Math Kangaroo-style Practice Test 1 (Grade 8)
A free Math Kangaroo competition practice paper for Grade 8 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. The digits of the year 2026 add up to 10. How many years from 2027 to 2099 (inclusive) also have digits that add up to 10?
Q2. The dots in the picture are 1 cm apart. What is the area of the shaded square?
Q3. Which of these numbers is the largest?
Q4. Four of these nets can be folded to make a cube. Which one cannot?
Q5. In a certain month there are exactly five Saturdays and exactly five Sundays. Every other day of the week occurs exactly four times. On which day of the week does the next month begin?
Q6. The three scales are balanced. Shapes of the same kind have the same weight. How much does one square weigh?
Q7. In a class, 60% of the students are girls. When 4 more boys join the class, there are exactly as many boys as girls. How many students are in the class now?
Q8. Four identical rectangles are placed to make a large square with a square hole in the middle, as shown. The large square has area 64 cm2 and the hole has area 4 cm2. What is the perimeter of one rectangle?
Q9. A digital clock shows times from 00:00 to 23:59. The time 12:21 reads the same forwards and backwards. How many times in one day read the same forwards and backwards?
Q10. A 5 × 4 × 3 box is built from 60 unit cubes. The whole outside of the box is painted. How many unit cubes have exactly one painted face?
Q11. A beetle walks along the lines of the grid from P to Q, moving only to the right or upwards. It must not pass through the point marked with the cross. How many different routes can it take?
Q12. For how many three-digit numbers is the sum of the digits equal to the product of the digits?
Q13. Five different positive whole numbers have mean 10 and median 12. What is the largest possible value of the biggest of these numbers?
Q14. The regular hexagon ABCDEF and the square ABGH share the side AB. What is the size of the angle x = ∠AHF?
Q15. A sequence starts 2, 3, … Each next number is the last digit of the product of the two numbers before it. So the sequence begins 2, 3, 6, 8, 8, 4, … What is the 2026th number of the sequence?
Q16. Two candles have the same height. The first burns down completely in 4 hours, the second in 6 hours, each at a steady rate. Both are lit at the same time. After how many hours is the second candle exactly twice as tall as the first?
Q17. Each of the numbers 1, 2, 3 and 4 must appear exactly once in every row and in every column of the table. Which number goes in the shaded cell?
Q18. How many squares (of any size) can be found in this figure?
Q19. In the sum ABC + ABC + ABC = CCC, different letters stand for different digits. What is A + B + C?
Q20. In how many ways can the numbers 1, 2, 3, 4, 5 be written in a row so that no two neighboring numbers differ by 1?
Q21. How many positive whole numbers less than 1000 have digits whose product is 12?
Q22. Three squares with sides 2, 3 and 5 stand side by side on a line. A straight segment joins the bottom left corner of the smallest square to the top right corner of the largest square. What is the total shaded area (the parts of the squares above the segment)?
Q23. Seven people sit around a round table. Each of them is either a knight, who always tells the truth, or a liar, who always lies. Each person says: “Both of my neighbors are liars.” How many liars are at the table?
Q24. Four teams played a tournament in which each team played every other team once. A win gave 3 points, a draw 1 point and a loss 0 points. Three of the teams finished with 6, 5 and 2 points. How many points did the fourth team have?
Q25. The positive integers are written one after another without spaces: 123456789101112131415… What is the 2026th digit written?
Q26. A 5 × 5 × 5 cube is built from 125 small cubes. Three straight tunnels with a 3 × 3 square cross-section are cut right through the cube, from the middle of each face to the middle of the opposite face. How many small cubes are left?
Q27. In how many ways can the 3 × 4 rectangle be covered completely by six 1 × 2 dominoes like the one shown? (Dominoes may be placed horizontally or vertically.)
Q28. The numbers 1 to 8 are placed around a circle so that the sum of every two neighboring numbers is a prime number. Arrangements that differ only by a rotation or a reflection count as the same. How many different arrangements are there?
Q29. Ann and Beth start together at the same point of a circular 400 m track and run in opposite directions without stopping. Ann runs at 5 m/s and Beth at 3 m/s. If they keep running for ever, at how many different points of the track will they meet (counting the starting point)?
Q30. A square sheet of paper is folded three times as shown, and then one hole is punched through all the layers. What does the sheet look like when it is unfolded?
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