Quantitative Reasoning

Question 1

How do you multiply fractions

Answer 1

Numerators x Numerators

Denominators x Denominators

Question 2

How do you divide fractions

Answer 2

Flip the second Fraction

Then multiply

Question 3

How do you add/subtract Fractions

Answer 3

get a common denominator and add/subtract the numerators (don’t change the denominator)

Question 4

How do you go about comparing Fractions

Answer 4

get a common denominator and compare

Question 5

How do you set up a ratio

Answer 5

of = on top
to = on bottom

Question 6

how do you solve a proportion

Answer 6

Cross multiply across the = sign

x/5 = 3/4
15/4

Question 7

How do you do long division

Answer 7

see how many times the deominator can go into the numerator

15/400 = .037

400 goes into .03 times
15.00 - 12.00 = 3
How many times does 400 go into 3 (.007)

Question 8

change .564 into a fraction

Answer 8

564/1000
282/500
141/250

Question 9

how do you divide decimals

Answer 9

make them whole numbers and divide

Question 10

what does percent =

Answer 10

part/whole

Question 11

How do you find % increase

Answer 11

amount of increase/ Original whole

Question 12

how do you find probability

Answer 12

of desired outcomes / # of possible outcomes

Question 13

If we rolled 2 dice, what would be the probability of a total of 4

Answer 13

3 possible desired outcomes / 36 total outcomes (6x6)

Question 14

how do you multiply powers with the same base

Answer 14

add the exponents

Question 15

how do you divide powers with the same base

Answer 15

subtract the exponents

Question 16

how do you raise the power to an exponent

Answer 16

multiply the exponents

Question 17

how do you multiply powers with the same exponent

Answer 17

multiply the bases keep the exponent

Question 18

how do you divide powers with the same exponent

Answer 18

divide the bases and keep the exponent

Question 19

how do you divide polynomials

Answer 19

you just simply do long division with polynomials

Question 20

What is finding a common factor in a polynomial

Answer 20

when you look at each part of the polynomial is there a common factor between all parts of the polynomial

Question 21

How do you recognize differences of squares

Answer 21

when you have two identifiable squares with a minus sign between them

Question 22

4x^2 - 9

Answer 22

(2x-3)(2x+3)

Question 23

Learn to recognize squares of binomials

Answer 23

a^2 + 2ab + b^2 = (a+2)^2

a^2 - 2ab + b^2 = (a-b)^2

Question 24

How can you factor out harder polynomials

Answer 24

plug in a 0 and see which answer equals the question. Then check all others to see if there are more. if there are more then plug in another number.

Question 25

What are two ways to get an unknown out of a denominator

Answer 25

1. multiply both sides by the unknown (if alone) | 2. get one fraction on each side and cross multiply

Question 26

how do get the unknown out of an exponent

Answer 26

You must get the bases to equal eachother. you do this by finding what they are both powers of (a common unpower)

Question 27

8^x = 16 ^ (x-1)

Answer 27

both are unpowers of 2 (2^3 = 8) (2^4 = 16) (2^3)^x = (2^4)^(x-1) 2^3x = 2^(4x-4) since the bases are equal you can just set the exponents equal to each other and solve for x

Question 28

How can you solve quadratic equations

Answer 28

1) get x^2 + x + # = 0 and try to factor the left side 2) quadratic formula (negative b plus or minus the square root of b squared minus 4 a c. all over 2a)

Question 29

How do you solve "in terms of" equations

Answer 29

get your variable all alone

Question 30

What do you do here ax-x = something

Answer 30

divide by a-1

Question 31

what do you do for aboslut values

Answer 31

think of it as two equations

Question 32

What to remember when solving for an inequality

Answer 32

if you multiply or divide by a negative number you must flip the sign

Question 33

When you have (absolute value) < X | or (absolute value) > X

Answer 33

you leave the sign the same - X < (absolute value) < X - X > (absolute value) > X

Question 34

how do you find the area of a triangle

Answer 34

1/2 (base)(Height)

Question 35

What is the triangle inequality theorum

Answer 35

the length of the third side is smaller than the two other sides added together, but larger than the larger side minus the smaller one

Question 36

what does the sum of the interior angles of a triangle =

Answer 36

180

Question 37

what does the sum of the exterior angles of a triangle =

Answer 37

360 (a polygons)

Question 38

What to remember about similar triangles

Answer 38

1. Figure out if they are indeed similar 2. If so they have the same angles, and their sides are proportional 3. The area of the triangles go as follows - proportional side ratio 2:1 area equals x^2 - proportional side ratio 3:1 area equals 3^2 (what ever the ratio is, that is raised to the power of two for area)

Question 39

Isosceles triangle

Answer 39

when two sides, and two base angles are the same

Question 40

How do you find the area of an equilateral triangle

Answer 40

S^2(Square root of 3)/4

Question 41

What are some pythagorean triplets

Answer 41

``` 3,4,5 5,12,13 7,24,25 8,15,17 9,40,41 11,60,61 ```

Question 42

What is the ratio of sides in a 45,45,90 triangle

Answer 42

1: 1:1(Square root of 2) 2: 2:2(square root of 2)

Question 43

What is the ratio of sides in a 30,60,90 triangle

Answer 43

1:(Square root of 3):2 2:2(square root of 3):2 Hypoteneuse is twice the size of the shortest leg, and the other leg is the short leg times by the square root of three

Question 44

What is the area of a trapezoid

Answer 44

(Base1 + base2)/2 *height | The bases are the two parallel sides

Question 45

What is the area of a parallelagram

Answer 45

base * height

Question 46

What is the area of a hexagon

Answer 46

3s^2(square root of three)/2

Question 47

How do you find the circumference of a circle

Answer 47

2(pie)r | (pie)d

Question 48

How do you find the length of an ARC

Answer 48

(n/360)(2"pie"r)

Question 49

how do you find The area of a circle

Answer 49

"pie"r^2

Question 50

How do you find the area of a sector

Answer 50

(n/360)("Pie"r^2)

Question 51

how do you find the lateral area of a cone

Answer 51

1/2cl c = base circumference l = slant height

Question 52

How do you find the volume of a cone

Answer 52

1/3"pie"r^2*h

Question 53

how do you find the surface area of a sphere

Answer 53

4"pie"r^2

Question 54

How do you find the volume of a sphere

Answer 54

4/3"pie"r^3

Question 55

How do you find the volume of a pyramid

Answer 55

1/3Bh

Question 56

how do you find the surface area of the rectangular solid

Answer 56

2lw + 2wh + 2 lh

Question 57

how do you find the volume of an uniform solid

Answer 57

area of the base * height

Question 58

how do you find the area of a rectangular solid

Answer 58

lwh

Question 59

How do you find the volume of a cube

Answer 59

side^3

Question 60

How do you find the volume of a cylinder

Answer 60

"pie"r^2 * h

Question 61

How do you find distance between points on a grid

Answer 61

Distance = Square root of (x1-x2)^2 + (y1-y2)^2

Question 62

What are the slopes of two perpendicular lines

Answer 62

one and it's opposite reciprocal | 2 and -1/2

Question 63

how do you find the turning point on a graph with an absolute value

Answer 63

Not sure yet, maybe whatever value makes the absolute value thing = 0

Question 64

What is the reciprocal of sine, cosine, and tangent

Answer 64

cosecant, secant, cotangent

Question 65

What does sin^2 x + cos^2 x = ?

Answer 65

sin^2 x +cos^2 x = 1

Question 66

What does tan^2 x + 1 =

Answer 66

tan ^2 x + 1 = sec ^2 x

Question 67

What does 1 + cot^2x = ?

Answer 67

1 + cot^2x = csc^2 x

Question 68

what does 2 pie radians =

Answer 68

360 degrees

Question 69

What does 1 Radian =

Answer 69

180/pie (57.3 degrees)

Question 70

what does 3 radians =

Answer 70

360/2pie

Question 71

what does sin 0 =

Answer 71

0

Question 72

What does sin 30 =

Answer 72

1/2

Question 73

what does sin 45 =

Answer 73

1/ square root of 2

Question 74

what does sin 60 =

Answer 74

3/2

Question 75

what does sin 90 =

Answer 75

1

Question 76

What does cos 0 =

Answer 76

1

Question 77

what does cos 30 =

Answer 77

3/2

Question 78

what does cos 45=

Answer 78

1/ square root of 2

Question 79

what does cos 60 =

Answer 79

1/2

Question 80

what does cos 90 =

Answer 80

0

Question 81

what does tan 0 =

Answer 81

0

Question 82

what does tan 30 =

Answer 82

1/ square root of 3

Question 83

what is tan 45

Answer 83

1

Question 84

what is tan 60

Answer 84

square root of 3

Question 85

what is tan 90

Answer 85

not defined

Question 86

what is cot 0

Answer 86

not defined

Question 87

what is cot 30

Answer 87

square root of 3

Question 88

what is cot 45

Answer 88

1

Question 89

what is cot 60

Answer 89

1/ square root of 3

Question 90

what is cot 90

Answer 90

0

Question 91

what is sec 0

Answer 91

1

Question 92

what is sec 30

Answer 92

2/ square root of 3

Question 93

what is sec 45

Answer 93

square root of 2

Question 94

what is sec 60

Answer 94

2

Question 95

what is sec 90

Answer 95

not defined

Question 96

what is cosec 0

Answer 96

not defined

Question 97

what is cosec 30

Answer 97

2

Question 98

what is cosec 45

Answer 98

square root of 2

Question 99

what is cosec 60

Answer 99

2/ square root of 3

Question 100

what is cosec 90

Answer 100

1

Question 101

What happens to the sins cos as you pass 90 degrees

Answer 101

you just begin to go back, so sin 60 = sin 120 cos 15 = cos 105

Question 102

What happens to the sins and cos as you pass 180 degrees

Answer 102

you just make the normal one negative | sin -30 = -1/2

Question 103

What does the sin -1 of 7/74

Answer 103

sin Angle = 7/74

Question 104

How do you get the volume of a prism

Answer 104

V = base area x h

Question 105

What is the area of an equilateral triangle

Answer 105

Area = [S^2 (square root of 3)]/4

Question 106

how do you find the center of a circle (X-2)^2 + (Y-5)^2

Answer 106

x= 2, y= 5 | (2,5) is the center of the circle

Question 107

What does tan (theta) =

Answer 107

sin (theta)/cos (theta)

Question 108

what does Sec =

Answer 108

1/cos

Question 109

what does sin^2 + cos^2 =

Answer 109

1

Question 110

what does sin =

Answer 110

Cos x Tan

Question 111

what are the sin/cos/tan values for Quadrant 1,2,3,4

Answer 111

Quadrant 1 +sin, +cos, +tan Quadrant 2 +sin, -cos, -tan Quadrant 3 -sin, -cos, + tan Quadrant 4 -sin, +cos, -tan

Question 112

what does pie/6 =

Answer 112

30 degrees

Question 113

what is the equation for annual interest

Answer 113

``` A = P(1 + (r/n)^nt A = amount in the account P = starting amount r = interest rate (decimal) n = number of times compounded anually t = time in years ```