Free GED-MATH sample questions

Correct answer: 700 sq in

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.

Correct answers: 3x(2x + 7) - 5(2x + 7); 6x² + 11x - 35

The distributive property multiplies each term of 3x − 5 by the whole factor (2x + 7). That gives 3x(2x + 7) − 5(2x + 7). It is the same product one step before multiplying out, so it is equivalent.

Multiply each term of 3x − 5 by each term of 2x + 7: 6x², 21x, −10x and −35. Combine the like terms: 21x − 10x = 11x. The product is 6x² + 11x − 35, so the two expressions are equivalent.

Correct answer: False

To solve the inequality: 15 - 3x > 6. Subtract 15 from both sides: -3x > -9. Divide by -3 and reverse the inequality sign: x < 3. The solution set is all numbers less than 3, which does not include the number 3 itself.

Correct answer: 3 units

Profit is P(x) = −2x² + 70x − 150. It is negative until the first break-even point, about 2.3 units. P(2) = −18, a loss, and P(3) = 42, a profit. So 3 units is the fewest that make a profit.

Correct answer: (2, 0.5)

To find the location exactly halfway between two points, use the midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2). Given points: (-4, 5) and (8, -4). x-coordinate: (-4 + 8) / 2 = 4 / 2 = 2. y-coordinate: (5 + (-4)) / 2 = 1 / 2 = 0.5. The midpoint coordinates are (2, 0.5).

Correct answer: 120/(n + 2)

After 2 friends join, there are n + 2 people. Each share is the whole bill divided by the number of people, so it is 120/(n + 2). The expression 120/n + 2 divides by the old group size, then adds $2.

Correct answer: 3.5°C per minute

To find the rate of change, calculate the total change in temperature and divide by the total time. Total change = Final temperature - Initial temperature = 27°C - (-8°C) = 27 + 8 = 35°C. Time = 10 minutes. Rate of change = 35°C / 10 minutes = 3.5°C per minute.

Correct answer: 18

First, calculate the number of students for each category: Action: 32% of 150 = 0.32 * 150 = 48 students. Comedy: 20% of 150 = 0.20 * 150 = 30 students. Next, find the difference: 48 (Action) - 30 (Comedy) = 18 students. Alternatively, find the difference in percentage first: 32% - 20% = 12%. Then calculate 12% of 150: 0.12 * 150 = 18 students.

Correct answer: -2

The slope formula is m = (y₂ - y₁) / (x₂ - x₁). Let (x₁, y₁) = (3, -6) and (x₂, y₂) = (-1, 2). m = (2 - (-6)) / (-1 - 3) m = (2 + 6) / (-4) m = 8 / -4 m = -2

Correct answer: 5 feet

Let 'x' be the uniform width of the deck. The total length of the pool and deck is (50 + 2x), and the total width is (25 + 2x). The total area is length * width = 2100. (50 + 2x)(25 + 2x) = 2100 1250 + 100x + 50x + 4x² = 2100 4x² + 150x + 1250 = 2100 4x² + 150x - 850 = 0 Divide by 2: 2x² + 75x - 425 = 0 Using the quadratic formula or by testing the answers, let's test x=5: Total Length = 50 + 2(5) = 60 feet Total Width = 25 + 2(5) = 35 feet Total Area = 60 * 35 = 2100 square feet. This matches the given information, so the width is 5 feet.