2021 Student Test | Test and Chat

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2021 Student (Grade 11 - 12)

Questions: 30 | Answered: 0

Q1. Paula's weather app shows a diagram of the predicted weather and maximum temperatures for the next seven days, as shown. Which of the following represents the corresponding graph of maxi- mum temperatures?

3 points

ABCDE

Question 1

Q2. How many integers are in the interval ( 20 −+ 21;20 21 ) ?

3 points

ABCDE

Question 2

Q3. A cube with edge 1 is cut into two identical cuboids. What is the surface area of one of these cuboids? 3

3 points

ABCDE

Question 3

Q4. A large square is divided into smaller squares, as shown. A shaded circle is inscribed in- side each of the smaller squares. What proportion of the area of the large square is s haded?

3 points

ABCDE

Question 4

Q5. After the storm last night, the flagpole on our school building is leaning over. Looking from northwest, its tip is to the right of its bottom point. Looking from the east, its tip is also to the right of its bottom point. In which direction coul d the flagpole be leaning over?

3 points

ABCDE

Question 5

Q6. A rectangular sheet of paper has length x and width y where xy  . The rectangle may be folded to form the curved surface of a circular cylinder in two different ways. What is the ratio of the volume of the longer cylinder to the volume of the shorter cylinder? 22 22

3 points

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Question 6

Q7. Let x = . Which of the following numbers is the largest? 4 4 2 4

3 points

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Question 7

Q8. How many 3 - digit - numbers formed using only the digits 1, 3 and 5 are divisible by 5 ? You may use digits more than once.

3 points

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Question 8

Q9. What is the area of the triangle whose vertices are ( p , q ) , ( 3 p , q ) e ( 2 p ,3 q ) , where pq ,0  ? pq

3 points

ABCDE

Question 9

Q10. The parabola in the figure has an equation of the form y = ax + bx + c for some distinct real numbers a , b and c . Which of the following equations could be an equation of the line in the figure?

3 points

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Question 10

Q11. 1

4 points

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Question 11

Q12. If A =  0,1   2,3  and B =  1,2   3,4  , what is the set of all numbers of the form ab + with a  A and b B ?

4 points

ABCDE

Question 12

Q13. How many three - digit natural numbers have the property that when their digits are written in reverse order, the result is a three - digit number which is 99 more than the original number?

4 points

ABCDE

Question 13

Q14. The first 1000 positive integers are written in a row in some order and all sums of any three adjacent numbers are calculated. What is the greatest number of odd sums that can be obtained?

4 points

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Question 14

Q15. A large triangle is divided into smaller triangles as shown. The number inside each small triangle indicates its perimeter. What is the perimeter of the large tri- angle?

4 points

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Question 15

Q16. An infinite list of numbers has the property that, for each positive integer n , the average of the first n terms is n . How many terms are there less than 2021?

4 points

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Question 16

Q17. In the 55  square shown the sum of the numbers in each row and in each column is the same . There is a number in every cell, but some of the numbers are not shown. What is the number in the cell marked with a question mark?

4 points

ABCDE

Question 17

Q18. A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: or like this: . What is the probability that the string is knotted aft er its ends are pulled?

4 points

ABCDE

Question 18

Q19. A naughty pup grabs the end of a roll of toilet paper and walks away at a constant speed. Which of the functions be- low best describes the thicknes s y of the roll as a function of the unrolled part x ?

4 points

ABCDE

Question 19

Q20. The diagram shows three squares, PQRS , T UVR and UWXY . They are placed to- gether, edge to edge. Points P , T and X lie on the same straight line. The area of PQRS is 36 and the area of TU VR is 16 . What is the area of triangle PXV ?

4 points

ABCDE

Question 20

Q21. The figure shows the graph of a function fR :  −→ 5,5  . How many distinct solutions does the equation f ( f ( x ) ) = 0 have?

5 points

ABCDE

Question 21

Q22. The numbers 1, 2, 7, 9, 10, 15 and 19 are written down on a blackboard. Two players alternately delete one number each until only one number remains on the blackboard. The sum of the numbers deleted by one of the players is twice the sum of the numbers deleted by the other player. What is the number that remains?

5 points

ABCDE

Question 22

Q23. The function f is such that f ( x + y ) = f ( x )  f ( y ) and f ( 12 ) = . f ( 2 ) f ( 3 ) f ( 2021 ) What is the value of + + + ? f ( 1 ) f ( 2 ) f ( 2020 ) 1

5 points

ABCDE

Question 23

Q24. Five kangaroos named A , B , C , D and E have one child each, named a , b , c , d and e , not necessarily in that order. In the first group photo shown ex- actly 2 of the children are standing next to their mothers. In the second group photo exactly 3 of the children are standing next to their mothers. Whose child is a ?

5 points

ABCDE

Question 24

Q25. The solid shown in the diagram has 12 regular pentagonal faces, the other faces being either equilateral triangles or squares. Each pentagonal face is surrounded by 5 square faces and each triangular face is surrounded by 3 square faces. John writes 1 on each triangular face, 5 on each pentagonal face and − 1 on each square. What is the total of the numbers written on the solid?

5 points

ABCDE

Question 25

Q26. On a circle 15 points are equally spaced. We can form triangles by joining any 3 of these. Congruent triangles, by rotation or reflection, are counted as only one triangle. How many different triangles can be drawn?

5 points

ABCDE

Question 26

Q27. A triangle ABC is divided into four parts by two straight lines, as shown. The areas of the smaller triangles are 1, 3 and 3. What is the area of the original triangle?

5 points

ABCDE

Question 27

Q28. Two plane mirrors OP and OQ are inclined at an acute angle (diagram is not to scale). A ray of light XY parallel to OQ strikes mirror OP at Y . The ray is reflected and hits mirror OQ , is reflected again and hits mirror OP and is reflected for a third time and strikes mirror OQ at rig ht angles at R as shown. If OR = 5 cm, what is the distance d of the ray XY from the mir- ror OQ ?

5 points

ABCDE

Question 28

Q29. Let Mk ( ) be the maximum value of 44 x −+ x k for x in the interval  − 1,1  , where k can be any real number. What is the minimum possible value of Mk ( ) ? 9 11

5 points

ABCDE

Question 29

Q30. A certain game is won when one player gets 3 points ahead. Two players A and B are playing the game and at a particular point, A is 1 point ahead. Each player has an equal probability of winning each point. What is the probability that A wins the game?

5 points

ABCDE

Question 30

2021 Student Test | Test and Chat