terms, finally applying the division property to solve for x.

Problem 6: Slope and Slope-Intercept Form

• Given Situation: Line with y-intercept 6 and slope -2/3.

• Recall Slope-Intercept Form: y = mx + b.

• Plugging in Values:

  • m = -2/3 and b = 6.

• Final Equation: y = -2/3x + 6.

Problem 7: Understanding Functions and Cost Models

• Cost Model Setup: $2 for shoes, $3 per game.

• Identifying Variables: Each additional game adds $3.

• Cost Function: C(games) = 2 + 3g (constant + variable for games).

• Rate of Change: The slope (cost per game), which is $3.

Problem 8: Simplifying Radicals

• Distributing Radicals: Break down radicals, such as 27 into 9 * 3 to simplify.

• Apply Difference of Squares: Recognize that when structured correctly, terms will cancel out during simplification.

• Final Calculation: Result after simplification yields a final simplified answer.

Problem 9: Fractional Exponents to Radical Form

• Understanding Fractional Exponents: The numerator indicates power, and the denominator indicates root.

• Standardizing: Radical representation of the expression.

• Choosing the Correct Answer: Recognize that if root is 2, it’s square root, and presentation matters in answers.

Conclusion

• Thank You Note: Thanks for participating in the review.

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