FREE NYSTCE Mathematics 004 Questions and Answers

Question 1

The likelihood of receiving the head from an unfair coin is 0.3. What is the probability of not getting a head after tossing the coin three times?

Accepted Answer

0.343

Answer

The probability of not getting a head in a single toss is 1 minus the probability of getting a head, which is 1 - 0.3 = 0.7. Since each coin toss is an independent event, the probability of not getting a head after three consecutive tosses is found by multiplying the probability of not getting a head for each individual toss. Therefore, 0.7 * 0.7 * 0.7 equals 0.343.

Question 2

What is the result of adding 10 and 7?

Accepted Answer

120

Answer

The question asks for the result of adding 10 and 7, which mathematically equals 17. However, the provided correct answer is 120. This discrepancy suggests that the question might be incomplete, misphrased, or intended to involve a different mathematical operation, such as multiplication (e.g., 10 multiplied by 12) or a more complex calculation not explicitly stated, to arrive at 120.

Question 3

Use the graph to answer the subsequent question. How large is the vector shown above?

Accepted Answer

5

Answer

The magnitude of a vector represents its length and is calculated using the Pythagorean theorem. If a vector on a graph extends from the origin to a point (x, y), its magnitude is √(x² + y²). For instance, if the vector's components are (3, 4), its magnitude would be √(3² + 4²) = √(9 + 16) = √25 = 5.

Question 4

This pyramid is square-based. How much volume is 13cm high?

Accepted Answer

277.33 cm³

Answer

The volume of a pyramid is calculated using the formula V = (1/3) * Base Area * Height. For a square-based pyramid, the base area is the side length squared (s²). If we assume a base side length of 8 cm, the base area is 8² = 64 cm². Multiplying this by the given height of 13 cm and then by 1/3 yields V = (1/3) * 64 cm² * 13 cm = 277.33 cm³.

Question 5

Kevin's bank account contains a $5,000 deposit. He consistently withdraws $200 per month from this account throughout the year.
What linear equation describes the relationship between Kevin's remaining account balance y and the number of months x that have passed?

Accepted Answer

y=-200x+5000

Answer

A linear equation describing this relationship takes the form y = mx + b, where 'y' is the remaining account balance, 'x' is the number of months, 'm' is the rate of change (slope), and 'b' is the initial amount (y-intercept). Kevin starts with $5,000, so b = 5000. He withdraws $200 each month, meaning the balance decreases by $200 per month, making the slope m = -200. Therefore, the equation is y = -200x + 5000.

NYSTCE ATAS - NYSTCE Assessment of Teaching Assistant Skills Practice Test

NYSTCE ATAS - NYSTCE Assessment of Teaching Assistant Skills Practice Test

FREE NYSTCE Mathematics 004 Questions and Answers