SASMO 2014 Secondary 2 (Grade 8) Contest

The first day of 2014 was a Wednesday. There are 365 days in 2014. In what
day of the week will 2015 begin?

i

What is the maximum number of parts that can be obtained from cutting a
circular cake using 3 straight cuts?

Evaluate 2014 x 2014 - 2013 x 2015.

bl ss
Se ee SSS eee

Solve Jx+ Vx txt... = 3.

Find the exact value of 1 — 0.99999...

Mersenne primes are prime numbers of the form Mp = 2? — 1, where pis a prime.

For example, 3 = 2? — 1 isa Mersenne prime. Find the 4" largest Mersenne prime.
EBxeneeeey 0) faassen ce a PS ens) | ena ee ens c. eaana ft | paann nen SSNOR RRS ASS
Sel : oe Seyi | ae
\

p =
eS

=| Simplify (x- a) (x- B) (x- 0) (x- d) (x- @)... (x- 2.

ES
: i

= How many squares are there in a 5 x 5 square grid?

If x and y are positive integers, find the values of x and y which satisfy the
equation
x? — dy? = 41,

pe
: | 1
Se

Find the dimensions of all the rectangles with integral sides whose area and
perimeter are numerically equal.

A whole number is between 40 and 70. When it is divided by 3, the remainder
is 1. When it is divided by 7, the remainder is 2. Find the number.

Find the value of ——~————..
2+12| a
* (: +12(2-
fees ed See ne eee (Sep Sec | See

‘Peal s
ee SSS SS SS SSS

Find the value of
: 1 3 5 |, 2013
2014 “ 2014 2014" 2014"

kee Find the sum of the terms in the n'* pair of brackets:
(1, 2, 3, 4), (5, 6, 7, 8), (9, 10, 11, 12), ...

In the diagram, PQ and RSare parallel, PA= PB and RA = RC. Find ZBAC.
p A
Z | \;
B
(@

°
Q

a
ie

There are 367 students in the school hall. What is the probability that two of the
students have their birthday falling on the same day of the year?

Let xbe a number such that x+1=5. Find the value of »° oe

x x

Divide the following shape into 4 identical parts.
= eS
i
=

Find all the solutions to the trigonometric equation (sin)? — (cos x)? = 1 for
O0‹x ‹ 360°.

‘
E

The diagram shows a square AFFG with an inscribed circle. ABCD is a rectangle
such that AB = 2 cm and AD = 4 cm. Find the radius of the circle.
Ae E
S
——— eS