SAT Practice Test 5 Math Module 2 Question 20: Unraveling the Mystery

Are you preparing for the SAT Math Module 2 test? If so, then buckle up and get ready to tackle Question 20, a perplexing problem that has left many students scratching their heads. In this comprehensive guide, we’ll break down the question, explore the common pitfalls to avoid, and equip you with a step-by-step approach to solve it confidently.

The Enigmatic Question 20

Question 20 presents you with a complex scenario involving the construction of a rectangular prism. The question asks you to determine the volume of the prism if its length, width, and height are represented by algebraic expressions.

A rectangular prism has a length of (x + 2) units, a width of (x - 3) units, and a height of (2x - 1) units. What is the volume of the prism?

Common Mistakes to Avoid

1. Miscalculating the Dimensions: Ensure that you correctly substitute the given expressions for length, width, and height when calculating the volume.

   

2. Forgetting the Units: Remember to include the appropriate units (units cubed) when expressing the final answer.

3. Not Expanding the Expressions: Fully expand all algebraic expressions before multiplying them to determine the volume.

   

Benefits of Mastering Question 20

1. SAT Score Success: Solving Question 20 correctly can significantly boost your SAT Math score.

2. Geometry Mastery: This question reinforces your understanding of basic geometry concepts, such as the volume of a rectangular prism.

3. Algebraic Proficiency: It tests your ability to manipulate algebraic expressions and apply them in practical scenarios.

   

Unlocking the Solution

1. Substitute the Dimensions: Replace the length, width, and height with their given expressions:

Length = (x + 2) units
Width = (x - 3) units
Height = (2x - 1) units

2. Calculate the Volume: Multiply the length, width, and height together to find the volume:

Volume = (x + 2) * (x - 3) * (2x - 1)

3. Expand the Expressions: Distribute the terms to simplify the expression:

Volume = (x^2 - x - 6) * (2x - 1)

4. Multiply the Binomials: Use FOIL (First, Outer, Inner, Last) to multiply the binomials:

Volume = 2x^3 - x^2 - 12x + 6

5. Simplify the Result: Combine like terms and express the answer in the correct units:

Volume = 2x^3 - 13x + 6 units cubed

Example Solution

Consider the following example:

If x = 3, then the length is (3 + 2) = 5 units, the width is (3 - 3) = 0 units, and the height is (2 * 3 - 1) = 5 units. Therefore, the volume is (5 * 0 * 5) = 0 units cubed.

Conclusion

Conquering SAT Practice Test 5 Math Module 2 Question 20 requires careful analysis and a systematic approach. By understanding the common pitfalls, applying the step-by-step solution, and practicing with various examples, you can confidently tackle this challenging question and enhance your SAT Math score. Remember, practice makes perfect, so don’t hesitate to revisit this guide and test your skills until you feel confident and ready to ace the exam.