GED Mathematical reasoning 3

Question 1

Which of the following is a solution to the system of equations?
x + y = 7
2x − y = 2

Accepted Answer

(3, 4)

Answer

For (3, 4): 3 + 4 = 7 ✓ and 2(3) − 4 = 6 − 4 = 2 ✓. Only (3, 4) satisfies both equations.

Question 2

Factor the expression: x² − 9

Accepted Answer

(x + 3)(x − 3)

Answer

x² − 9 is a difference of squares: a² − b² = (a + b)(a − b). Here a = x and b = 3, giving (x + 3)(x − 3).

Question 3

The graph of which equation is a parabola opening downward?

Accepted Answer

y = −3x² + 2x − 1

Answer

A parabola opens downward when the coefficient of x² is negative. In y = −3x² + 2x − 1, the coefficient is −3 < 0.

Question 4

What is the slope of the line passing through the points (−2, 3) and (4, −1)?

Accepted Answer

−2/3

Answer

Slope = (y₂ − y₁)/(x₂ − x₁) = (−1 − 3)/(4 − (−2)) = −4/6 = −2/3.

Question 5

Solve for x: (x/3) + 2 = 5

Accepted Answer

x = 9

Answer

Subtract 2: x/3 = 3. Multiply by 3: x = 9.

GED Practice Test