Math Kangaroo-style Practice Test 1 (Grade 9)
A free Math Kangaroo competition practice paper for Grade 9 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 the one correct answer (A–E) for each question. In the real contest questions in Sections A, B and C are worth 3, 4 and 5 points and there is no penalty for a wrong answer, so answer every question. Here each correct answer counts once. Attempt it online — every question is marked instantly and the correct answers are shown at the end.
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Q1. What is the value of the product (1 − 1/2) × (1 − 1/3) × (1 − 1/4) × … × (1 − 1/2026)?
Q2. The rectangle is divided into 24 equal squares. What fraction of the rectangle is shaded?
Q3. Three bags of sand are weighed two at a time. The three pairs weigh 12 kg, 15 kg and 17 kg. How heavy is the heaviest bag?
Q4. The net is folded to make a cube. Which letter is on the face opposite the face with the letter R?
Q5. A row of 3 hexagons is made from 16 matchsticks, as shown. A longer row of hexagons is made in the same way from exactly 101 matchsticks. How many hexagons are in that row?
Q6. The product of three consecutive whole numbers is 7980. What is their sum?
Q7. A wall clock has no numbers, only marks; the thick mark is 12 o'clock at the top. The picture shows the clock as Mia sees it in a mirror. What is the real time?
Q8. The shape is made of 7 equal squares. Its perimeter is 48 cm. What is its area?
Q9. One of four children ate the last piece of cake. Ava says: "I did not eat it." Ben says: "Cole ate it." Cole says: "Dina ate it." Dina says: "Cole is lying." Exactly one of the four is telling the truth. Who ate the cake?
Q10. How many of the whole numbers from 1 to 100 are divisible by 3 or by 5, but not by both?
Q11. Two quarter circles are drawn inside a square of side 6. Their centers are the two bottom corners of the square. What is the area of the shaded region?
Q12. In how many different ways can you make exactly one dollar (100 cents) using only nickels (5 cents), dimes (10 cents) and quarters (25 cents)? You do not have to use all three kinds of coin.
Q13. The picture shows a building made of cubes, seen from above. The number in each square tells how many cubes are stacked there. Which picture shows the building seen from the front?
Q14. How many pairs of positive whole numbers a and b satisfy a2 − b2 = 45?
Q15. In this table, the three numbers in each row, in each column and on each of the two diagonals have the same sum. Which number belongs in the shaded cell?
Q16. A mother and her three children have ages that add up to 64 years. In 6 years' time, the mother's age will equal the sum of the ages of her three children. How old is the mother now?
Q17. ABCD is a rectangle. E is the midpoint of BC, and F is the point on CD with CF equal to one third of CD. What fraction of the rectangle is shaded?
Q18. N is the smallest positive whole number whose digits multiply to 400. What is the sum of the digits of N?
Q19. Two fair six-sided dice are rolled. What is the probability that the product of the two numbers rolled is a perfect square?
Q20. Four of the five shapes below can each be made by putting together two copies of the piece shown (the pieces may be turned over). Which shape cannot be made?
Q21. A die has opposite faces adding up to 7. It stands on the bottom-left square with 1 on top, 2 on the face toward you and 3 on the face to the right. It rolls over its edges from square to square along the marked path. Which number is on top when it reaches the end?
Q22. How many of the numbers 1, 2, 3, …, 2026 can be written as the difference of the squares of two whole numbers (such as 7 = 42 − 32 or 4 = 22 − 02)?
Q23. Ten people stand in a row. Each is either a knight, who always tells the truth, or a liar, who always lies. Every one of them says: "Exactly one of my neighbors is a liar." How many liars are in the row?
Q24. An ant walks along the edges of a cube from corner A to the opposite corner B. It never visits any corner twice. How many different routes can it take?
Q25. How many three-digit numbers are equal to 11 times the sum of their own digits?
Q26. The numbers 1 to 8 are written in the table, one in each cell, so that the numbers increase from left to right in each row and from top to bottom in each column. As the picture shows, 1 and 8 must go in two corners. In how many ways can the table be filled?
Q27. What is the largest number of different numbers you can choose from 1, 2, 3, …, 20 so that no chosen number is exactly twice another chosen number?
Q28. Two squares stand side by side on a line. The larger square has sides of 8 cm; the size of the smaller square is not given. What is the area of the shaded triangle?
Q29. The number x satisfies x + 1/x = 3. What is the value of x4 + 1/x4?
Q30. The pattern is first reflected in a vertical line, then turned 90° clockwise, and finally reflected in a horizontal line. Which picture shows the result?
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