Math Kangaroo-style Practice Test 1 (Grade 7)
A free Math Kangaroo competition practice paper for Grade 7 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. Each question has exactly one correct answer (A–E). In the real contest Section A questions are worth 3 points, Section B 4 points and Section C 5 points, and there is no penalty for a wrong answer, 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. A digital clock shows times from 00:00 to 23:59. How many times during one day does the display read the same forwards and backwards, like 15:51?
Q2. How many triangles of any size can you find in the picture?
Q3. Kanga writes all the whole numbers from 1 to 30. How many times does she write the digit 2?
Q4. The net shown is folded to make a cube. Which number is on the face opposite the face with 2?
Q5. A kangaroo starts at the 0 m mark of a straight track. It jumps 3 m forward, then 1 m back, then 3 m forward, then 1 m back, and so on. During which jump does it first reach the 20 m mark?
Q6. Some squares of the 4 × 4 grid are shaded. What is the smallest number of extra squares that must be shaded so that the whole grid with its shading has a line of symmetry?
Q7. The rectangle is made from one large square and two equal small squares. The perimeter of each small square is 12 cm. What is the perimeter of the rectangle?
Q8. One of four young kangaroos ate the cake. Kip says: "Lou did it." Lou says: "Ned did it." Max says: "I did not do it." Ned says: "Lou is lying." Exactly one of them is telling the truth. Who ate the cake?
Q9. The word KANGAROO is written again and again without spaces: KANGAROOKANGAROOKANGAROO... How many letters O are there among the first 2031 letters?
Q10. What is the value of (1 + 3 + 5 + ... + 97 + 99) − (2 + 4 + 6 + ... + 96 + 98)?
Q11. Which of these nets can be folded to make a cube?
Q12. The square tile shown is turned a quarter turn (90°) clockwise. Which picture shows the tile after the turn?
Q13. How many three-digit numbers have digits that add up to 5?
Q14. Ann ate one third of the cookies in a jar. Then Ben ate one quarter of the cookies that were left. Then Cleo ate half of the cookies that were left after that. Now there are 6 cookies in the jar. How many cookies were there at the start?
Q15. The large square is divided into 36 small squares. What fraction of the large square is shaded?
Q16. Ava, Ben, Cora, Dan and Eli sit in a row of five seats. Ben does not sit next to Cora. Ava sits exactly two seats away from Ben. Dan sits exactly two seats to the right of Ava. Who sits next to Ben?
Q17. The average of four numbers is 15. When one of the numbers is removed, the average of the other three is 12. Which number was removed?
Q18. Both balances are level. Shapes that look the same have the same weight. How many triangles weigh the same as one square?
Q19. A rectangle is divided into four smaller rectangles by one horizontal and one vertical line. The areas of three of them are shown. What is the area of the fourth rectangle? (The picture is not to scale.)
Q20. A beetle walks along the lines of the grid from A to B, always moving right or up. It must not pass through the point X. How many different routes can it take?
Q21. How many four-digit numbers have digits whose product is 12? (For example, 2161 is one of them.)
Q22. Each of the five regions of the picture is to be painted in one of 4 colors. Regions that share a border must get different colors. Not every color has to be used. In how many different ways can the picture be painted?
Q23. Ten people sit around a round table. Each is either a knight, who always tells the truth, or a liar, who always lies. Every one of them says: "Both of my neighbors are liars." What is the smallest possible number of knights at the table?
Q24. In a 5 × 3 rectangle made of unit squares, a diagonal passes through the inside of 7 squares, as shown. Through the inside of how many squares does a diagonal of a 12 × 8 rectangle pass?
Q25. Five different positive whole numbers have an average of 10, and the middle number (when they are put in order) is 8. What is the largest possible value of the biggest number?
Q26. A 5 × 3 × 2 box is built from 30 small cubes. All six outside faces of the box are painted. How many of the small cubes have exactly two painted faces?
Q27. In a certain month there are five Saturdays and five Sundays, but only four Fridays. On which day of the week is the 20th of that month?
Q28. The numbers 1, 2, 3, 4, 5 and 6 are placed in the circles, one in each, so that the three numbers along each side of the triangle have the same sum. What is the largest possible value of this sum?
Q29. What is the smallest whole number whose digits are all different and add up to 26?
Q30. Four teams play a tournament in which every team plays every other team once. A win gives 3 points, a draw gives 1 point to each team and a loss gives 0 points. At the end, team P has 7 points, team Q has 5 points and team R has 3 points. How many points does team S have?
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