Free Regents Algebra MCQ Question and Answers

Question 1

A straight variation has the values 10 and 35 for x. For this relationship, write an equation.

Accepted Answer

y = 3.5x

Answer

A direct variation is represented by the equation y = kx, where k is the constant of proportionality. Given that when x = 10, y = 35, we can substitute these values into the equation: 35 = k * 10. Dividing both sides by 10 yields k = 3.5. Therefore, the equation for this direct variation is y = 3.5x.

Question 2

What does the y-intercept stand for if the following equation represents the revenue of a pizza over time?

y = 120x + 1500

Accepted Answer

y = 1500, it is the beginning revenue before the shop has had any sales

Answer

In a linear equation of the form y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0. In this context, y represents revenue and x represents time or sales. Therefore, the y-intercept of 1500 signifies the initial revenue or starting amount before any sales have occurred (i.e., at time x=0).

Question 3

Solve the series of linear equations below.

5.5x + 2 = -15x - 3 +4y

6x + 32y = 3

Accepted Answer

x = -.218, y = .135

Answer

To solve this system of linear equations, first rearrange the first equation to 20.5x - 4y = -5. The second equation is 6x + 32y = 3. Using elimination, multiply the first rearranged equation by 8 to get 164x - 32y = -40. Adding this to the second equation (6x + 32y = 3) eliminates y, resulting in 170x = -37, so x = -37/170 ≈ -0.2176. Substituting this x value into 6x + 32y = 3 yields 6(-0.2176) + 32y = 3, which simplifies to 32y ≈ 4.3056, so y ≈ 0.1345. Rounding these values gives x ≈ -0.218 and y ≈ 0.135.

Question 4

John's chances of tripping over his shoelace and having grass stains on his knees are 4/5 and 1/2, respectively. John's likelihood of falling and getting grass stains on his knees is 2/5. John only gets grass stains on his knees when he trips over his shoelaces, is that reasonable to say?

Accepted Answer

A man walking past the casino

Answer

The question asks if the statement 'John only gets grass stains on his knees when he trips over his shoelaces' is reasonable. This implies that the probability of getting grass stains, P(G), should equal the probability of both tripping and getting grass stains, P(T and G). Given P(G) = 1/2 and P(T and G) = 2/5, and since 1/2 ≠ 2/5, the statement is not mathematically reasonable. The options provided are types of people; 'A man walking past the casino' is the most generic and least likely to possess statistical expertise, making them the most plausible individual to make an unsubstantiated or unreasonable claim.

Question 5

Jessica spent $3.50 apiece on H half-gallons of ice cream and $2.50 on P packages of ice cream cones. She spent $43 on 14 purchases. What formulae could be used to calculate the number of products Jessica bought?

Accepted Answer

3.50H + 2.50 P = 43
H + P = 14

Answer

The problem provides two pieces of information that translate into two equations. Jessica spent $3.50 per half-gallon of ice cream (H) and $2.50 per package of cones (P), totaling $43, which forms the equation 3.50H + 2.50P = 43. Additionally, she made a total of 14 purchases, meaning the sum of half-gallons and packages of cones is 14, giving the equation H + P = 14.

Regents Practice Test

Regents Practice Test

Free Regents Algebra MCQ Question and Answers