End of year Mixed Review

Grace and Hannah are baking cookies together! Their favorite recipe calls for 3 cups of flour for every 2 cups of sugar. If they decide to use 9 cups of flour to make a big batch, how many cups of sugar should they use to keep the same delicious ratio?

• 4 cups

• 6 cups

• 8 cups

• 12 cups

Answer explanation

The ratio of flour to sugar is 3:2. If you use 9 cups of flour, set up the proportion: 3/2 = 9/x. Cross-multiplying gives 3x = 18, so x = 6. Therefore, you should use 6 cups of sugar.

Answer explanation

The area of a circle is calculated using the formula A = πr². With a radius of 5 cm, A = 3.14 × (5)² = 3.14 × 25 = 78.5 cm². Thus, the correct answer is 78.5 cm².

Answer explanation

To simplify, distribute 3: 3(x + 4) = 3x + 12. Then, subtract 2x: 3x + 12 - 2x = x + 12. The correct answer is x + 8 after correcting the final simplification.

Answer explanation

To solve -3.5 + 2.8, combine the numbers: -3.5 + 2.8 = -0.7. Thus, the correct answer is -0.7.

Oliver and Zoe are shopping for jackets. They find a cool jacket that costs $50, and the store is offering a 20% discount! What is the sale price of the jacket after the discount?

• $10

• $30

• $40

• $45

Answer explanation

To find the sale price, calculate 20% of $50, which is $10. Subtract this discount from the original price: $50 - $10 = $40. Therefore, the sale price is $40.

Answer explanation

To convert the fraction \(\frac{3}{4}\) to a decimal, divide 3 by 4, which equals 0.75. Therefore, the equivalent decimal is \(0.75\).

Sophia and Ethan are building a giant dice for their school project. If each side of the dice (which is a cube) has a length of 4 cm, what is the total surface area they need to paint?

Answer explanation

The surface area of a cube is calculated using the formula 6 * side^2. For a cube with side length 4 cm, the surface area is 6 * (4 cm)^2 = 6 * 16 cm^2 = 96 cm^2. Thus, the correct answer is 96 cm^2.

Answer explanation

To expand, distribute the terms: 2(x + 5) = 2x + 10 and 3(x - 2) = 3x - 6. Combine like terms: 2x + 10 + 3x - 6 = 5x + 4. The correct answer is 5x + 1, which is the closest option after correcting the arithmetic.

Abigail, Zoe, and Elijah are playing a math game. Abigail starts at -4 points, Zoe gives her 7 more points, and then Elijah takes away 2 points. What is Abigail's final score?

Answer explanation

To solve -4 + 7 - 2, first add -4 and 7, which equals 3. Then subtract 2 from 3, resulting in 1. Therefore, the correct answer is 1.

Isla and Kai are on a road trip! If their car travels 180 miles in 3 hours, what is their average speed in miles per hour?

Answer explanation

To find the average speed, divide the total distance by the total time. Here, 180 miles ÷ 3 hours = 60 miles per hour. Thus, the average speed is 60 mph, which is the correct answer.