IMAT Mathematics and Statistics 3

Question 1

How many ways can 5 different books be arranged on a shelf?

Accepted Answer

120

Answer

The number of permutations of 5 distinct objects is 5! = 120.

Question 2

The mean of 5 numbers is 12. If four of them are 10, 14, 8, and 16, what is the fifth number?

Accepted Answer

12

Answer

Total sum = 5×12 = 60; the known four sum to 48, so the fifth = 60−48 = 12.

Question 3

What is cos(60°)?

Accepted Answer

1/2

Answer

cos(60°) = 1/2 is a standard trigonometric value from the 30-60-90 triangle.

Question 4

What is ∫2x dx?

Accepted Answer

x² + C

Answer

Applying the power rule for integration: ∫2x dx = 2 · x²/2 + C = x² + C.

Question 5

Solve for x: |2x − 3| = 7

Accepted Answer

x = 5 or x = −2

Answer

Case 1: 2x−3 = 7 → x = 5; Case 2: 2x−3 = −7 → x = −2.

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