DAT Quantitative Reasoning

LCM (least common multiple)

least positive integer that is a multiple of 2+ numbers

GCF (greatest common factor)

greatest positive integer that is a divisor of 2+ numbers

Integer 0 is positive/negative and a even/odd number?

neither pos/neg, even number

x/0 is defined?

undefined

when x is negative, √x is defined?

undefined, cannot take the square root of a negative number in DAT due to no imaginary numbers in the test

when x is positive, √x is ?

positive, e.g. √25 is 5

when x² = a² , x = ?

± a

∥

parallel symbol

⊥

perpendicular symbol

Profit =

revenue - cost

Area of circle

π r²

Circumference of circle

2π r

Arc length of circle

S = 2π r (θ/360)

where θ is the angle of the arc

Area of arc of circle

A_sector = π r² (θ/360)

Equation of circle

(x-h)² + (y-k)² = r²

where (h,k) is the center of the circle

Area of triangle

½ bh

where b is base length and h is height length

Perimeter of triangle

add up side lengths

Area of equilateral triangle

(√3)/4 s²

where s is the side length

Area of rectangle

Lw

where L is length and w is width

Perimeter of rectangle

2L + 2w

Area of square

s²

Surface area of rectangular prism

SA = 2(Lw + Lh + hw)

Volume of rectangular prism

V = Lwh

Surface area of cylinder

SA = 2π rh + 2π r²

Volume of cylinder

V = π r²h

Surface area of sphere

SA = 4π r²

Volume of sphere

V = 4/3 π r³

Pythagorean theorem: for right triangles

a² + b² = c²

remember 3, 4, 5 and 5, 12, 13 right triangles and their triples

1 mile to feet

5280 feet

1 inch to cm

2.54 cm

1 mile to km

1.6 km

1 kg to lbs

2.2 lbs

1 gallon to liters

3.8 L

Speed up and downstream:

Sp_upstream= sp_boat - sp_river = x - y

Sp_downstream= sp_boat + sp_river = x + y

Simple Interest

A = P(1 + rt)

Compound Interest

A = P(1 + r/n)^nt

Discriminant

used to determine number of solutions;

Δ = b² - 4ac

Δ > 0

There are 2 distinct, real solutions

Δ < 0

There are no real solutions

Δ = 0

There is 1 real solution

Work-rate formula

Job = (Rate 1 + Rate 2) x time

Vertex of a parabola

x = -b/2a