why is there a 600

Domain and Range

100

Find the domain of

h(x) = 41x + 67

{x|x∈R}

200

For which values of x is the following function not defined?

e(x) = 1/(x² - 1)

at x = 1, -1

300

Evaluate the range of

L(x) = √(4 - x²)

{y|0≤y≤2, y∈R}

400

My domain is {x≤2, x∈R}

My range is {y|y≥0, y∈R}

What function could I be?

√(2-x)

[or any other which fits]

600

Find the range of the general monic quadratic function

y = x² + px + q

{y| y ≥ q - p²/4, y∈R}

Set Notation and Exclusion Principle

100

A = {odd numbers less than 10}

Find the number of elements in A

n(A) = 5

200

A = {positive even numbers less than 100}

B = {positive perfect squares less than 100}

C = A ∩ B

Find and write the contents of C

C = {4, 16, 36, 64}

300

If:

n(A) = 15

n(B) = 12

n(A ∪ B) = 20

n(A ∩ B) = ?

7

400

Some students were interviewed in a sports survey.

12 people play Basketball, 21 people play Football, and 15 people play Volleyball. 8 people play Basketball and Football, 7 people play Basketball and Volleyball, 12 people play Football and Volleyball. If 5 people played all sports, and 4 people don't play sports at all, how many students were surveyed?

30

600

How many numbers from 1 to 1000 are divisible by 2 OR 3?

(Hint: Consider A to be the set of numbers divisible by 2, then consider B to be the set of numbers divisible by 3)

667

Vectors

100

Given that:

A = 2i + 3j

B = -6i + 7j

Find A + B

-4i + 10j

200

Show that the dot product of a plane and a line which are orthogonal equal to 0 using column vectors and matrices

april fools; free 200 points

300

It is given that Vector A = 2a - 3b

If Vector B = 4a + kb, and A is parallel to B, find the value of k

-6

600

Draw a parallelogram ABCD. P is the midpoint of BC, Q is the midpoint of CD, R is the midpoint of AD, and S is the midpoint of AB.

What is the shape of quadrilateral PQRS? (Hint: Consider vectors AB = b and AD = a)

Parallelogram

Functions

100

If f(x) = 2x + 1

Find f(3)

7

200

Given that f(x) = (x+1)/2

Find f^-1(2)

3

300

f(x) = 3x - 1

g(x) = x² - x + 3

Find the value of x where f(x) = g(x)

x = 2

400

Given that f(x) = (10 - 2x)/(x + 2)

Evaluate ffffff(4)

4

600

Given that:

f(x) is a linear function in the form of 2x + A

g(x) is a quadratic function in the form of x² + px + q

If gf(2) = q, find the value of A

Hint: It'd be too obvious if I gave you one...

-4

Combinatoricsand Probability

100

How many ways are there to arrange 5 letters (A,B,C,D,E)?

120

200

A dice is rolled 3 times. What is the probability that the dice shows the number "5" at least once?

91/216

300

A four digit-code (each digit ranges from 0-9 with no repeating digits) is guaranteed to begin with the number 6. If I had to guess the code, what is the probability that I get it correct?

1/504

400

How many ways are there to sort 6 apples and 4 oranges?

210

600

Given the following letters: S, T, L, U, C, I, A

What is the probability that if these letters are randomly arranged, the result has vowels on both ends (example: ASCTLUI)

(hint: the very first step is to find how many ways there are to choose 2 vowels to be on both ends)

1/7