Math Kangaroo-style Practice Test 1 (Grade 6)
A free Math Kangaroo competition practice paper for Grade 6 in the format of the real test: 30 questions in 75 minutes, covering Section A — 3-point questions; Section B — 4-point questions; Section C — 5-point questions. 75 minutes, no calculator. Choose one answer (A–E) for each question. In the real contest, questions are worth 3, 4 or 5 points by section and there is no penalty for a wrong answer; here each correct answer counts once, so answer every question. Attempt it online — every question is marked instantly and the correct answers are shown at the end.
Free · attempted online · no download
Q1. What is the smallest whole number whose digits add up to 26?
Q2. The figure below is turned a quarter turn clockwise (90° to the right). Which picture shows the result?
Q3. How many rectangles of any size can be found in this figure? (Squares count as rectangles too.)
Q4. A rope is folded in half, and then folded in half again. The folded rope is then cut straight through at one point (not at a fold). How many pieces of rope are there now?
Q5. A kangaroo starts at 0 on a number line. It jumps 3 forward, then 2 back, then 3 forward, then 2 back, and so on. After how many jumps does it land on 10 for the first time?
Q6. A month has exactly five Fridays and exactly four Saturdays. On which day of the week is the first day of the next month?
Q7. How many three-digit numbers have digits that multiply to 12? (For example, 134 is one of them.)
Q8. The shape is made of 7 squares, each with sides of 2 cm. What is the perimeter of the shape?
Q9. 3 apples weigh the same as 2 pears. 1 pear weighs the same as 3 plums. How many plums weigh the same as 5 apples?
Q10. Rows of triangles are made with matches as shown. How many triangles are in the row made with 51 matches?
Q11. The net below is folded to make a cube. Which number is on the face opposite the face with the number 1?
Q12. A square sheet of paper is folded twice and then a hole is punched, as shown. Which picture shows the sheet when it is unfolded?
Q13. A digital clock shows hours and minutes from 00:00 to 23:59. At some times the four digits read the same forwards and backwards, like 15:51. How many such times are there in one day?
Q14. How many triangles of any size are there in this figure?
Q15. How many three-digit numbers have their digits in increasing order from left to right (like 158) and the sum of their digits equal to 12?
Q16. A square is divided into 16 equal small squares. What fraction of the big square is shaded?
Q17. The sum of five consecutive whole numbers is 2025. What is the sum of the next five consecutive whole numbers?
Q18. A rectangle is made of 6 squares as shown. The two smallest squares (dark) have sides of 1 cm. What is the perimeter of the rectangle?
Q19. In the sum AB + AB + AB = CAB, the letters A, B and C stand for three different digits (AB is a two-digit number and CAB is a three-digit number). What is A + B + C?
Q20. A rectangle is cut into four smaller rectangles by one straight vertical cut and one straight horizontal cut. The areas of three of them are shown in cm². What is the area of the fourth rectangle?
Q21. Lena writes the whole numbers from 1 to 100. She crosses out every multiple of 3, and then crosses out every number that contains the digit 3. How many numbers are not crossed out?
Q22. Ana, Ben, Cara, Dev and Eli sit on five chairs in a row. Ana sits at one end, and Ben sits next to Ana. Cara does not sit at either end, and she does not sit next to Eli. Dev sits somewhere to the right of Eli. Who sits at the left end of the row?
Q23. A bug walks along the lines of the grid from S to F. It only ever moves right or up, and it must not pass through either of the two crossed-out points. How many different routes can it take?
Q24. In how many ways can you choose 3 of the 9 squares of a 3 × 3 board so that no two chosen squares share a side?
Q25. A list of numbers starts 2, 3. Each next number is the last digit of the product of the two numbers before it. So the list begins 2, 3, 6, 8, 8, 4, … What is the sum of the first 20 numbers in the list?
Q26. Some identical cubes are placed in stacks on a 3 × 3 square board. The pictures show the stacks seen from the front and from the right side. What is the greatest number of cubes there can be?
Q27. How many whole numbers from 1 to 1000 have digits that add up to 5?
Q28. Ten children stand in a row. Each child is either a knight, who always tells the truth, or a liar, who always lies. Every child says: "Exactly one of my neighbors is a liar." How many liars are in the row?
Q29. In how many different ways can the 2 × 6 board be completely covered with 6 dominoes? Each domino covers exactly two neighboring squares.
Q30. Some numbers can be written as a sum of two or more consecutive positive whole numbers, for example 9 = 4 + 5 and 10 = 1 + 2 + 3 + 4. How many of the numbers from 1 to 50 can be written in this way?
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