Click when ready... Individual Competition Part I

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IndividualCompetition

Part I

• There are 50 multiple choice questions

• You have 2 minutes to finish each question

• There will be a break after 25 questions

• A trial question will now follow

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Trial Question (2 minutes)

(a) 2n+2 (b) 23n+3 (c) 42n+2

(d) 42n+1 (e) 24n-2

2n+1 X 4n+1 equals


1. How many squares are there in the following figure?

A)187

B)188

C)189

D)190

E)191


2. Worker A can paint a building in 7 days while worker B can paint a building in 3 days. If they both work together, how long will it take them to paint a building?

A) 50.2 hours B) 50.4 hours C) 50.6 hours D) 50.8 hours E) 60 hours


3. How many triangles are there in the following figure?

A) 24

B) 25

C) 26

D) 27

E) 28


4. A triangle has sides 9cm, 40cm

and 41cm. What is its area?

A) 820cm2 B) 180cm2

C) 184.5cm2 D) 90cm2

E) 360cm2


5. Each exterior angle of a regular polygon is 8. How many sides does the polygon have?

A 30 B 90 C 40 D 45 E 50


6. A 12 sided polygon is shown below: Evaluate angle A + angle B + angle C + angle D + angle E + angle F

A)180º

B)360º

C)540º

D)720º

E)Cannot tell


7. Two concentric circles are drawn such that a chord of the larger circle, which is of length 12 cm, is tangent to the smaller circle. What is the shaded area between the two circles?

A) 6π

B) 12π

C) 24π

D) 36π

E) Cannot tell


8. What is the sum of the integers which are divisible by 3 and lie between 1 and 1000?

A 166830 B 166833C 166836 D 166839E 166842


9. What is the highest common factor of 648, 744 and 864?

A 8 B 12C 16 D 24E 48


10. A school teaches 3 foreign languages: French, German and Spanish. Every student in class 7A studies at least one foreign

language. If there are 49 students in class 7A and the following statements all hold:

23 students study French 31 students study German 32 students study Spanish 8 students study French and German 12 students study French and Spanish 19 students study German and Spanish Find the number of students that study all 3 languages.

A) 0 B) 1 C) 2 D) 3 E) 4


11. How many ways can the letters of the word “SUPERINTELLIGENT” be arranged?

A) 16!

B) 16!/(2!2!2!2!3!)

C) 1!1!1!1!1!2!2!2!2!3!

D) 16!/(2x2x2x2x3)

E) 16!/11!


12. The prime factorization of 1050625 is abcd. Evaluate a+b+c+d.

A) 52

B) 53

C) 54

D) 55

E) 56


13. An analogue clock displays the time

as 7:43. What is the angle between the hour hand and minute hand?

A) 18º

B) 26.5º

C) 27.5º

D) 28.5º

E) 48º


14. A square of side length l is inscribed in a circle inscribed in a square of side length L. Find l/L.

A) cos 30º B) cos 45º C) cos 60º D) tan 30º E) 1/3


15. A circle with centre O is shown:

ABC CDE

If EF=8 cm and BE=3 cm, how long is OF?

A)√55 cm

B)√39 cm

C) 5 cm

D) 4√2 cm

E)Cannot tell


16. An equilateral triangle is divided by arcs as shown:

AB=BC=CD=DE=EF=AF=1 cm. What is the area of the shaded region?

A)√3-π

B)√3-π/2

C)√3-π/3

D)√6-π/3

E)√6-π/2


17. By 8p.m. all the guests had arrived at the party. By 9p.m. a third had left. By 10p.m. a third of those remaining had gone. By 11p.m. a third of those remaining had again departed and eight guests were left at the party. How many guests were there originally at 8p.m.?

A) 36 B) 33 C) 30 D) 27 E) 24


18. A car travels from town A to town B at

an average speed of 20 mph and returns at an average speed of 30 mph. What is the average speed for the whole journey?

A) 22 B) 23 C) 24 D) 25 E) 26


19. A newspaper has four pages missing. One of them is page 21. If the back page is 28, what are the numbers of the other three missing pages?

A) 6,7,20 B) 7,8,20

C) 7,8,22) D) 8,9,22

E) 9,10,22


20. What is the next number in the sequence 47, 86, 149, 242, 371, ….

A 542 B 544C 534 D 528E Cannot tell


21. A person travels 3 m east, 5 m north, 8 m west, 13 m south, 21 m east, 34 m north, 55 m west and 89 m south. How far is he from his starting point?

A) 102 m B) 5√205 m

C) 7√130 m D) √1830 m

E) 3√610 m


22. A regular pentagon ABCDE has side length 1. What is the length of AC?

A) sin 36º

B) cos 36º

C) (√5+1)/2

D) (√5+1)/4

E) 4sin2 36º–3


23. Which of the following is equal to tan 22.5º?

A) 0.5tan 45º B) 2-√2

C) √2-1 D) 2+√2

E) √2+1


24. All the five digit numbers that can be made from the digits 1, 6, 7, 8 and 9, without repetition, are summed. What is the total?

A 10399944 B 7539432 C 8295384 D 8266584 E 10666584


25. Complete the sequence: 1, 2, 5, 16, 45, 106, 217, 400, ___

A) 680 B) 681 C) 682 D) 683 E) 684

BREAKTIME

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IndividualCompetition

Part 2


26. A certain company offers "750 hours of free Internet use for new subscribers”. On closer inspection it becomes clear that this time must be used during the new subscriber's first month of membership!

What is the maximum number of hours in any one month of the year?

A 168 B 692 C 720 D 744E 750


27. "20% off everything", screamed the sale posters. I paid £60. What would I have paid before the sale?

A £60 B £66 C £72 D £75 E £80

.61

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28. Which of the following has the greatest value?

A. 0.3 X 7 B. 0.5 X 5 C. 0.2 X 11

D. 0.09 X 30 E. 0.026 X 100


29. Alice's room is furnished with three-legged stools and four-legged chairs. There are 17 legs in all (excluding Alice's!). How many three-legged stools are there?

A. 1 B. 2 C. 3 D. 4

E. 5


30. Old Martha has 5 children, each of whom has 4 children, each of whom has 3 children, each of whom is childless. How many descendants does Old Martha have?

A 12 B 20 C 25 D 60E 85


31. In the diagram the lines PQ and SR are parallel, as are the lines PS and QT. What is the value of x?

A 139 B 138 C 124 D 98 E 97

32. The engineering company, Sparks and Tensor has a complicated system of conveyor belts in its factory. Components must travel along these belts in the directions shown by the arrows.How many different routes are there from A to F along the conveyor belts?

A 4 B 5C 6 D 7E 8



33. Which is the smallest?

A B C

D E

6)(4

3)(2

6)(4

3)(2

46

23

6)(4

3)(2

6)(4

3)(2


34. In the diagram PQ = PR = RS. What is the size of angle x?

A 54° B 720° C 90° D 108° E 144°


35. It is evening and Meg. who is 1m tall, casts a shadow of length 3m. If Meg stands on her brother's shoulders, which are 1.5m above the ground, how long a shadow will she and her brother cast?

A 3m B 4.5m C 5.5m D 6.5mE 7.5m

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36. Equal regular pentagons are placed together to form a ring in the manner shown. The diagram shows the first three pentagons. How many more are needed to complete the ring?

A 6 B 7 C 8D 9 E 10


37. In a fit of madness, the bee Zerk left the hive and flew 1m due North, then 1m due East, then 1m vertically up. She then made a beeline for the hive, flying directly home in a straight line. How far, in m did she fly altogether?

A 4 B 3 + C 3 + D 5 E6

2 3


38. From the information given in the diagram shown alongside, what is the value of a + b?

A 3 B 4 C 5 D 6 E 7


39. The diagram shows a semicircle containing a circle which touches the circumference of the semicircle and goes through its centre. What fraction of the semicircle is shaded?

A B C

D E

3

2

2

1

1

2

3


40. The letter-product of a number is obtained by Multiplying the number by the number of letters in the corresponding word. For example, the letter-product of 5 is 20, since there are 4 letters in the word 'five' and 5 X 4 - 20. Which of the following has the largest letter-product?

A 6 B 7 C 8 D 9 E 10


41. How many of the numbers

are greater than 1 ?

A 1 B 2 C 3 D 4 E 5

3 11 4 7 5 5 6 3 7 2


42. Below are three statements. (I) 310 is even (II) 310 is odd (III) 310 is square

Exactly which ones are true?

A (i) only B (ii) only C (iii) only D (i) and (iii) E (ii) and (iii)


43. I walk to the bike shop at 3 miles per hour and cycle back along the same route at 12 miles per hour. What is my average speed, in miles per hour, for the time I am actually travelling on the route?

A 3.75 B 4.8 C 6 D 8 E 9


44. A ream of paper (500 sheets) is 5.4 cm thick. What is the thickness of a single sheet, correct to one significant figure?

A 1 mm B 0.5 mm C 0.1 mm D 0.05 mm E 0.01 mm


45. If then what is the value of

A 6 B 8 C 10 D 12 E 18

,4 abba?8)62(


46. Susan is taller than Sophie, but shorter than Sandra. Stephanie is taller than Sarah, but shorter than Susan. Who is the tallest of these five girls?

A Susan B Sophie C Sandra D Stephanie E Sarah


47. Anna has 3 brothers and 5 sisters. Her brother Tom has S sisters and B brothers. What is the value of S X B ?

A 8 B 10 C 12 D 15 E 18


48 What is the value of

(a) -1000 (b) -80 (c) 0

(d) 924 (e) 1000

102210


49. Ima Divvy used her calculator and multiplied a number by 20 instead of by 2. What could she now do to obtain the correct answer?

A divide by 20 B divide by 40 C multiply by 10 D multiply by 0.5 E multiply by 0.1


50. A tourist attraction, which opens every day, needs 30 000 visitors per day on average to break even. Last week there were 120 000 visitors. What is the number of visitors needed this week to break even over the two-week period?

A 43 000 B 90 000 C 180 000 D 210000 E 300 000

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Click when ready... Individual Competition Part I