2018 Student Test | Test and Chat

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2018 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. In the diagram you can see the calendar page of a certain month. Unfortunately ink has run across parts of the page. Which day of the week does the 27th of that month fall on?

3 points

ABCDE

Question 1

Q2. Which of the following expressions has the biggest value?

3 points

ABCDE

Question 2

Q3. The diagram shows the floor plan of Renate's house. Renate enters her house from the terrace (Terrasse) and walks through every door of the house exactly once. Which room does she end up in?

3 points

ABCDE

Question 3

Q4. Thor has seven stones and a hammer. With his hammer he hits a stone and it breaks into five small stones. He does that a few times. Which of these numbers could be the number of stones he ends up with?

3 points

ABCDE

Question 4

Q5. The diagram show s an object made up of 12 dice glued - together. The object is d ipped into some colour so that the entire outside is coloured in t his new colour. How many of the small dice will have exactly four faces coloured in ?

3 points

ABCDE

Question 5

Q6. The following two statements are true: Some aliens are green and all others are purple. Green aliens live on Mars only. Which one of the following logical conclusions can be made?

3 points

ABCDE

Question 6

Q7. Four identical rhombuses (diamonds) and two squares are fitted together to fo rm a regular octagon as shown. How big are the obtuse interior angles in the rhombuses ?

3 points

ABCDE

Question 7

Q8. There are 65 balls in a box , 8 of which are white, the rest are black. Up to 5 balls can be taken out of the box in one draw. I t is not allowed to put any balls back into the box. What is the minimum number of draws which have to be made to be certain that at least one white ball is drawn from the box?

3 points

ABCDE

Question 8

Q9. The faces of the brick have the areas A, B and C as shown. How big is the volume of the brick? 3

3 points

ABCDE

Question 9

Q10. How many ways are there to write the number 1001 as the sum of two prime numbers?

3 points

ABCDE

Question 10

Q11. √ 3 √ 3

4 points

ABCDE

Question 11

Q12. The five vases shown are filled with water. The filling rate is constant. For which of the five vases does the graph shown describe the height of the water h as a function of the time t?

4 points

ABCDE

Question 12

Q13. | √ 17 − 5 | + | √ 17 + 5 | =

4 points

ABCDE

Question 13

Q14. An octahedron is inscribed into a die with side length 1. The vertices of the octahedron are the midpoints of the faces of the die. How big is the volume of the octahedron?

4 points

ABCDE

Question 14

Q15. The vertic es of a triangle have the co - ordinates A(p | q), B(r | s) and C(t | u) as shown. The midpoints of the sides of the triangle are the points M(  2 | 1), N(2 |  1) and P(3 | 2). Determine the value of the expression 푝 + 푞 + 푟 + 푠 + 푡 + 푢 5

4 points

ABCDE

Question 15

Q16. Be f or e the football game , Real Madrid vs. Manchester United , the following five predictions were made: i) The game will not end in a draw. ii) Real Madrid will score at least one goal. iv ) Real Madrid wi ll win. iii) Real Madrid wi ll not lose. v ) Exactly three goals will be scored . It turns out that exactly three of these predictions then com e true. How many goals d id Real Madrid score?

4 points

ABCDE

Question 16

Q17. A regular pentagon is cut out of a page of lined paper. Step by step this pentagon is then rotated 21° counter clockwise about its midpoint. The result after step one is shown in the diagram. Which of the diagrams shows the situation when the pentagon fil ls the hole entirely again for the first time?

4 points

ABCDE

Question 17

Q18. Which of the following numbers is not a factor of 1 8 + 1 8 ?

4 points

ABCDE

Question 18

Q19. Three of the cards shown will be dealt to Nadia, the rest to Riny . Nadia multiplies the three values of her cards and Riny multiplies the two values of his cards. It turns out that the sum of those two products is a prime number. Determine the sum of the values of Nadia ’ s cards.

4 points

ABCDE

Question 19

Q20. Two rectangles form the angles 40° and 30° respectively , with a straight line (see diagram). How big is angle  ?

4 points

ABCDE

Question 20

Q21. The faces of the prism shown , are made up of two triangles and three squares. The six vertices are labelled using the number s 1 to 6. T he sum of the four numbers around each square is always the same. The numbers 1 and 5 are given in the diagram. Which number is written at vertex X?

5 points

ABCDE

Question 21

Q22. 푚 and 푛 are the solutions of the equation 푥 − 푥 − 2018 = 0 . What is the value of the expression 푛 + 푚 ?

5 points

ABCDE

Question 22

Q23. Fours brothers with the harmonious name s A , B , C and D are all of different height s . They make the following claims: A : I am neither the tallest nor the smallest. B : I am not the smallest. C : I am the tallest . D : I am the smallest. Exactly one of them lies. Who is the tallest brother?

5 points

ABCDE

Question 23

Q24. A f unction 푓 fulfills the property 푓 ( 푥 + 푦 ) = 푓 ( 푥 ) ∙ 푓 ( 푦 ) for all whole numbers 푥 and 푦 . Furthermore 푓 ( 1 ) =

5 points

ABCDE

Question 24

Q25. A quadratic function of the form 푓 ( 푥 ) = 푥 + 푝푥 + 푞 intersects the x - axis and the y - axis in three different points. The circle through these three points intersects the graph of t he function f in a fourth point. What are the co - ordinates of this fourth point of intersection? 푞 푞 2

5 points

ABCDE

Question 25

Q26. On an idealised rectangular billiard table with side lengths 3 m and 2 m a ball (point - shaped ) is pushed away from point M on the long side AB . It is reflected exactly once on each of the other sides as shown. at which distance from the vertex A will the ball hit this side again if 퐵푀 = 1 , 2 푚 and 퐵푁 = 0 , 8 푚 ?

5 points

ABCDE

Question 26

Q27. How many real solutions does the equation | | 4 − 3 | − 2 | = 1 have?

5 points

ABCDE

Question 27

Q28. ABCDEF is a regular hexagon , as shown in the diagram . G is the midpoint of AB. H and I are the intercepts of the line segments GD and GE respectively , with the line segment FC. How big is the ratio of the areas of the triangle GIF and the trapezium IHDE?

5 points

ABCDE

Question 28

Q29. In a class there are 40% more girls than boys. The probability that a student representative team of two students 1 randomly selected from this class is made up of exactly one girl and one boy is exactly . How many children are 2 there in this class?

5 points

ABCDE

Question 29

Q30. Archimedes has calculated 15! . The result is on the board. Unfortunately two of t he digits, the second and the t enth, cannot be read. What are the two missing digits? (Remark: 15! = 15  14  13  …  2  1)

5 points

ABCDE

Question 30

2018 Student Test | Test and Chat