ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 11
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#1. Solve for x: 4(x – 3) = 2(x + 5)
Expand both sides: 4x – 12 = 2x + 10. Subtract 2x from both sides: 2x – 12 = 10. Add 12 to both sides: 2x = 22. Divide by 2: x = 11.
#2. What is the slope of the line passing through points (2, 3) and (8, 15)?
Slope formula m = (y2 – y1) / (x2 – x1). Substitute points: m = (15 – 3) / (8 – 2) = 12 / 6 = 2.
#3. Find the area of a circle with a radius of 7 cm (Use π ≈ 22/7).
Area formula A = π * r². Substitute r = 7 and π = 22/7: A = (22/7) * 7² = (22/7) * 49 = 22 * 7 = 154 cm².
#4. Factor completely: x² – 8x + 15
Find two numbers that multiply to 15 and add to -8. The numbers are -3 and -5. Factored form: (x – 3)(x – 5).
#5. A recipe calls for 3 cups of flour to make 24 cookies. How many cups of flour are needed to make 60 cookies?
Set up a proportion: 3 / 24 = x / 60. Simplify 3/24 to 1/8. So 1/8 = x / 60 => x = 60 / 8 = 7.5 cups.
#6. Which inequality represents the statement: ‘Five less than twice a number x is at least 13’?
‘Twice a number x’ is 2x. ‘Five less than twice a number x’ is 2x – 5. ‘At least 13’ means greater than or equal to 13 (>= 13). So 2x – 5 >= 13.
#7. What is the hypotenuse of a right-angled triangle with leg lengths 6 cm and 8 cm?
Pythagorean theorem c = sqrt(a² + b²) = sqrt(6² + 8²) = sqrt(36 + 64) = sqrt(100) = 10 cm.
#8. Calculate the simple interest on $3,000 at 6% per annum for 4 years.
Simple interest formula I = P * r * t. Substitute P = 3000, r = 0.06, t = 4: I = 3000 * 0.06 * 4 = 180 * 4 = $720.
#9. Simplify the algebraic expression: 5x³ * 2x⁴
Multiply numerical coefficients: 5 * 2 = 10. Add exponents for x: 3 + 4 = 7. Result = 10x⁷.
#10. Find the median of the following dataset: 12, 5, 22, 17, 9, 30
Arrange dataset in ascending order: 5, 9, 12, 17, 22, 30. The middle two values are 12 and 17. Median = (12 + 17) / 2 = 29 / 2 = 14.5.
#11. Evaluate f(3) for the function f(x) = -x² + 4x – 2.
Substitute x = 3: f(3) = -(3)² + 4(3) – 2 = -9 + 12 – 2 = 1.
#12. What is the equation of a line with slope -3 passing through (0, 7)?
Slope-intercept form y = mx + b. Given slope m = -3 and y-intercept (0, 7) so b = 7. Equation: y = -3x + 7.
#13. A bag has 3 black, 5 red, and 2 green marbles. What is the probability of picking a red marble?
Total marbles = 3 + 5 + 2 = 10. Number of red marbles = 5. Probability = 5 / 10 = 1/2.
#14. Solve the linear system for x: y = 3x – 2 and 2x + y = 13
Substitute y = 3x – 2 into 2x + y = 13: 2x + (3x – 2) = 13 => 5x – 2 = 13 => 5x = 15 => x = 3.
#15. What is the volume of a rectangular box with length 10 cm, width 4 cm, and height 5 cm?
Volume formula V = length * width * height = 10 * 4 * 5 = 200 cm³.
#16. Simplify: (25x² – 9) / (5x + 3)
Factor numerator as difference of squares: 25x² – 9 = (5x – 3)(5x + 3). Divide by (5x + 3): result = 5x – 3.
#17. A TV originally costing $500 is sold at a 20% discount. What is the final price?
Discount = 500 * 0.20 = $100. Final price = $500 – $100 = $400.
#18. What is the surface area of a cube with a side length of 4 inches?
Surface area formula SA = 6 * s². Substitute s = 4: SA = 6 * 4² = 6 * 16 = 96 sq in.
#19. Which of the following is equivalent to 3(x + 4) – 2(2x – 1)?
Expand: 3x + 12 – 4x + 2. Combine like terms: (3x – 4x) + (12 + 2) = -x + 14.
#20. Convert 72 kilometers per hour to meters per second.
To convert km/h to m/s, divide by 3.6: 72 / 3.6 = 20 m/s.