Free Math Kangaroo practice test — Grade 5

Correct answer: A

Let's denote the cost of the ball as x. The bat costs $1.00 more than the ball, so the bat costs x + $1.00. The total cost of the bat and the ball together is $1.10, so we can write the equation: x + (x + $1.00) = $1.10. Simplifying the equation, we get 2x + $1.00 = $1.10. Subtracting $1.00 from both sides, we get 2x = $0.10. Dividing both sides by 2, we get x = $0.05. 💡 Tip: Use algebra to represent the unknown cost of the ball and set up an equation based on the given information.

Correct answer: B

Looking at the differences between consecutive terms: +1 (from 1 to 2), +2 (from 2 to 4), +3 (from 4 to 7), +4 (from 7 to 11). The pattern in the differences is adding 1 more each time. So, the next difference should be +5, making the next number in the sequence 11 + 5 = 16. 💡 Tip: Identify the pattern in the differences between terms to predict the next number in the sequence.

Correct answer: B

First, let's calculate the total number of books added to the bookshelf: 20 + 15 = 35 books. Then, 8 books are removed, resulting in 35 - 8 = 27 books. Since each shelf can hold 8 books, we divide the total number of books by the capacity of each shelf: 27 ÷ 8 = 3 with a remainder of 3. This means that 3 shelves will be completely filled with 8 books each, and there will be 3 books left over for the next shelf. 💡 Tip: Pay attention to the order of operations and the remainder when dividing the total number of books by the capacity of each shelf.

Correct answer: C

Let's denote the side length of the large square as S. The area of the large square is S^2. The side length of the small square is 1/3 * S, so its area is (1/3 * S)^2 = 1/9 * S^2. The area left after the cut is S^2 - 1/9 * S^2 = 8/9 * S^2. Thus, the fraction of the original area left is 8/9. 💡 Tip: Visualize the problem, understand the relationship between the areas of the squares, and calculate the fraction of the area left after the cut.

Correct answer: B

The snail climbs 3 feet up and slips 2 feet back each day, so it effectively moves 1 foot up each day. However, on the last day of its climb to the top, it won't slip back. Thus, we need to find out how many days it takes to climb 17 feet (20 - 3 = 17), because on the 18th day, when it climbs the final 3 feet, it will reach the top and won't slip back. Since the snail moves 1 foot up effectively each day, it takes 17 days to climb 17 feet. On the 18th day, it climbs the last 3 feet to reach the top. 💡 Tip: Consider the net progress of the snail each day and the final day's climb to the top.