ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 9
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#1. Which of the following points is the solution to the system of equations: y = 2x + 1 and x + y = 7?
Substitute y = 2x + 1 into x + y = 7: x + (2x + 1) = 7 => 3x + 1 = 7 => 3x = 6 => x = 2. Then y = 2(2) + 1 = 5. So the solution point is (2, 5).
#2. A sphere has a radius of 6 cm. What is its total surface area in terms of π?
The formula for the surface area of a sphere is SA = 4 * π * r². Substituting r = 6 gives SA = 4 * π * 6² = 4 * π * 36 = 144π cm².
#3. Solve for x: 2(x – 4) + 3x = 3(x + 2)
Expand both sides: 2x – 8 + 3x = 3x + 6 => 5x – 8 = 3x + 6. Subtract 3x from both sides: 2x – 8 = 6. Add 8 to both sides: 2x = 14 => x = 7.
#4. What is the median of the following set of numbers: 15, 9, 23, 11, 18, 31, 14?
First, arrange the numbers in ascending order: 9, 11, 14, 15, 18, 23, 31. The median is the middle value, which is the 4th value: 15.
#5. Find the slope of a line that is perpendicular to the line y = -2/5 x + 4.
Perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is -2/5, so the perpendicular slope is -1 / (-2/5) = 5/2.
#6. If the area of a square is 169 square inches, what is the perimeter of the square?
The side length of the square is s = sqrt(169) = 13 inches. The perimeter is 4 * s = 4 * 13 = 52 inches.
#7. An item originally priced at $120 is marked down by 25%. What is the new price of the item?
Discount amount = 120 * 0.25 = $30. New price = $120 – $30 = $90.
#8. Evaluate: 4³ – 3 * (5 + 2²)
Evaluate inside parentheses first: 2² = 4, so (5 + 4) = 9. Evaluate exponent: 4³ = 64. Perform multiplication: 3 * 9 = 27. Finally, subtract: 64 – 27 = 37.
#9. What is the vertex of the parabola given by y = (x – 3)² + 5?
The vertex form of a parabola is y = a(x – h)² + k, where (h, k) is the vertex. Here h = 3 and k = 5, so the vertex is (3, 5).
#10. A car consumes 8 gallons of gasoline to travel 240 miles. How many gallons will it need to travel 360 miles at the same rate?
Fuel efficiency = 240 / 8 = 30 miles per gallon. For 360 miles, gallons needed = 360 / 30 = 12 gallons.
#11. Factor completely: 3x² – 12
Factor out the GCF of 3 first: 3(x² – 4). Then factor the difference of squares (x² – 4) = (x – 2)(x + 2). Complete factored form: 3(x – 2)(x + 2).
#12. What is the mid-point of the segment connecting points (-4, 2) and (6, 10)?
The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2). Substitute (-4, 2) and (6, 10): ((-4 + 6)/2, (2 + 10)/2) = (2/2, 12/2) = (1, 6).
#13. If a right cylinder has a base area of 25π cm² and a volume of 200π cm³, what is its height?
Volume of a cylinder = Base Area * height => 200π = 25π * h. Divide both sides by 25π: h = 200π / 25π = 8 cm.
#14. Simplify the exponential expression: (2x³y²)³
Apply the power of a product rule: (2)³ * (x³)³ * (y²)³ = 8 * x^(3*3) * y^(2*3) = 8x⁹y⁶.
#15. A box contains 5 red balls, 3 white balls, and 2 green balls. What is the probability of picking a white ball, replacing it, and then picking a red ball?
Total balls = 10. Probability of white ball = 3/10. Since it’s replaced, probability of red ball on 2nd draw = 5/10 = 1/2. Total probability = (3/10) * (1/2) = 3/20.
#16. Find the value of x if log₂(x) = 5.
Convert logarithmic form to exponential form: x = 2⁵ = 32.
#17. What is the range of the following function data set: {(-2, 4), (0, 1), (2, 5), (4, 9)}?
The range of a function is the set of all y-values (outputs). Collecting y-values from each pair gives {4, 1, 5, 9}, which ordered is {1, 4, 5, 9}.
#18. If a loan of $1,500 accumulates $180 simple interest at an annual rate of 4%, how many years was the loan for?
Simple interest formula I = P * r * t => 180 = 1500 * 0.04 * t => 180 = 60 * t => t = 180 / 60 = 3 years.
#19. What is the circumference of a circle whose radius is equal to the hypotenuse of a right triangle with legs 3 cm and 4 cm?
Hypotenuse = sqrt(3² + 4²) = sqrt(9 + 16) = sqrt(25) = 5 cm. Radius r = 5 cm. Circumference C = 2 * π * r = 2 * π * 5 = 10π cm.
#20. Solve the inequality: -2x + 6 <= 14
Subtract 6 from both sides: -2x = -4.