# 6th Class

``` Provincial Finalist Exam for 6th Class Students Do not turn the page until you are instructed to do so.
Answer each question in the box provided next to the question on this
sheet. Only one answer should be given unless the question states
You may use a separate piece of paper if you need more space to complete
You will have 40 minutes to complete 8 problems of varying difficulty.
You may not leave until the exam has finished.
USE BLOCK CAPITAL LETTERS Name: ____________________ Student ID: ____________________
School: ____________________ County: ____________________ THIS IS ON YOUR BADGE 1. A train left Belfast at 3:45pm. It arrived in Dublin 2 hours and 38 minutes later. What time did it arrive in Dublin? 2. What is the sum of the first ten prime numbers minus the sum of the first four square numbers? Final answer: 3.
Final answer: The area of a rectangle is 112cm2. The length is 9cm longer than the breadth. Find the length of the rectangle. Final answer: √
2
2
θ is an angle
√ such√that sin θ =
√ 3/3, then 8 sin θ + 7 cos θ equals
. 5 b. 4 3 c. 5 3 d. 10 3/3
e. 22/3
he perimeter
square
is equal
the circumference
a fcircle
C.of tWhich
of 1the
4. of
How many ofof area
the t1hree digit nto
umbers that can be mof
ade rom all he digits , 3 and 5 ollowing numbers
is closest
area
ofoC?
(When they ato
re the
used only nce each) are prime? . 1 b. 1.1 c. 1.2
d. 1.3
e. 1.4
olve the following equation.
2 log10 (x) + log10 (x + 4) = log10 (4) + log10 (x) + log10 (x + 1).
√
√
. x = 1 b. x = 2 c. x = 10 d. x = 3 + 10
e. x = 5
et L be the line that is tangent to the circle (x − 7)2 + (y − 4)2 = 25 at the point (3, 7). The
ne L intersects
the y-axis at the point (0, b). What is b?
. −2 b.
e. 9
0 c. 3 d. 5
A swimming
pool has an input pump for filling the pool and an output pump for emptying the
ool. The
pool ainnswer: 3 hours,
input pump can fill the Final and the output pump can drain the pool in
hours. As you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. At
midnight, you awake to find the pool half empty. Immediately, you turn on the input pump, but
ou are sleepy
and forget to turn oﬀ the output pump. At what time will the pool become full?
. 1:30 am 5.
b. We 2:45kam
c. 3:30
am
d.f t3:45
e. f4:30
now that each one o
he dam
isplayed ive cam
ards (shown face up) has a number on one side and a letter on the other side. We know that each one of the displayed five cards (shown face up) has a number on one side
nd a letter on the other side.
S
3
H
3
8
onsider the assertion: ‘If a card has an S on one side, then it has a 3 on the other side.’ Let m
Consider the athat
ssertion: If a card has aover
n S oin
n oorder
ne side, then it that
has athe
3 oassertion
n the other e the least number
of cards
you ‘need
to turn
to prove
is side.’ Let m be t
he l
east n
umber o
f c
ards t
hat y
ou n
eed t
o t
urn o
ver i
n o
rder t
o p
rove t
hat t
he assertion rue. Determine m.
. 1 b. 2 c. is 3 true. d. D
4 etermine e. 5 m. Wile E. Coyote
and Road Runner have a 100-mile race. Road Runner runs 10 miles per hour
aster than Wile E. Coyote and finishes 1 hour ahead of Wile E. Coyote. How fast does Road
(in miles per hour)?
Runner √
run
√
√
. 5 + 5 41 b. 37 c. 110 d. 120
e. 30 + 37
2n
n
or how many positive integers n is 22 < 1010 ?
. 1 b. 2 c. 3 d. 4
e. An infinite number of n
onsider the set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. For every subset A of S, John computes the sum of
ll elements
in A and writes the result on the blackboard. Mary then computes the sum of all
he numbers
that John wrote on the board. The final result is equal to
. 11385 b. 11430 c. 11475 d. 11500
e. 11520
he integers
from 2 to 1000 are written on the blackboard. The students in school play the
ollowing game. Each student in turn
picks
a number
on the blackboard and erases it together
its
multiples.
The
game
ends
when
only
primes
are left written on the board. What
the smallest number of students that need to play before the game ends?
. 11 b. 31 c. 51 d. 71
e. 91
6. Which number should replce the question mark? Final answer: 7. Jane is about to travel by bus, and she knows that she must have the exact fare. She is not sure what this is, but she knows that it is greater than €1 and less than €3. What is the minimum number of coins she must carry to be sure of carrying the correct fare? (assume that the available coins are 1 cent, 2 cent , 5 cent , 10 cent,20 cent, 50 cent , €1 and €2) Final answer: 8. How many sets of 2 or more consecutive whole numbers(starting at 0) sum up to 15? Final answer: ```