NYSTCE NYSTCE Mathematics (004) 4

Question 1

A student claims that √(a² + b²) = a + b for all positive values of a and b. Which counterexample best disproves this claim?

Accepted Answer

a = 3, b = 4: √(9+16) = 5 ≠ 7

Answer

With a=3, b=4, √(9+16)=5 but a+b=7, clearly disproving the equality.

Question 2

Which of the following best describes a function that is onto (surjective)?

Accepted Answer

Every element in the codomain has at least one preimage

Answer

A surjective function maps onto its entire codomain, meaning every output value is achieved by at least one input.

Question 3

A jar contains 5 red and 3 blue marbles. Two marbles are drawn without replacement. What is the probability both are red?

Accepted Answer

5/14

Answer

P(both red) = (5/8) × (4/7) = 20/56 = 5/14.

Question 4

Which transformation maps the graph of y = x² to the graph of y = (x − 3)² + 2?

Accepted Answer

Shift right 3 units and up 2 units

Answer

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

Question 5

A rectangle has a perimeter of 48 cm and an area of 128 cm². What are the dimensions?

Accepted Answer

8 cm × 16 cm

Answer

Solving 2(l+w)=48 and l×w=128 gives l=16 and w=8.

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