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SASMO 2014 Secondary 3 (Grade 9) Contest

Question 1

Solve for x and yin the following equation |x — 7| +./y +8 = 0.

f

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Question 2

Arrange 2!8, 3!? and 4° in ascending order (i.e. from smallest to biggest).

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Question 3

Mersenne numbers are numbers of the form Mp = 2° — 1, where pis a prime. For
example, 3 = 2? - 1 is a Mersenne number that is also a prime. Find the smallest
Mersenne number that is nota prime.

kh | 9
a SS

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Question 4

Find the exact value of 3 — 1.99999...

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Question 5

.
The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, ..., where each term after the
second term is obtained by adding the previous two terms. How many of the first
2014 Fibonacci numbers are odd?

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Question 6

If x and y are positive integers, find the values of x and y which satisfy the
equation

x? —9y? = 43,
= See) | eae) Pn ered (rere

—_—— ee

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Question 8

Find the smallest whole number that leaves a remainder of 1 when divided by 3,
a remainder of 2 when divided by 5, and a remainder of 3 when divided by 7.

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Question 9

Evaluate 20142015 x 20152014 - 20142014 x 20152015.
fel cy
=
BS
a EES

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Question 10

Find the sum of the terms in the n" pair of brackets:
(5, 6, 7), (8, 9, 10), (11, 12, 13), (14, 15, 16), ....

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Question 11

The diagram shows a triangle ABC where AB = AC. Dis a point on AB such that
DC= BC, and Eis a point on DCsuch that FB = DB. If BC= 16 cmand EC = 12
cm, find the length of AB,
A
D
B {\ Cc
ESSeees Eas SS SS Se See ee
: = ;

i

ea!
: s :
:

is

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Question 12

Ft eet “UNIO Ree) tag o
tole te a express Ie tga eu aes in terms of x.

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Question 13

: If the four-digit number X88Y is divisible by 45, find the possible values of X and
SS %

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Question 14

} Find the exact value of —+—.
i

fea]
2B

B
e
——

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Question 15

The diagram shows a square AEFG with an inscribed circle. ABCD is a rectangle
such that AB = 3 cm and AD = 6 cm. Find the radius of the circle.

A rT E

6 _ 7

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Question 16

Let x be a number such that x+1=5. Find the value of »* —

x #

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Question 17

Find the next term of the following sequence: 1, 4, 9, 7, 7, 9, 4, 1,9, 1, ..
i ;
:
i

{ss =
SS eee

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Question 18

If mis an even positive integer and 0 ‹ x ‹ 360°, find all the solutions to the
trigonometric equation (sin x)" — (cos x)” = 1.
‘

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Question 19

/ The diagram shows a square of length 6 cm and two quarter-circular arcs of
radius 6 cm. Find the area of the shaded region, leaving your answer in terms of
SS mand surds.

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