Vectors
Counting and probability
Proof
Random
Random
100

Find the dot product of the following two vectors:

a = 2i + 3j    b = -5i 

-10

100

How many cards need to be dealt from a standard deck of 52 cards to ensure that you will have at least 2 cards that share the same rank?

14
100

State the contrapositive of "if a number is even then the square of the number will be even"

and state if it is sometimes, always, or never true

If the square of a number is odd then the number will be odd

true

100

Where are the asympotes on a graph of y=sec(x)

(0 to 2pi)

90 and 270

or pi/2 and 3pi/4

100

If vector AB is <2,1> and the position vector of B is -5i, find the position vector of A

AB=OB-OA

OA=OB-AB = -7i - j

200

How can you confirm mathematically if two vectors are perpendicular?

Dot product = 0

200

How many arrangements of the word DUPLICATE have two vowels and three consonants?

7200

200

Disprove the following statement:

"No squares have perimeters equal to their areas"

a 4x4 square exists

200

Express as a sum or product:

cos(2x)cos(3x)

0.5cos5x + 0.5cosx

200

If A=  2    3      , find 5AI

0    -2 

10         15


5            -5

300

Find the vector of magnitude 6 in the same direction as u=3i+4j

6/5 (3i+4j)

300

Using the digits 0,1,2,3,4,5 without repetition, how many odd four digit numbers can be formed?

144

300

An arc subtends an angle of 36 degrees at the centre of a circle.  What is the size of the angle that is subtended by the same arc on the circumference of the circle?

18 degrees

300

Find the solution to cosx=0.5

30 + 2kpi, k=Z

(-30) + 2kpi, k=Z

300

Find im[(2+i)/(2-i)]

4/3

400

Find x if the vector 4i-5j is parallel to the vector <-10i, x>

12.5

400

Four students are to be chosen from a group of eight students for the school tennis team.  Two members of the group, Sam and Tess, do not get along and cannot both be on the team. How many ways can the team be selected?

55

400

State the contradiction statement of the following:

"There exists an even prime number"

All prime numbers are odd

400

How many subsets of {1,2,3} exist?

8

empty, 1, 2, 3, 12, 13, 23, 123

400

If A is transformed to A' by 0   1

                                        1    2

Find the matrix that will transform A' back to A

- (  2    -1   )

     -1     0

500

What does the vector projection of a in the direction of b represent geometrically?

The component of that is parallel to b

500

Your friend offers you any of six books that she no longer wants. How many selections are possible assuming that you take at least one book?

2^6 - 1 = 63

500

Is 5n^2 + 3n + 7 odd or even? Briefly describe your process.

Sub n=2m and simplify.  Will get 2()+1 therefore odd.

500

A triangle of area 5 is transformed by matrix

1   2

3    1

What is the area of the resulting triangle?


25

500

State the transformation matrix for a reflection in the line y=x

0     1

1     0