1. (8?2)×3-(7-5)=10. To make this statement true, the question mark between the 8 and 2
should be replaced by
A+
BC×
D÷
E None of these.
2. How many distinct factors, including 1 and itself, does 1000 have?
A 12
B 13
C 14
D 15
E 16
3. Peter decides to bicycle to school and can average a speed of 15km/h. At the end of the day
he realises that he has a flat tire and has to walk home, averaging a speed of 5km/h. What is
the average speed of his round trip?
A 7km/h
B 7.5km/h
C 8km/h
D 8.5km/h
E 9km/h
4. What is the difference between the sum of the first 2009 even counting numbers and the
sum of the first 2009 odd counting numbers?
A0
B1
C2
D 2009
E 4018
5. When it is raining I take my umbrella with me. If this statement is true, which of the
following must also be true?
I.
If I do not take an umbrella then it is not raining
II.
If it is not raining then I do not take an umbrella
III.
If I take my umbrella then it is raining
A I only
B II only
C III only
D I and II
E II and III
6. How many whole numbers lie between 𝜋 −2 and 𝜋 2
A none
B3
C6
D9
E infinitely many
7. In a supermarket display apples are stacked in pyramid like structure. The base is an
equilateral triangle consisting of 15 apples. Each apple in the level above the first rests in a
pocket formed by the three apples in the level below it. The stack is completed by a single
apple. How many apples are in the structure?
A 35
B 36
C 37
D 38
E 39
8. Al and Bob are both given 20m of string to mark out a flower bed. Al decides to use a
rectangular shape which measures 4m by 6m. Bob decides to use a square. In terms of area
how much bigger is Bob’s flowerbed than Al’s to the nearest 1%?
A 4%
B 5%
C 6%
D 7%
E 8%
9. Which of these numbers is greater than it’s reciprocal?
A -2
B -1
C -0.5
D 0.5
E1
10. A department store decides to launch a sale by taking 20% off selected products. Later they
decide to take 10% off these prices. One of the assistants claims that the new saving is now
30%. What is the real price reduction when compared to the original prices?
A 28%
B 29%
C 30%
D 31%
E 32%
11. Mary and her older brother Nigel look after elephants in a zoo. Mary takes 50 minutes to
wash an elephant and her brother can complete the same task in 40 minutes. If they work
together how long will it take them to wash a single elephant?
A just under 22 minutes
B just over 22 minutes
C just under 23 minutes
D just over 23 minutes
E just under 24 minutes.
12. Which of the following numbers is largest?
A 2090
B 9020
C 2900
D 9200
E 2009
13. Simplify √𝑥√𝑥 √𝑥
15
4
A √𝑥 3
7
B √𝑥 16
C √𝑥 8
8
D √𝑥 7
16
E √𝑥 15
14. A tiled floor is made up of regular octagons tessellating
with squares. What fraction of the area is taken up with
square tiles?
1
1
1
A5
B 3+2√2
C 2+3√2
1
D 2+3√3
1
E 3+2√3
15. A number is taken at random from the set {1,2,3,4,.....,100}. What is the probability that the
number is divisible by 3 and not 5.
1
13
27
14
29
A4
B 50
C 100
D 50
E 100
16. The each of the numbers 2, 5, 10, 11 and 13 is to be placed in one
of the five squares so that the sum of the three numbers in the
horizontal row equals the sum of the three numbers in the
vertical column. Which value must go in the middle square?
A2
B5
C 10 D 11 E 13
17. Tak goes to the school shop to by some pens. The shop only sells red, blue or black pens but
they have lots of each type. If Tak decides to buy 7 pens how many possible assortments
could he choose?
A 14
B 36
C 45
D 72
E 246
18. Nine trees are equally spaced along the side of a straight road. The distance from the first to
the third tree is 50 metres. What is the distance from the first to the last tree?
A 150
B 175
C 200
D 225
E 250
X
19. The line XY divides the area of the square in the ratio of 7:3.
If the length of the side of the square is 5 how long is XY?
A √30 B √31 C √32 D √33 E √34
Y
20. The mean of a set of five positive integers is 20 and the median is 23. The maximum
possible for the largest number is
A 51
B 52
C 65
D 72
E 73
21. A cube is inscribed in a sphere so that the vertices of the cube all just touch the sphere. A
second sphere is then inscribed inside of the cube so that it just touches each of the faces of
the cube. If the larger sphere has a surface area of 36cm2 then what is the surface area of
the smaller sphere in cm2?
A9
B 12
C 18
D 12√3
E 18√2
P
22. The points P, Q and R are the vertices of an equilateral
triangle, and the points L, M and N are the midpoints of
its sides. How many noncongruent triangles can be drawn
using any three of these six points as vertices?
A1
B2
C3
D4
E 20
L
Q
M
N
R
23. There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly
once. Only one of these four-digit numbers is a multiple of another one. Which one is it?
A 5724
B 7245
C 7254
D 7425
E 7542
24. Suppose that 𝑎 and 𝑏 are unequal, positive integers such that 𝑎𝑏 = 𝑏 𝑎 . Then the value of
𝑎 + 𝑏 is
A2
B3
C4
D5
E6
25. Let 𝑓(𝑥⁄2) = 𝑥 2 − 2𝑥. If 𝑓(2𝑦) = 8 then the difference between the two possible values
for 𝑦 is.
A 3⁄2
B 4⁄3
C 5⁄4
D 6⁄5
E 7⁄6