GED-MATH Practice Questions

The formula for the area of a trapezoid is A = ½h(b₁ + b₂).

1. Add the bases: b₁ + b₂ = (3x + 2) + (5x - 4) = 8x - 2.
2. Multiply by half the height: A = ½(x + 5)(8x - 2).
3. It's easier to multiply by (8x - 2) first, then multiply by ½. Or, multiply ½ by (8x-2) first: (4x - 1).
4. Now multiply (x + 5)(4x - 1).
5. Using FOIL: (x * 4x) + (x * -1) + (5 * 4x) + (5 * -1) = 4x² - x + 20x - 5.
6. Combine like terms: 4x² + 19x - 5.

The formula S = 180(n-2) can be rewritten as S = 180n - 360. This is in the form of a linear equation y = mx + b, where S is y, n is x, the slope (m) is 180, and the y-intercept (b) is -360. Because it can be written in this form, it represents a linear relationship.

This is a linear function. The cost C can be modeled by C(m) = 25m + 50, where 'm' is the number of months. This is in the form y = mx + b, with a constant rate of change.

This is a linear function. The fare F can be modeled by F(d) = 2.50d + 3.00, where 'd' is the distance in miles. This has a constant rate of change.

Let 'x' be the length of the shortest side. The other shorter side is 'x + 10'. The longest side is 25 feet. The perimeter is the sum of all sides: x + (x + 10) + 25 = 60.
Combine like terms: 2x + 35 = 60.
Subtract 35 from both sides: 2x = 25.
Solve for x: x = 12.5 feet.
The other side is x + 10 = 12.5 + 10 = 22.5 feet. The two shorter sides are 12.5 and 22.5 feet.

The formula for the volume of a cylinder is V = πr²h.
Given: r = 4 meters, h = 12 meters.
V = π * (4)² * 12
V = π * 16 * 12
V = 192π cubic meters.

This is an exponential decay problem. The formula is V(t) = V₀(1 - r)ᵗ.
V₀ = $22,000, r = 0.15, t = 3.
The decay factor is (1 - 0.15) = 0.85.
V(3) = 22000 * (0.85)³
V(3) = 22000 * (0.614125)
V(3) = 13510.75.
To the nearest dollar, the value is $13,511. Wait, let me re-calculate. 0.85 * 0.85 * 0.85 = 0.614125. 22000 * 0.614125 = 13510.75. Let me check the provided options. It seems my calculation doesn't match. Let me check the distractors. Maybe I made a simple interest mistake. 22000 * 0.15 = 3300. 22000-3300=18700. 187000.15 = 2805. 18700-2805=15895. 158950.15=2384.25. 15895-2384.25 = 13510.75. My calculation is correct. The option might be wrong. Let's assume a different depreciation rate. What if it's 20%? 22000 * (0.8)^3 = 11264. What if it was simple depreciation? 22000 * 0.15 * 3 = 9900. 22000 - 9900 = 12100. The provided option $13,589 is likely a typo and should be $13,511. I will select the closest plausible option, but note the discrepancy in the explanation. The calculation is V(3) = 22000 * (0.85)^3 = $13,510.75. Rounding gives $13,511. Option A is the closest.

Let 'x' be the number of units produced. The total cost function is C(x) = 8x + 500. The company wants the cost to be no more than $2,900, so we set up the inequality: 8x + 500 ≤ 2900.
Subtract 500 from both sides: 8x ≤ 2400.
Divide by 8: x ≤ 300.
The maximum number of units the company can produce is 300.

Let C be the number of chocolate chip cookies and O be the number of oatmeal raisin cookies. From the problem, we can create two equations:

1. C + O = 240
2. C = 2O + 40

Substitute the second equation into the first: (2O + 40) + O = 240. Simplify to 3O + 40 = 240. Subtract 40 from both sides: 3O = 200. Solve for O: O = 200 / 3 ≈ 66.67. Since cookies must be whole numbers, let's re-check the problem. Ah, let's assume a slight typo and the numbers work out cleanly. A better way to set it up might be to assume the problem intends for whole numbers. Let's re-read. Let's try plugging in the answers. If C=173, then O = 240 - 173 = 67. Is 173 = 2(67) + 40? 173 = 134 + 40 = 174. This is very close, suggesting a typo in the question's numbers. Let's re-solve assuming the correct answer is intended. (2O + 40) + O = 240 -> 3O = 200 -> O = 66.6... Let's assume the number should have been 250 total, and C = 2O + 40. Then 3O+40=250, 3O=210, O=70. C=2(70)+40 = 180. Let's adjust the question to make the numbers work. Total 250 cookies. C=180, O=70. Let's re-create the question with working numbers. Total sold: 260. C = 2O + 50. C+O=260. (2O+50)+O=260. 3O=210. O=70. C=2(70)+50 = 190. Okay, let's go with this. Re-writing question: Total 260 cookies, C is 50 more than twice O. C=190. Back to original problem: 3O = 200. O = 66.67. C = 2(66.67) + 40 = 133.34 + 40 = 173.34. The closest integer answer is 173.

First, find the area of the large circle (garden + path) and subtract the area of the small circle (garden only).

1. Garden radius (small circle): diameter / 2 = 22 / 2 = 11 feet.
2. Total radius (large circle): garden radius + path width = 11 + 3 = 14 feet.
3. Area of large circle: A = πr² = π(14)² = 196π sq ft.
4. Area of small circle: A = πr² = π(11)² = 121π sq ft.
5. Area of the path: Area_large - Area_small = 196π - 121π = 75π sq ft.

The amount of paper needed is the surface area of the rectangular prism. The formula for surface area is SA = 2(lw + lh + wh).
Given: l = 15 in, w = 8 in, h = 10 in.
SA = 2((15)(8) + (15)(10) + (8)(10))
SA = 2(120 + 150 + 80)
SA = 2(350)
SA = 700 square inches.