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1A rectangle has a base of 4 cm and a height of 10 cm. What is its area, in square centimeters?
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Answer: 40
Area = base × height, so the area is 40 square centimeters. A student who instead finds the perimeter or forgets to halve the product of a triangle's dimensions would select a distractor.
2A car travels at a constant speed and covers 30 miles in 6 hours. What is the car's unit rate in miles per hour?
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Answer: 5
Unit rate = total distance ÷ total time = 30 ÷ 6 = 5 miles per hour.
3A pump fills 15 liters every 3 minutes at a constant rate. What is the unit rate in liters per minute?
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Answer: 5 liters per minute
Divide the total liters (15) by the number of time units (3) to find the unit rate: 15 ÷ 3 = 5 liters per minute.
4What is 28.3 + 8.9?
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Answer: 37.2
Performing the operation digit by digit with proper decimal alignment gives 28.3 + 8.9 = 37.2.
5Grace has 6 liters of juice and pours it into 300 ml bottles, filling as many full bottles as possible. Those full bottles are then shared equally among 4 people. How many bottles does each person get?
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Answer: 5
Step 1: total juice in milliliters (6 liters × 1000) = 6000 Step 2: how many full 300 ml bottles can be filled (6000 ÷ 300) = 20 Step 3: juice left over after filling those bottles (6000 − 20 × 300) = 0 Step 4: bottles each of 4 people gets if they're shared equally, ignoring leftovers (20 ÷ 4) = 5 So the answer is 5 — bottles per person.
6A triangle has a base of 10 cm and a height of 3 cm. What is its area, in square centimeters?
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Answer: 15
Area of a triangle = (base × height) ÷ 2 = (10 × 3) ÷ 2 = 15 square centimeters.
7What is 3/5 ÷ 3/10?
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Answer: 2
Multiply by the reciprocal: 3/5 × 10/3 = 2.
8A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 8 cups of sugar?
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Answer: 12 cups
Set up the proportion 3/2 = x/8. Since 8 ÷ 2 = 4, multiply 3 × 4 = 12 cups of flour.
9A rectangular prism has length 2 in, width 2 in, and height 7 in. What is its volume, in cubic inches?
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Answer: 28
Volume of a rectangular prism = length × width × height = 2 × 2 × 7 = 28 cubic inches. Confusing volume with surface area is a common error.
10A sneakers normally costs $100. The store is having a 10% off sale. Owen has $105 saved up. If Owen buys the sneakers at the sale price, how much money is left over?
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Answer: 15
Step 1: amount taken off the $100 price at 10% off (100 × 10 ÷ 100) = 10 Step 2: the sale price after the discount (100 − 10) = 90 Step 3: money left from the $105 budget after buying it (105 − 90) = 15 So the answer is 15 — money left over after the sale.