2013 Junior Test | Test and Chat

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2013 Junior (Grade 9 - 10)

Questions: 30 | Answered: 0

Q1. Which of the numbers is not a factor of 200013 – 2013?

3 points

ABCDE

Question 1

Q2. Maria ha s six equally big square pieces of plain paper. On each piece of paper she draws one of the figures shown below . How many of these f igure s have the same perimeter as the plain piece of paper itself ?

3 points

ABCDE

Question 2

Q3. Mrs. Maisl buys four pieces of corn - on - the - cob for each of the four cob offer! members of her family and get the discount offered. How much does she 1 Cob 20 Cent end up paying ? Every 6th cob free!

3 points

ABCDE

Question 3

Q4. The product of three numbers out of the numbers 2, 4, 16, 25, 50, 125 is 1000. How big is the sum of those three numbers ?

3 points

ABCDE

Question 4

Q5. On a square grid made up of unit squares, six points are marked as shown on the right. Three of which form a triangle with the least area. How big is this smallest area?

3 points

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Question 5

Q6. If you add 4 and 8 , you obtain a number that is a power of two. Determine that number !

3 points

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Question 6

Q7. A cube is coloured on the outside as if it was made up of four white and four black cubes where no cubes of the same colour are next to each other (see picture). Which of the following figures represents a possible net of the coloured cube?

3 points

ABCDE

Question 7

Q8. The number n is the biggest natural number for which 4n is three - digits long and m is the smallest natural number for which 4m is three - digits long. Which value does 4n – 4m have?

3 points

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Question 8

Q9. In a drawing we can see a three quarter circle wi th centre M and an indicated orientation arrow. This three - quarter circle is first turned 90° anti - clockwise about M and then reflected in the x – axis. Which is the resulting picture ?

3 points

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Question 9

Q10. Which of the following numbers is biggest?

3 points

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Question 10

Q11. Triangle RZT is generated by rotating the equilateral triangle AZC about point Z. Angle β = ∠ CZR = 70°. Determine angle α = ∠ CAR.

4 points

ABCDE

Question 11

Q12. The figure on the right is made up of six unit squares. Its perimeter is 14 cm. S quares will be added to this figure in the same way until it is made up of 2013 unit squares (zigzag: alternating bottom right and top right). How big is the perimeter of the newly created figure ?

4 points

ABCDE

Question 12

Q13. A and B are opposite vertices of a regular six - side shape, the points C and D are the mi d- points of two opposite sides . The area of the regular six - sided shape is 60. Determine the product of the lengths of the lines AB and CD!

4 points

ABCDE

Question 13

Q14. A class has written a test. If every boy had obtained 3 more points , the points average would be 1.2 points higher than now . Which percentage of the children in this class are girls ?

4 points

ABCDE

Question 14

Q15. The sides of the rectangle ABCD are parallel to the co - ordinate axis. The re c- tangle lies below the x - axis and to the right of the y - axis, as shown in the diagram. F or each of the points A, B, C, D the quotient (y - coordinate):(x - coordinate) is calculated . F or which point will you obtain the smallest quotient?

4 points

ABCDE

Question 15

Q16. Today is Hans’ and his son’s birthday. Hans multiplies his age with the age of his son and obtains C

4 points

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Question 16

Q17. Tarzan wanted to draw a rhombus made up of two equilateral triangles. He drew the line segments inaccurately. When Jane checked the measurements of the four angles shown, she sees that they are not equally big (see diagram). Which of the five line s egments in this diagram is the longest?

4 points

ABCDE

Question 17

Q18. Five consecutive positive integers have the following property: T he sum of three of the number s is as big as the sum of the other two . How many sets of 5 such numbers are there?

4 points

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Question 18

Q19. How many different ways are there in the diagram shown , to get from point A to point B if you are only allowed to move in the directions indicated?

4 points

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Question 19

Q20. Given a six - digit number whose digit sum is even and whose digit product is odd. Which of the following statements are true for this number ?

4 points

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Question 20

Q21. How many decimal places are necessary to write the number 1024000 as a decimal ?

5 points

ABCDE

Question 21

Q22. The date 2013 is made up of four consecutive digits 0, 1, 2, 3. How many years before the year

5 points

ABCDE

Question 22

Q23. We are looking at rectangles where one side is of length 5.0 cm. Amongst those are some that can be cut into a square and a rectangle one of which has an area of 4,0 cm². How many such rectangles are there ?

5 points

ABCDE

Question 23

Q24. “Sum change” is a procedure wher e in a set of three numbers , each number is replaced by the sum of the other two. So for instance {3, 4, 6} becomes the set {10, 9, 7} and this again becomes {16, 17,

5 points

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Question 24

Q25. Let Q be the number of square numbers amongst the natural numbers from 1 to 2013 and K the 6 number of cubic numbers (powers of three) amongst the natural numbers from 1 to 2013 . Which of the following holds true : 3 2

5 points

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Question 25

Q26. Using the numbers 1, 2, 3, …, 22, 11 fractions b are formed where each number is used ex a ctly once. What is the maximum number of fractions with whole number values that can be obtained?

5 points

ABCDE

Question 26

Q27. Any three vertices of a regular 13 - sided - shape are joined up to form a triangle. How many of these triangles contain the circumcentre of the 1 3 - sided - shape ?

5 points

ABCDE

Question 27

Q28. A car starts in point A and drives on a straight road at 50 km/h. Every hour after that another car leaves point A with a speed 1 km/h faster than the one before. The last car leaves A 50 hours after the first car and drives with a speed of 100 km/h. What is the speed of the car that is leading 100 hours after the start of the first car?

5 points

ABCDE

Question 28

Q29. 100 trees (oaks and birches) are standing in a row. The number of trees between any two oaks is not equal to 5. What is the maximum number of trees out of the 100 that can be oak trees?

5 points

ABCDE

Question 29

Q30. A positive integer N is smaller than the sum of its three biggest true factors (N itself is not a true factor of N). Which of the following statements is true ?

5 points

ABCDE

2013 Junior Test | Test and Chat