ACT Math Review

multiplying matrices on calculator

1. press second then x^-1 (below “matrix”)

2. edit dimensions of A (rows x columns), then enter numbers

3. edit dimensions of B then enter numbers

4. press 2nd mode, go back to matrix and enter A then multiply by B

multiplying matrices by hand

1. use rows x columns, find dimensions for both

2. number of columns of first should match number of rows of second

3. resulting matrix will have outside numbers- number of rows of first by number of columns of second

4. first row x first column- add up then goes in left corner entry

scalene triangle

no vertical line of symmetry

quadratic formula

-b plus or minus square root of b² - 4ac over 2a

difference of squares

(x + y) (x - y) = x² - y²

Find the nth digit after the decimal

ex: 275th digit after repeating decimal 0.6295

divide the _____th digit by however many places there are in the repeating decimal. whatever the remainder is —is the number in that place of the repeating decimal

answer: 9

note: decimal x divisor = remainder

sum of 2 vectors

1. sliding- slide so the endpoint of the first one = the initial point of the second (tip to tail)

2. sum- line from initial point of first to end point of second

subtract 2 vectors

1. make 2nd vector’s direction opposite with the same magnitude

2. proceed adding vectors as normal

bimodal

two modes (like camel hump)

skewed left/skewed right

hump to left, hump to right

normal skew

hump in middle

uniform skewed

equal probability- one line

standard deviation

amount away from mean; when mean increases by a number, standard deviation stays the same

equation of an ellipse

(x-h)² /a² + (y-k)²/b² = 1

parts of an elipse

center: (h,k)

half of major: a

half of minor: b

distance of focus from center: c

find c: a² - b² = c²

average speed =

total distance/total time

log rules

log_b (xy) = log_b (x) + log_b (y)

log_b (x/y) = log_b (x) - log_b (y)

log_b (x^m) = m (log_b x)

log_{e =}

ln

If (hypothesis), then (conclusion)

converse: If (conclusion), then (hypothesis)

inverse: If not (hypothesis) then not (conclusion)

contrapositive: If not (conclusion), then not (hypothesis)

• always true

• switch it then make inverse

absolute value of a function

makes everything below x axis positive

sin x = 1/2

sin^-1 (1/2)

law of sines

a/sin A = b/sin B = c/sin C

law of cosines

a² = b² + c² - 2bc cos A

For a right triangle:

1. given 2 sides to find a side

2. given one side and one angle to find a side

1. pythagorean theorem

2. trig functions

For a non-right triangle:

1. AAS to find side

2. SSA to find angle

3. SAS to find side

4. SSS to find angle

1. law of sines

2. law of sines

3. law of cosines

4. law of cosines

area formula for non-right triangles

Area = ½ ab sin (C)

distance formula

square root of (x₂ - x₁)² + (y₂ - y₁)²

area of a parallelogram

A = bh

area of a trapezoid

A = ½ (b₁ + b₂)(h)

area of a regular polygon

A = ½ ap (p: perimeter)

volume of a prism

A = bh

surface area of a right prism

SA = 2B + Ph (B: area of base)

Volume of circular cylinder

V = πr²h

Surface area of a right circular cylinder

SA = 2πr² + 2πrh

Volume of a pyramid

V = Bh

surface area of a right pyramid

SA = B + ½ Ps (s: slant height)

Volume of a circular cone

V = 1/3 πr²h

surface area of a right circular cone

SA = πr² + πrs

volume of a sphere

V = 4/3 πr³

surface area of a sphere

SA = 4πr²

sum of degree measures in a polygon

(n-2)180

area of sector in a circle

(x/360)πr² (x = degree measure of central angle)

arithmetic sequence

a_n = a₁ + (n-1)d

arithmetic series

s_n = n/2 (a₁ + a_n)

simple interest

I = prt

compound interest

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

Distance =

rate x time

45 - 45 - 90 triangle

• hypotenuse: x√2

• base & height: x

30 - 60 - 90 triangle

• hypotenuse: 2x

• base opposite to 30 degrees: x

• base opposite to 60 degrees: x√3