ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 8
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#1. Simplify the algebraic expression: 4(2x – 3) – 2(x + 5)
Distribute the constants across the parentheses: 4(2x – 3) = 8x – 12 and -2(x + 5) = -2x – 10. Combine like terms: (8x – 2x) + (-12 – 10) = 6x – 22.
#2. Solve the linear equation for x: 5x – 7 = 3x + 11
Subtract 3x from both sides: 2x – 7 = 11. Add 7 to both sides: 2x = 18. Divide by 2: x = 9.
#3. What is the slope-intercept form of the line passing through (0, 4) with a slope of -3?
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Here m = -3 and the point (0, 4) gives the y-intercept b = 4. Thus, y = -3x + 4.
#4. Find the area of a trapezoid with parallel bases of lengths 8 cm and 12 cm, and a height of 5 cm.
The area formula for a trapezoid is Area = (1/2) * (base1 + base2) * height. Substitute the given values: Area = (1/2) * (8 + 12) * 5 = (1/2) * 20 * 5 = 10 * 5 = 50 cm².
#5. A store increases the price of an item from $80 to $100. What is the percent increase?
Amount of increase = $100 – $80 = $20. Percent increase = (Increase / Original Price) * 100 = (20 / 80) * 100 = 0.25 * 100 = 25%.
#6. What are the solutions to the quadratic equation x² – 9x + 20 = 0?
Factor the quadratic expression: x² – 9x + 20 = (x – 4)(x – 5) = 0. Set each factor to zero: x – 4 = 0 => x = 4, and x – 5 = 0 => x = 5.
#7. A cylinder has a radius of 3 inches and a height of 10 inches. What is its volume in terms of π?
The volume formula for a cylinder is V = π * r² * h. Substitute r = 3 and h = 10: V = π * 3² * 10 = π * 9 * 10 = 90π cubic inches.
#8. Evaluate the function f(x) = -2x² + 3x – 1 for x = -3.
Substitute x = -3 into f(x): f(-3) = -2(-3)² + 3(-3) – 1 = -2(9) – 9 – 1 = -18 – 9 – 1 = -28.
#9. Solve the inequality: 3x – 5 > 4x + 2
Subtract 3x from both sides: -5 > x + 2. Subtract 2 from both sides: -7 > x, which is equivalent to x < -7.
#10. If a map uses a scale where 1/2 inch represents 15 miles, how many miles are represented by 3.5 inches?
Set up a proportion: (0.5 inches / 15 miles) = (3.5 inches / x miles). Cross-multiply: 0.5x = 15 * 3.5 = 52.5. Divide by 0.5: x = 52.5 / 0.5 = 105 miles.
#11. Calculate the mean of the following data set: 12, 18, 22, 14, 34
The mean is the sum of all values divided by the count: Sum = 12 + 18 + 22 + 14 + 34 = 100. Count = 5. Mean = 100 / 5 = 20.
#12. What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?
Use the distance formula d = sqrt((x2 – x1)² + (y2 – y1)²): d = sqrt((4 – 1)² + (6 – 2)²) = sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25) = 5.
#13. A bag contains 4 red marbles, 6 blue marbles, and 5 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue?
Total marbles = 4 + 6 + 5 = 15. The number of marbles that are NOT blue = 4 (red) + 5 (green) = 9. Probability = 9 / 15 = 3/5.
#14. Convert 4.5 meters per second to kilometers per hour.
To convert m/s to km/h, multiply by 3.6: 4.5 * 3.6 = 16.2 km/h.
#15. A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the area of the triangle?
Find the other leg b using Pythagorean theorem: b = sqrt(13² – 5²) = sqrt(169 – 25) = sqrt(144) = 12 cm. Area = (1/2) * base * height = (1/2) * 5 * 12 = 30 cm².
#16. If a account grows from $500 to $560 in one year, what is the simple interest rate?
Interest earned I = $560 – $500 = $60. Simple interest formula I = P * r * t => 60 = 500 * r * 1. Solve for r: r = 60 / 500 = 0.12 = 12%.
#17. What is the value of 3⁴ – 2³ * 5?
Evaluate exponents first: 3⁴ = 81 and 2³ = 8. Next multiply: 8 * 5 = 40. Finally subtract: 81 – 40 = 41.
#18. In a sample of 250 items, 15 were found to be defective. What percentage of the sample is defective?
Percent defective = (Defective count / Total count) * 100 = (15 / 250) * 100 = 0.06 * 100 = 6%.
#19. A rectangular prism has dimensions 4 m by 5 m by 8 m. What is its total surface area?
Surface area formula = 2(lw + lh + wh) = 2(4*5 + 4*8 + 5*8) = 2(20 + 32 + 40) = 2(92) = 184 m².
#20. Which value of x makes the expression (x – 2) / (x + 7) undefined?
A rational expression is undefined when its denominator is equal to 0. Set x + 7 = 0 => x = -7.