Selective school mathematics sample test

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Selective School Mathematics Sample Test
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Q 1. Nicole packed 5 Christmas gift separately in small boxes that are 4 cm
long, 5 cm wide and 3 cm high. To send these gifts to New York she has to
pack them into a carton that is 12 cm long, 5 cm wide and 6 cm high. How
many more small boxes can she pack into the carton?
6 1 2 5
Q 2. A bike bigger toothed wheel with 30 cm diameter is attached to a smaller
toothed wheel of diameter 10 cm with a chain. How many revolutions will the
smaller wheel will make when the bigger one makes 18 revolutions?
27 36 54 25
Q 3. Boeing 747 passenger aeroplane fly at a speed of 260 m/sec and it flies
from Sydney to Auckland in 4 hours. To reach Auckland in 3 hours, it must fly
at a speed of:
347 m/sec 500 m/sec 225 m/sec 447 m/sec
Q 4. The traffic lights at three different road crossings change after every 5
min, 6 min, and 7 min respectively. If they all change simultaneously at 8:20
am then at what time will they again change simultaneously?
11:50 AM 10:50 AM 11:25 AM 11:50 PM
Q 5. In a Cole’s promotion, Ming Rong received an '8 cent per litre discount'
petrol voucher after spending $110.00. On the way, he bought 39.9 litres of
petrol at 142.9 cents per litre from Shell Petrol Station. He used the Coles
petrol concession voucher. Find the approximate amount he paid.
57 54 164 110
Q 6. X is a circle with radius 8 cm, and Y is a circle with radius 6 cm. Daniel
wants the two circles to touch tangentially (touch at one point). He knows
that there are two possibilities for the distance between their centers. What
are these two distances?
2 cm and 8
cm
3 cm and
5 cm
2 cm and
14 cm
6 cm and 8
cm
Q 7. The difference of the sum of even numbers and sum of odd numbers from
1 and 20 is
20 54 40 10

Q 8. Find the odd one out from the series 121, 144, 169, 196, 225, 256, 279
256 279 196 121
Q 9. A clock is started at noon. By 10 minutes past 6, the hour hand has
turned through:
185
degrees
135
degrees
175
degrees
180
degrees
Q 10. In a public school 750 students were enrolled in 2012. Each class had
equal number of students. The school principal expects to collect $100 from
each student. Answer the questions from 29 to 32 on the base of the data
shown in the table
What percentage of students had not paid the donation in 2013?
10% 15% 40% 5%

Answer 1:
The bigger carton is 12 cm long and small box is 4 cm long; so along length it
can fix 12/4 = 3 small boxes; In width the bigger box can only allow one box
because the width is similar in both cases; since height of carton is double of
small box so it can stack one box on top of other. So in total 2 small boxes; total
small boxes inside the carton 3*1*2 = 6; so it can accommodate one smaller
box
Answer 2:
Distance covered by bigger wheel = 2 ∏ R = 2 ∏ 15 = 30 ∏ ; distance covered
by smaller wheel =2 ∏ R = 2 ∏ 5 = 10 ∏ ;
Let smaller wheel make X revolutions when the bigger makes
× 10 = 18 × 30
∴ = 54
Answer 3:
Speed = 260 m/sec = 260 *18 /5 = 936 km/hr;
Distance between Sydney and Auckland = speed * time = 936 * 4 = 3744 kms,
Speed required to travel in 3 hrs = 3744/3 = 1248 km/sec = 1248 *5/18 =
346.66 m/sec which is same as the speed of sound.
Answer 4:
Interval of change = LCM of 5, 6 and 7 = 210 min = 210/60 =3.5 hrs = 3 hrs
and 30 minutes; Hence the next simultaneous change will take place at 8:20 am
+ 3 hrs and 30 minutes = 11:50 am
Answer 5:
Petrol Price =143 cents / litre; Discounted price with Coles Petrol Voucher =
143-8 =135 cents/litre; Ming bought 40 litres of petrol. Approximate cost = 135
x 40 = $54

Answer 6:
Circle with centre x has a radius 8cm and circle with centre y has radius is 6 cm.
When the two circle are tangent (touch each other at one point) the difference
between the centre of two circle = 8-6=2 cm and 8+6 = 14 cm
Answer 7:
NOTE: Sum of consecutive numbers = n(n+1)/2; for example 1+2+3...+20 =
20* (20+1)/2 = 210; Sum of even numbers = n(n+1) for example sum of even
number from 1 to 20 = 10*(10+1)=110; Sum of odd numbers = n*n for
example sum of odd number from 1 to 20 = 10*10=100
Answer 8:
The patter = Number2
112
, 122
132
142
152
162
172
182
192
202
121, 144, 169, 196, 225, 256, 289, 324, 361, 400
Answer 9:
Angle traced by hour hand in 6 hrs 10 min
= +

=
= × = 185
Answer 10:
Donation collected $67500, total expected $75000, deficit = 75000-
67500=7500, number of students who had not paid donation = 7500/100 = 75;
%of student who had not paid the donation = (75/750) *100 = 10%

Selective School Mathematics
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