Mixed Deck — All MPT Topics Flashcards

Using the Law of Cosines, if a=5, b=7, and C=60°, what is c²?

Answer: 39

c² = 25 + 49 - 2(5)(7)cos(60°) = 74 - 70(0.5) = 74 - 35 = 39.

Which transformation maps y = x² to y = (x - 2)² + 3?

Answer: Shift right 2 and up 3

Replacing x with (x-2) shifts right 2; adding 3 outside shifts up 3.

What is 40% of 75?

Answer: 30

40% of 75 = 0.40 × 75 = 30.

Why is continuing education important in Problem Solving?

Answer: To stay current with evolving standards and practices

Continuing education keeps professionals updated with the latest developments, standards, and best practices in their field.

Why is it important to show your work when solving math problems outside of multiple-choice exams?

Answer: It allows partial credit and helps identify where errors occur

Documented work earns partial credit on open-response problems and pinpoints the source of mistakes.

A recipe calls for 2¼ cups of flour. If you want to make 1.5 times the recipe, how many cups of flour do you need?

Answer: 3⅜ cups

2¼ = 9/4; (9/4) × (3/2) = 27/8 = 3⅜ cups.

How does documentation support quality in Standards?

Answer: It creates records, ensures consistency, and enables improvement

Proper documentation creates accountability, ensures consistency, supports quality improvement, and provides legal protection.

Simplify: (x² - 9)/(x + 3)

Answer: x - 3

x² - 9 = (x-3)(x+3), and dividing by (x+3) leaves (x - 3).

When reviewing a completed math problem, which strategy best helps catch arithmetic errors?

Answer: Plug your answer back into the original equation

Substituting your answer back into the original equation verifies whether it satisfies the conditions.

What is 12 ÷ 3?

Answer: 4

Division is a basic arithmetic operation that involves splitting a number into equal parts. When you divide 12 by 3, you are determining how many groups of 3 can be made from 12. The result is 4, because 3 multiplied by 4 equals 12.

Which of the following numbers is divisible by both 3 and 4?

Answer: 36

36 ÷ 3 = 12 and 36 ÷ 4 = 9, so 36 is divisible by both 3 and 4.

What is the exact value of tan(135°)?

Answer: -1

tan(135°) = tan(180° - 45°) = -tan(45°) = -1.

Two angles of a triangle measure 45° and 75°. What is the measure of the third angle?

Answer: 60°

The sum of angles in a triangle is 180°, so the third angle = 180° − 45° − 75° = 60°.

Sales tax is 7.5%. What is the total cost of an item priced at $40?

Answer: $43.00

Tax = 7.5% × $40 = $3.00; total = $40 + $3 = $43.00.

What is the primary purpose of professional certification in Technical Foundations?

Answer: To validate competency and knowledge in the field

Certification validates that a professional has met established standards of knowledge and competency in Technical Foundations.

Which of the following is a factor of x² - 7x + 12?

Answer: (x - 3)

x² - 7x + 12 = (x - 3)(x - 4), so (x - 3) is a factor.

A best practice for estimating whether your answer to a word problem is reasonable is to:

Answer: Check that the magnitude and units of the answer match the context

Checking magnitude and units catches setup errors; for example, a negative length or impossibly large percentage signals a mistake.

Which of the following is equivalent to 16^(3/4)?

Answer: 8

16^(1/4)=2 (the fourth root of 16), then 2³=8.

Solve the inequality: −3x > 12

Answer: x < −4

Dividing by −3 reverses the inequality: x < −4.

Convert 0.375 to a fraction in lowest terms.

Answer: 3/8

0.375 = 375/1000 = 3/8 after dividing numerator and denominator by 125.