2014 Kadett Test | Test and Chat

Back to KangarooMath

2014 Kadett (Grade 7 - 8)

Questions: 30 | Answered: 0

Q1. The Mathematical Kangaroo takes place each year on the third Thursday of March. What is the latest possible date on which the competition could take place?

3 points

ABCDE

Question 1

Q2. and exactly 13 of these numbers are divisible by 13. The biggest number on the board is M . What is the smallest value that M can have?

3 points

ABCDE

Question 2

Q3. What is the answer to 2014 × 2014 ÷ 2014 − 2014 ?

3 points

ABCDE

Question 3

Q4. The area of rectangle ABCD in the diagram is 10. M and N are the midpoints of the sides sides AD and BC respectively. How big is the area of the quadrilateral MBND ?

3 points

ABCDE

Question 4

Q5. The product of two natural numbers is 36, and their sum 37. How big is the (positive) difference between the two numbers?

3 points

ABCDE

Question 5

Q6. Wanda has lots of pages of square paper, whereby each page has an area of 4. She cuts each of the pages into right - angled triangles and squares (see the left hand diagram). She takes a few of these pieces and forms the shape in the right hand diagram. How big is the area of this shape?

3 points

ABCDE

Question 6

Q7. A bucket is filled halfway with water. A cleaning liquid fills another 2 litres of liquid into the bucket. Now the bucket is three - quarters fu ll. How many litres of water in total can fit into the bucket?

3 points

ABCDE

Question 7

Q8. George builds the sculpture shown from seven cubes each of edge length 1. How many more of these cubes must he add to the sculpture so that he builds a large cube of edge length 3?

3 points

ABCDE

Question 8

Q9. Which of the following sums gives the biggest answer?

3 points

ABCDE

Question 9

Q10. Gray and white pearls are threaded onto a string. Tony pulls pearls from the ends of the chain. After pulling off the fifth gray pearl he stops. At most, how many white pearls could he have pulled off?

3 points

ABCDE

Question 10

Q11. Max has a one hour piano lesson twice a week, Hanna only has a one hour lesson every second week. The piano lessons run over a particular number of weeks. How many weeks is this, if during this time Max has 15 more hours of lessons than Hann a?

4 points

ABCDE

Question 11

Q12. , C + E = 2100, B + E = 800, B + C = 900, A + E = 700. Which ball is the heaviest?

4 points

ABCDE

Question 12

Q13. A grandmother, her daughter and her granddaughter find that the sum of their ages is 100. Also each age is a power of two (that is, several two’s multiplied together). How old is the granddaughter?

4 points

ABCDE

Question 13

Q14. 5 congruent rectangles ar e positioned in a square with side length 24 as shown in the diagram. How big is the area of one of these rectangles?

4 points

ABCDE

Question 14

Q15. In the following figure, the heart and the arrow are arranged as pictured. At th e same moment the heart and the arrow begin to move. The arrow moves around the figure 3 spaces clockwise and the heart 4 spaces anticlockwise and then they stop. This process repeats itself over and over again. After how many repetitions does the arrow f ind itself for the first time in the same triangle as the heart?

4 points

ABCDE

Question 15

Q16. In triangle ABC (see sketch) AD is the angle bisector of the angle at A and BH is the height from side AC . The obtuse angle between BH an d AD is four times the size of angle ∠ DAB . How big is the angle ∠ CAB ?

4 points

ABCDE

Question 16

Q17. Six boys live together in an apartment, which has two bathrooms. Each morning from 7:00 they use both of the bathrooms before breakfast whereby they are 8, 10, 12, 17, 21, and 22 minutes respectively, constantly alone in one of the two bathrooms. What is the earliest time that all six boys can have breakfast together?

4 points

ABCDE

Question 17

Q18. The sides of a rectangle are 6cm an d 11cm long. You select one of the long sides. Then the angle bisectors of the angles at the ends of this side are drawn. They split the opposite long side into three pieces. How long are these pieces?

4 points

ABCDE

Question 18

Q19. Captain Sparrow and his pirates loot some gold coins. They share the coins equally amongst themselves. If they were four pirates less they would each get 10 coins more. If the number of coins was 50 le ss, they would each get 5 coins less. How many coins did they share between themselves?

4 points

ABCDE

Question 19

Q20. The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is the average value big ger than the other number?

4 points

ABCDE

Question 20

Q21. Andy fills a 3 × 3 table with all the digits from 1 to 9 so that each cell only contains one digit. He has already put the digits 1, 2, 3 and 4 in the table as shown in the diagram. Two numbers are ‘neighbouring’ when the cells they are in share one side. After he had fin ished filling in the table he noticed: The sum of the numbers neighbouring 9 equals 15. How big is the sum of the numbers neighbouring 8?

5 points

ABCDE

Question 21

Q22. 2

5 points

ABCDE

Question 22

Q23. The quadrilateral ABCD has right angles only in corners A and D. The numbers in the diagram give the respective areas of the triangles in which they are located. How big is the area of ABCD ?

5 points

ABCDE

Question 23

Q24. Jan and Eva undertake a challenge to solve mathematics questions. They each get an id entical list of 100 questions. For each correctly solved question, the first to solve it gets 4 points while the slower person gets 1 point. Jan solved 60 questions and Eva also solved 60 questions. Together they score 312 points. How many questions were s olved by both Jan and Eva?

5 points

ABCDE

Question 24

Q25. David cycles from Edinburgh to his aunty who lives outside of Edinburgh. He wants to arrive at exactly 15:00 hours. After 2/3 of his planned travel time he had covered 3/4 of the way. There fore he began to cycle slower and arrived exactly on time at his destination. In which ratio are the average speeds of the two sections of his journey?

5 points

ABCDE

Question 25

Q26. Four identical cubes (see diagram) were fitted to gether. If the resulting shape is viewed from the front you see a black circle (picture on the right). What will you see on the back of the shape?

5 points

ABCDE

Question 26

Q27. A group of 25 people is made up of knights, rascals and shilly - shalliers. The knights always tell the truth, the rascals are always untruthful, and the shilly - shalliers answer alternately truthfully and falsely (or the other way around). After the first question asked to everybody, “are you a knight?” 17 of them answered “yes!” After the second question asked to everybody “are you a shilly - shallier?” 12 of them answered “yes!” After the third question asked to everybody “are you a rascal?” 8 of them answered “yes!” How many knights are in this group of people?

5 points

ABCDE

Question 27

Q28. Lots of different positive whole numbers were written on a blackboard. Exactly two of these numbers are divisible by

5 points

ABCDE

Question 28

Q29. On a pond 16 lilly pads are arranged in a 4 × 4 grid as can be seen in the diagram. A frog sits on a lilly pad in one of the corners of the grid (see picture). The frog jumps from one lilly pad to anothe r horizontally or vertically. In doing so he always jumps over at least one lilly pad. He never lands on the same lilly pad twice. What is the maximum number of lilly pads, including the one he is sitting on, on which he can land?

5 points

ABCDE

Question 29

Q30. A 5 × 5 square is covered with 1 × 1 tiles. The design on each tile is made up of three dark triangles and one light triangle (see diagram). The triangles of neighbouring tiles always have the same colour where they join along an edge. The border of the large square is made of dark and light triangles. What is the smallest number of dark triangles that could be amongst them?

5 points

ABCDE

Question 30

2014 Kadett Test | Test and Chat