Quant

Question 1

Primes

Answer 1

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Question 2

% change formula

Answer 2

(change amount/original amount)*100

Question 3

Slope

Answer 3

Rise/Run –> (y2-y1)/(x2-x1)

Question 4

Special Products: Difference of Squares

Answer 4

x^2-y^2 –> (x+y) (x-y)

Question 5

Special Products: (x+y)^2

Answer 5

x^2+2xy+y^2

Question 6

Special Products: (x-y)^2

Answer 6

x^2-2xy+y^2

Question 7

Area of a Triangle

Answer 7

area = 1/2 base*height

Question 8

Angles in a Triangle

Answer 8

All angles sum to 180* –> x+y+z=180

Question 9

Similar Triangles

Answer 9

Similar Triangles have all the same angles and sides that are proportionate (a:c equals d:f)

Question 10

The Side Rule

Answer 10

The third side of a triangle is greater than the difference of the other two sides and less than their sum (a+b) > c > (b-a)

Question 11

Area of a rectangle

Answer 11

length * width

Question 12

Area of a square

Answer 12

side^2

Question 13

Area of a parallelogram

Answer 13

base * height

Question 14

Sum of angles in a polygon

Answer 14

sum of angles in a polygon = 180(n-2) –> (n = number of sides)

Question 15

volume of a box

Answer 15

volume = lwh

Question 16

surface area of a box

Answer 16

2lw + 2wh + 2lh

Question 17

volume of a cylinder

Answer 17

volume = ∏r^2h

Question 18

Surface area of a cylinder

Answer 18

Surface area = 2∏r^2 + 2∏rh

Question 19

Central angle

Answer 19

A central angle has a vertex that lies at the center point of the circle. An inscribed angle has its vertex on the circle itself rather than on the center of the circle. An inscribed angle is equal to half of the arc it intercepts

Question 20

Diameter of a circle

Answer 20

2r - if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle must be a right angle.

Question 21

Area of a circle

Answer 21

Area = ∏r^2

Question 22

Circumference

Answer 22

∏d OR 2∏r

Question 23

Pythagorean Theorem

Answer 23

In a right triangle, a^2 + b^2 = c^2 –> where a and b are the legs (shorter sides) and c is the hypotenuse

Question 24

Pythagorean Triples

Answer 24

The most common are: 3-4-5, 5-12-13, 7-24-25, and 8-15-17

Question 25

Angle/side relationship

Answer 25

Side length corresponds with angle size.

Question 26

Special Right Triangles

Answer 26

30-60-90 and 45-45-90

Question 27

Isosceles Triangle

Answer 27

Two sides are the same length

Question 28

Equilateral Triangle

Answer 28

All sides are the same length and all angles are 60*

Question 29

Sector

Answer 29

Sector area and arc length are proportional to angle size. Here, the angle is 60*. Since there are 360* in a circle, the sector (grey area) takes up 1/6 of the circle. Thus, its area is 1/6 of the total area, and its arc length is 1/6 of the circumference.

Question 30

Lines and Angles Equation

Answer 30

All angles in a line add to 180* --> x+y = 180

Question 31

Parallel Lines

Answer 31

When a line intersects with two parallel angles, the resulting intersections are identical

Question 32

Intersecting Lines

Answer 32

When two lines intersect, opposite angles are equal

Question 33

Distance Formula

Answer 33

√(x2-x1)^2 + (y2-y1)^2

Question 34

Line Equation on a graph

Answer 34

y=mx+b --> m=slope, b=y-intercept

Question 35

Midpoint Formula

Answer 35

((x1+x2)/2, (y1+y2)/2)

Question 36

Find Degrees of Polygons (i.e hexagon)

Answer 36

(n-2) * 180

Question 37

Find the degree of a single angle of a polygon (i.e hexagon)

Answer 37

(n-2) * 180/n

Question 38

Evenly Spaced List Formulas

Answer 38

Mean = median Mean OR Median = (first + last)/2) # of #’s for consecutive integers = (last - first/1) + 1 # of #’s for odd integers = (last - first/2) + 1 Sum = (# of #’s) * mean

Question 39

Percent/Fraction/Decimal Conversions: 1%

Answer 39

1/100 - .01

Question 40

Percent/Fraction/Decimal Conversions: 5%

Answer 40

1/20 - .05

Question 41

Percent/Fraction/Decimal Conversions: 12.5%

Answer 41

1/8 - .125

Question 42

Percent/Fraction/Decimal Conversions: 25%

Answer 42

1/4 - .25

Question 43

Percent/Fraction/Decimal Conversions: 33.33%

Answer 43

1/3 - .33333

Question 44

Percent/Fraction/Decimal Conversions: 37.5%

Answer 44

3/8 - .375

Question 45

Percent/Fraction/Decimal Conversions: 40%

Answer 45

2/5 - .4

Question 46

Percent/Fraction/Decimal Conversions: 50%

Answer 46

1/2 - .5

Question 47

Percent/Fraction/Decimal Conversions: 60%

Answer 47

3/5 - .6

Question 48

Percent/Fraction/Decimal Conversions: 80%

Answer 48

4/5 - .8

Question 49

Percent/Fraction/Decimal Conversions: 87.5%

Answer 49

7/8 - .875

Question 50

Percent/Fraction/Decimal Conversions: 90%

Answer 50

9/10 - .9

Question 51

When I see comparison (>0, <0)

Answer 51

I know I’m dealing with positives and negatives

Question 52

When I see x^2

Answer 52

I know the result is positive OR 0 but x itself can be positive, negative or 0

Question 53

When I see x & y do not intersect

Answer 53

I know Line x & y are parallel

Question 54

When I see x only has one factor, m, such that 1

Answer 54

I know integer x is prime

Question 55

When I see x^4-9 OR x^2-1

Answer 55

I know this is a special product (difference of squares: x^2-y^2 = (x+y)(x-y)

Question 56

When I see (-1)^2x vs. (-1)^2x+1

Answer 56

I know 2x is even and 2x+1 is odd, therefore the first quantity is positive and the second is negative → true for all values of x

Question 57

What percentage falls between 1 standard deviation in both directions of a normal distribution?

Answer 57

68%

Question 58

What percentage falls between 2 standard deviations in both directions of a normal distribution?

Answer 58

95%