ข้อสอบGED MATHEMATICAL REASONING [Calculator] ชุดที่ 7
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#1. Evaluate the expression: 5 + 8×(-2) – (4 + 22×5) / 6
Order of operations (PEMDAS): First evaluate inside parentheses: 4 + 22×5 = 4 + 110 = 114. Next perform multiplication and division from left to right: 8×(-2) = -16 and 114 / 6 = 19. Finally, perform addition and subtraction: 5 + (-16) – 19 = 5 – 16 – 19 = -25.
#2. A shirt originally priced at $200 receives a 15% discount, and a month later it receives an additional 15% discount off the new price. Which expression represents the final sale price?
The first 15% discount means paying 100% – 15% = 85% of the original price, represented by multiplying by 0.85. The second 15% discount takes 85% of that discounted price, so you multiply by 0.85 again. The final price expression is (200)(0.85)(0.85).
#3. Which of the following ordered pairs lies on the line defined by 2x + 4y = 10?
Substitute * = -1 and y = 3 into the equation 2x + 4y = 10: 2(-1) + 4(3) = -2 + 12 = 10. Since the left side equals the right side, (-1, 3) is a valid point on the line.
#4. The ratio of boys to girls in a school is 2:3. If there are 600 students in total, how many boys are in the school?
Total ratio parts = 2 + 3 = 5 parts. Each part represents 600 / 5 = 120 students. Since boys represent 2 parts, the number of boys is 2×120 = 240.
#5. If 60% of A equals 20% of B, what percentage of A is B?
Set up the equation: 0.60×A = 0.20×B. Divide both sides by 0.20: B = (0.60 / 0.20) * A = 3×A. Since 3 expressed as a percentage is 300%, B is 300% of A.
#6. A right triangle has legs measuring 6 cm and 8 cm. What is the length of the hypotenuse?
Apply the Pythagorean theorem: a^2 + b^2 = c^2. Here 6^2 + 8^2 = 36 + 64 = 100. Taking the square root gives c = sqrt(100) = 10 cm.
#7. A ladder leans against a vertical wall, making a 60-degree angle with the ground. If the base of the ladder is 30 feet away from the wall, how long is the ladder?
Use trigonometry: cos(60°) = adjacent / hypotenuse = 30 / ladder length. Since cos(60°) = 0.5, we have 0.5 = 30 / ladder length, so ladder length = 30 / 0.5 = 60 feet.
#8. When a certain number is subtracted from 24 and the result is divided by that number, the answer is 3. What is the number?
Set up the equation: (24 – x) / * = 3. Multiply both sides by x: 24 – * = 3x. Add * to both sides: 24 = 4x. Divide by 4: * = 6.
#9. A t-shirt originally priced at $40 is on sale for $28. What is the percent discount on the t-shirt?
Discount amount = $40 – $28 = $12. Percent discount = (12 / 40) * 100% = 0.3 * 100% = 30%.
#10. The length of a rectangular box is 3 times its width, and its height is 1/3 of its width. If the box is 27 cm long, what is its volume?
Length (L) = 27 cm. Since L = 3 * Width (W), W = 27 / 3 = 9 cm. Height (H) = (1/3) * W = 9 / 3 = 3 cm. Volume = L * W * H = 27×9×3 = 729 cm³.
#11. A circle has an area of 64π. What is the circumference of the circle?
Area formula is A = π * r^2. Given π * r^2 = 64π, so r^2 = 64, which means r = 8. Circumference formula is C = 2 * π * r = 2 * π * 8 = 16π.
#12. Driving a distance of 420 miles at an average speed of 50 miles per hour, how long will the trip take?
Time = Distance / Speed = 420 / 50 = 8.4 hours. Convert 0.4 hours into minutes: 0.4×60 = 24 minutes. So the total time is 8 hours 24 minutes.
#13. An angle measures 1/5 of its supplementary angle. What is the measure of the angle in degrees?
Supplementary angles add up to 180 degrees. Let the angle be x. Its supplement is (180 – x). The equation is * = (1/5)(180 – x). Multiply by 5: 5x = 180 – x. Add x: 6x = 180, so * = 30 degrees.
#14. John travels 150 km in 6 hours. Alice travels 180 km in 4 hours. What is the ratio of John’s average speed to Alice’s average speed?
John’s speed = 150 / 6 = 25 km/h. Alice’s speed = 180 / 4 = 45 km/h. Ratio of John’s speed to Alice’s speed = 25:45. Simplify by dividing both by 5 to get 5:9.
#15. A pack of paper contains 400 sheets. If a student needs 3 binders filled with 150 sheets each, how many packs must be purchased and how many sheets will remain unused?
Total paper needed = 3×150 = 450 sheets. Since paper is sold in packs of 400 sheets, 1 pack (400 sheets) is not enough. The student must buy 2 packs = 800 sheets. Remaining sheets = 800 – 450 = 350 sheets.
#16. What is the sum of the interior angles of a pentagon?
The formula for the sum of interior angles of an n-sided polygon is (n – 2) * 180°. For a pentagon (n = 5), sum = (5 – 2) * 180° = 3×180° = 540 degrees.
#17. What is the slope of the line passing through the points (2, 5) and (4, 11)?
Slope formula m = (y2 – y1) / (x2 – x1) = (11 – 5) / (4 – 2) = 6 / 2 = 3.
#18. If $2,000 is deposited into a simple interest savings account at an annual rate of 5% for 3 years, how much total interest will be earned?
Simple interest formula I = P * r * t, where P = 2000, r = 0.05, and t = 3. Interest I = 2000×0.05×3 = $300.
#19. What is the probability of obtaining heads on all 3 tosses when flipping a fair coin 3 times?
Each coin flip has a probability of 1/2 for landing heads. For 3 independent flips, the probability of getting heads all three times is (1/2) * (1/2) * (1/2) = 1/8.
#20. Simplify the expression: (x + y + z) – (-2x + 2y + z)
Distribute the negative sign across the second parenthesis: * + y + z + 2x – 2y – z. Combine like terms: (x + 2x) + (y – 2y) + (z – z) = 3x – y + 0 = 3x – y.