ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 10
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#1. Which value of x satisfies the equation: 3(2x – 1) – 4 = 2(x + 5)?
Expand both sides: 6x – 3 – 4 = 2x + 10 => 6x – 7 = 2x + 10. Subtract 2x: 4x – 7 = 10. Add 7: 4x = 17. Divide by 4: x = 17/4 = 4.25.
#2. What is the slope of the line that passes through the points (-2, 5) and (4, -7)?
Slope formula m = (y2 – y1) / (x2 – x1). Substitute points: m = (-7 – 5) / (4 – (-2)) = -12 / 6 = -2.
#3. A cylindrical tank has a diameter of 10 feet and a height of 12 feet. What is its volume in terms of π?
Radius r = diameter / 2 = 10 / 2 = 5 feet. Volume formula V = π * r² * h = π * 5² * 12 = π * 25 * 12 = 300π cubic feet.
#4. Solve the quadratic equation: x² – 6x – 16 = 0
Factor the quadratic expression: (x – 8)(x + 2) = 0. Setting each factor to zero gives x = 8 and x = -2.
#5. Find the simple interest earned on a principal of $2,400 at a rate of 5% per year for 3 years.
Simple interest formula I = P * r * t. Substitute P = 2400, r = 0.05, t = 3: I = 2400 * 0.05 * 3 = 120 * 3 = $360.
#6. What is the inequality solution for: 5 – 2x > 11?
Subtract 5 from both sides: -2x > 6. Divide both sides by -2 and flip the inequality sign: x < -3.
#7. A right triangle has a base of 9 cm and a hypotenuse of 15 cm. What is the length of the height?
By Pythagorean theorem, height h = sqrt(15² – 9²) = sqrt(225 – 81) = sqrt(144) = 12 cm.
#8. Convert a rate of 90 kilometers per hour into meters per second.
To convert km/h to m/s, divide by 3.6: 90 / 3.6 = 25 m/s.
#9. Which expression is equivalent to (3x²y³) * (4x³y⁴)?
Multiply numerical coefficients: 3 * 4 = 12. Add exponents for x: 2 + 3 = 5. Add exponents for y: 3 + 4 = 7. Result = 12x⁵y⁷.
#10. The mean score of 4 tests is 85. If a 5th test score of 95 is added, what is the new mean score?
Total sum of first 4 tests = 4 * 85 = 340. New total sum = 340 + 95 = 435. New mean = 435 / 5 = 87.
#11. If f(x) = 3x² – 2x + 4, find f(-2).
Substitute x = -2: f(-2) = 3(-2)² – 2(-2) + 4 = 3(4) + 4 + 4 = 12 + 8 = 20.
#12. A line has an equation y = 4x – 7. What is the y-intercept of a line parallel to it passing through (2, 5)?
Parallel lines have equal slope m = 4. Use point-slope form with (2, 5): y – 5 = 4(x – 2) => y = 4x – 8 + 5 => y = 4x – 3. The y-intercept is -3.
#13. A fair 6-sided die is rolled twice. What is the probability of rolling a 5 on the first roll and an even number on the second roll?
P(rolling 5) = 1/6. P(rolling even) = 3/6 = 1/2. Combined probability = (1/6) * (1/2) = 1/12.
#14. Simplify the algebraic expression: (x² – 16) / (x – 4)
Factor the numerator as a difference of squares: (x – 4)(x + 4). Cancel (x – 4) with denominator: result = x + 4.
#15. A circular rug has a circumference of 16π feet. What is the area of the rug in terms of π?
Circumference C = 2 * π * r = 16π => r = 8 feet. Area A = π * r² = π * 8² = 64π sq ft.
#16. Solve for x in the proportion: (x + 2) / 5 = (2x – 1) / 3
Cross-multiply: 3(x + 2) = 5(2x – 1) => 3x + 6 = 10x – 5. Subtract 3x: 6 = 7x – 5. Add 5: 11 = 7x => x = 11/7.
#17. What is the domain of the function f(x) = sqrt(2x – 8)?
The term under a square root must be non-negative: 2x – 8 >= 0 => 2x >= 8 => x >= 4.
#18. A coat is originally $150 and is on sale for $105. What is the percent discount?
Discount amount = 150 – 105 = $45. Percent discount = (45 / 150) * 100 = 0.30 * 100 = 30%.
#19. Find the total volume of a cube with a surface area of 150 square meters.
Surface area of cube = 6 * s² = 150 => s² = 25 => s = 5 meters. Volume = s³ = 5³ = 125 cubic meters.
#20. Evaluate: 2 * 3³ – (4 + 2) * 5
Exponent: 3³ = 27. Multiplication: 2 * 27 = 54. Parentheses: 4 + 2 = 6. Multiplication: 6 * 5 = 30. Subtraction: 54 – 30 = 24.