Semester 1 Midterm!!

Question 1

N

Answer 1

Natural Numbers

Question 2

Z

Answer 2

Integers

Question 3

Q

Answer 3

Rational Numbers

Question 4

Qc

Answer 4

Irrational Numbers

Question 5

R

Answer 5

Real Numbers

Question 6

C

Answer 6

Complex Numbers

Question 7

∈

Answer 7

is an element of, or belongs to
ex: a ∈ A

Question 8

∃

Answer 8

there exists

Question 9

∀

Answer 9

for all or for every

Question 10

: or |

Answer 10

such that

Question 11

->

Answer 11

an implication or mapping (when used with functions)
ex: f : A -> B is a function that maps or related elements of set A to those in set B

Question 12

Set

Answer 12

a well-defined collection of elements

Question 13

[a, b]

Answer 13

a ≤ x ≤ b

Question 14

(a, b)

Answer 14

a < x < b

Question 15

∪

Answer 15

or statement (all the elements are considered in any of the listed sets)

Question 16

Closure Addition

Answer 16

x + y ∈ R

Question 17

Commutative Addition

Answer 17

x + y = y + x

Question 18

Associative Addition

Answer 18

(x + y) + z = x + (y + z)

Question 19

Identity Addition

Answer 19

x + 0 = x

Question 20

Inverse Addition

Answer 20

x + (-x) = 0

Question 21

Closure Multiplication

Answer 21

x * y ∈ R

Question 22

Commutative Multiplication

Answer 22

x * y = y * x

Question 23

Associative Rules

Answer 23

(xy) z = x (yz)

Question 24

Identity Multiplication

Answer 24

x * 1 = x

Question 25

Inverse Multiplication

Answer 25

x * 1/x = 1, for x ≠ 0

Question 26

slope-intercept form

Answer 26

y = mx + b

Question 27

point-slope form

Answer 27

y - y1 = m(x - x1)

Question 28

standard form

Answer 28

Ax + By = C

Question 29

horizontal shift

Answer 29

g(x) = f(x + k)
k is positive: left shift
k is negative: right shift

Question 30

vertical shift

Answer 30

g(x) = f(x) + k
k is positive: shift up
k is negative: shift down

Question 31

reflection about y-axis

Answer 31

g(x) = f(-x)

Question 32

reflection about x-axis

Answer 32

g(x) = -f(x)

Question 33

vertical stretch or compression

Answer 33

g(x) = kf(x)
k > 1: stretch
0 < k < 1: compressed
k < 0: combination of vertical or combination, along with a vertical reflection

Question 34

find inverse

Answer 34

solve for x
put the y in the solution as an x
set as y = that thing you just did

ex:
y = 3x + 5
y - 5 = 3x
x = y-5/3
inverse function = x-5/3

Question 35

dotted line

Answer 35

points on line are NOT part of solution set

Question 36

solid line

Answer 36

points on line ARE part of solution set

Question 37

y <

Answer 37

shade below line

Question 38

y >

Answer 38

shade above line

Question 39

using matrices to solve systems

Answer 39

A * C = B
[(x1)^2 x1 1] * a = y1
[(x2)^2 x2 1] * b = y2
[(x3)^2 x3 1] * c = y3
C = A^-1 * B

Question 40

how to find determinant

Answer 40

A = ad - bc

Question 41

inverse of 2x2

Answer 41

1/det * [d -b]
[-c a]

Question 42

solve for matrix B

Answer 42

B = A^-1 * C
(A * B = C)

Question 43

Cramer’s Rule

Answer 43

{ax + by = e
{cx + dy = f

[a b] [x] = [e]
[c d] [y] = [f]

CRAMERS RULE:
x = Dx/D, y = Dy/D
D = (ad) - (bc)
Dx = (de) - (bf)
Dy = (af) - (ce)

Question 44

quadratic equation

Answer 44

x = (-b +- √b^2-4ac)/2a

Question 45

vertex

Answer 45

-b/2a

Question 46

vertex form

Answer 46

y = a(x - h)^2 + k

Question 47

vertical and horizontal translations

Answer 47

put in vertex form
h represents horizontal shift
k represents vertical shift

Question 48

reflection and dilation

Answer 48

if a is negative, parabola is reflected across x-axis
if |a| > 1, parabola is stretched vertically
is 0 < |a| < 1, parabola is compressed vertically

Question 49

discriminant

Answer 49

b^2 - 4ac
if d > 0: 2 roots
if d = 0: 1 root
if d < 0: no roots

Question 50

focal length

Answer 50

1/4a

Question 51

focal point

Answer 51

(h, k + a)

Question 52

directrix

Answer 52

y = k - p

Question 53

p

Answer 53

distance from the vertex to the focus

Question 54

modulus

Answer 54

√(a² + b²)

Question 55

find quadratic function from complex roots

Answer 55

convert (x - (a + bi))(x - (a - bi))
into y = ax^2 + bx +c