NJGPA - New Jersey Graduation Proficiency Assessment Algebra I and Geometry Concepts Questions and Answers

Question 1

A local gym charges a one-time registration fee and a monthly membership fee. The table below shows the total cost (y) for a certain number of months (x).

| Months (x) | Total Cost (y) |
|------------|----------------|
| 2          | $130           |
| 4          | $210           |
| 6          | $290           |

Which of the following linear equations models the total cost for x months of membership?

Accepted Answer

y = 40x + 50

Answer

y = 50x + 30

Answer

y = 80x - 30

Answer

y = 45x + 40

Question 2

A rectangular garden has a length of (x + 7) feet and a width of (x - 2) feet. If the area of the garden is 50 square feet, which equation can be used to find the value of x?

Accepted Answer

x² + 5x - 14 = 50

Answer

x² - 14x + 5 = 50

Answer

2x + 5 = 50

Answer

x² + 9x - 14 = 50

Question 3

In the figure below, line m is parallel to line n, and they are intersected by transversal line t. If the measure of angle 2 is 115°, what is the measure of angle 7?

Accepted Answer

65°

Answer

115°

Answer

75°

Answer

Cannot be determined

Question 4

A city park is shaped like a right triangle. The two legs of the triangle measure 8 miles and 15 miles. A new path is being built along the hypotenuse of the triangle. What is the length of the new path?

Accepted Answer

17 miles

Answer

23 miles

Answer

sqrt(161) miles

Answer

161 miles

Question 5

Which of the following are the solutions to the quadratic equation x² - 3x - 10 = 0?

Accepted Answer

x = 5 and x = -2

Answer

x = -5 and x = 2

Answer

x = 10 and x = -1

Answer

x = -10 and x = 1

Question 6

A homeowner is calculating the area of a room that has an L-shape. The composite shape can be divided into two rectangles. The first rectangle measures 10 feet by 12 feet. The second, smaller rectangle measures 6 feet by 7 feet. What is the total area of the room?

Accepted Answer

162 square feet

Answer

194 square feet

Answer

120 square feet

Answer

42 square feet