UBC Grade 67 Workshop Problems, 20092010
1. A playing field is three times as long as it is wide. Its length is 111 m. What is the perimeter
of the field?
2. Lyle is a passionate snowboarder. He rushes out and buys a seasons pass for Grouse
Mountain for $
Homework 3
1.
(a)
3 11 19
8 16 24
13 21 29
(b)
Using that 5+23 = 14 we get the number at the center. Notice that in any column the sum will of the rst
2
row plus the last row is 2 times the one in the middle, by construction. Therefore the sum of any colu
Homework 1
1.
Since we draw the marbles at random we have that:
3 total black and gold marbles
9
=
=
7
total number of marbles
17 + whites
Therefore we have whites = 4.
2.
The number six digits number abcde f that we are looking can be write as AB where A
Homework 5
1.
We can think a, b, c as the sides of a rectangular triangle. Let be the angle form by the side b and the
hypotenuse c.
c c
+
a b
2
2
1
sin2 + cos2 + 2 sin cos
1 + 2 sin(2 )
1
=
=
+
2
2
cos sin
sin cos
sin2 (2 )/4
4
4
+
= 2
sin(2 )
sin (2 )
Homework 6
1.
(a)
In one step, he can only reach 1, 2, 3, each one with a
one step is 3 .
4
1
4
probability. Therefore the probability of exit in
(b)
In one step, he can reach 1, 2, 3, each one with a 1 probability. In exactly two steps, he can reach 4, 5
Homework 3
1.
First we can place the As and Cs. For those letters we have 8 spaces with no restriction. Then we have
8C3 different ways of arranging the As and Cs.
The places for the Bs are between each A or C, and we have 9 of those spaces, (7 between ea
THE UNIVERSITY OF BRITISH COLUMBIA
Homework 1
Math 414 Section 101
Due by 1pm on Sept. 13, 2013
1. Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles,
and 6 red marbles. Mark adds a number of white marbles to the bag and tells
UBC Grade 1112 Workshop Problems, 20092010
1. A sequence cfw_tn satisfies the formula tn = 2tn 1 + tn 2 for all n > 2. If t4 = 4 and t6 = 20, what
is t8?
2. A mathematician tends carefully to her prized apple tree, and it grows to a very unusual
shape. Th
UBC Grade 810 Workshop Problems, 20092010
1. James leaves a point A at 7:00 a.m. and travels at 30 km/h. An hour later, Kevin leaves the
same point A and travels along the same road, but at 45 km/h. At what time will Kevin meet
James?
2. In a rectangular