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

To find the linear equation y = mx + b, first find the slope (m), which is the monthly fee. Using two points from the table, (2, 130) and (4, 210), the slope m = (210 - 130) / (4 - 2) = 80 / 2 = $40 per month. Now, substitute the slope and one of the points into the slope-intercept form to find the y-intercept (b), which is the registration fee. Using (2, 130): 130 = 40(2) + b. 130 = 80 + b. b = 50. Therefore, the equation is y = 40x + 50.

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

The area of a rectangle is calculated by multiplying its length by its width. In this scenario, the area is (x + 7)(x - 2). To set up the equation, expand the binomials: (x + 7)(x - 2) = x(x) + x(-2) + 7(x) + 7(-2) = x² - 2x + 7x - 14 = x² + 5x - 14. Since the area is given as 50 square feet, the resulting equation is x² + 5x - 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

Angle 2 and angle 6 are corresponding angles, so they are congruent; m∠6 = 115°. Angle 6 and angle 7 are supplementary angles because they form a linear pair. Therefore, their sum is 180°. To find the measure of angle 7, subtract the measure of angle 6 from 180°: 180° - 115° = 65°. Alternatively, Angle 2 and Angle 3 are supplementary (180 - 115 = 65). Angle 3 and Angle 7 are alternate interior angles, so they are congruent. Thus, m∠7 = 65°.

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

This problem requires the use of the Pythagorean theorem, a² + b² = c², where 'a' and 'b' are the legs of the right triangle and 'c' is the hypotenuse. Substitute the given values: 8² + 15² = c². Calculate the squares: 64 + 225 = c². Add the results: 289 = c². Finally, find the square root of 289 to solve for c: c = √289 = 17. The length of the path is 17 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

To solve the quadratic equation, we need to factor the trinomial x² - 3x - 10. We are looking for two numbers that multiply to -10 and add up to -3. These numbers are +2 and -5. Therefore, the factored form is (x + 2)(x - 5) = 0. According to the zero-product property, we set each factor equal to zero to find the solutions. So, x + 2 = 0 gives x = -2, and x - 5 = 0 gives x = 5.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

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