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Mathematics Formula Handbook
Kim Hanson
Dover Adult Learning Center
2009
This handbook is a study aid designed to complement the GED Math
formulas that are given with the GED test. The formula page is attached
at the end.
Table of Contents
AREA OF SQUARES 2
AREA OF RECTANGLE 3
AREA OF PARALLELOGRAMS 4
AREA OF TRIANGLES 5
AREA OF TRAPEZOIDS 6
AREA OF CIRCLES 7
PERIMETER OF SQUARES 8
PERIMETER OF RECTANGLE 9
PERIMETER OF TRIANGLES 10
CIRCUMFERENCE OF A CIRCLE 11
VOLUME OF A CUBE 13
VOLUME OF A RECTANGULAR SOLID 15
VOLUME OF A SQUARE PYRAMID 16
VOLUME OF A CYLINDER 17
VOLUME OF A CONE 18
THE DISTANCE FORMULA 19
THE SLOPE FORMULA 20
THE PYTHAGOREAN RELATIONSHIP 21
MEAN & MEDIAN 22
SIMPLE INTEREST 23
DISTANCE 24
1
TOTAL COST 26
2
Area of Squares *************************************************************
************
To find the area (A) of any square, multiply its side times its side.
A = side 2OR A = side × side
A = s 2 OR A = s × s
s = 5 A = 5 2 OR A = 5 × 5
A = 25
s = 5
*************************************************************
************
Find the area of each square. Round answers to nearest hundredth.
1. 2. 3.
3in 6.3ft 98m
A =
A =
A =
4. A picture frame measures 2
12
feet on each side. Which
expression below represents the
area of the frame?
a) 4 !"
#$%
&
2
12
b) 2
2
12 !
"
#$%
&
c) 42
2
12 !
"
#$%
&
d) 3
2
12 !
"
#$%
&
5. If a square has an area of 1600
square feet, what is the length of
each side in feet?
a) 20 b) 40 c) 100 d) 400 e) 800
3
Area of Rectangle *************************************************************
************
To find the area (A) of any rectangle, multiply its length times its width.
A = length × width
A = l × w
w = 3 A = 6 × 3
A = 18
l = 6
*************************************************************
************
Find the area of each rectangle. Round answers to nearest hundredth.
1. 2.
w = 3m
l = 5m w = 5.2in
l = 9.7 in
A = _____________
A = _____________
3. w = 12yd.
l = 22yd.
A = _____________
4. A tile-layer is working on a
bathroom that is 8ft. by 6ft. If he
is using 12-inch square tiles how
many does he need to complete
this job?
a) 576 b) 96 c) 72 d) 48 e) 14
4
5. A rectangular garden has an
area of 154 square feet. If the
width is 11 feet, what is the
length?
a) 1694 feet
b) 165 feet c) 143 feet d) 14 feet e) 11 feet
Area of Parallelograms *************************************************************
************
To find the area (A) of any parallelogram multiply its base times its
height.
A = base × height
A = b × h
A = 9 × 8
A = 72
b = 9
*************************************************************
************
Find the area of each parallelogram. Round answers to nearest
hundredth.
1.
6in
A = _____________
2. 4.7cm
A = _____________
3.
A = _____________
h = 8
2.3cm 5in
8 ft
15ft
5
4. The area of a parallelogram is
1236.75 m 2 . Find the base in
meters when the height is 25.5m.
Round answer to the nearest tenth.
a) 48.5 b) 618.4 c) 643.8 d) 1211.3 e) 1262.3
5. Find the area of the
parallelogram in inches with a
base of 30in and a height of 2ft.
a) 32 b) 60 c) 120 d) 360 e) 720
Area of Triangles *************************************************************
************
To find the area (A) of any triangle, multiply2
1its base times its height.
b = 10
A = 2
1× base × height
A = 2
1× 10 × 6
A = 2
1× 60
A = 30
*************************************************************
************
Find the area of each triangle. Round answers to nearest hundredth.
1.
4m
A = _____________
2.
A = _____________
3.
h = 6
4m 3.4yd
5.7yd
6
A = _____________
4. Matt bought a sailboat and knows
the area of one triangular sail is
45yd2. If the base of the sail is 9yds,
what is the height?
a) 5yd
b) 10yd
c) 36yd
d) 54yd
e) not enough information
5. Jane wants to make triangular
flags. The base is 6in. and the
height is 8in. How many flags can
she make from a piece of
rectangular canvas 2ft by 3ft.
a) 4
b) 8
c) 9
d) 18
e) 36
Area of Trapezoids *************************************************************
************
To find the area (A) of any trapezoid, multiply2
1the sum of the bases times its height.
71=b
10
2=b
A = 2
1× (base
1+ base
2)× height
A = ( ) 41072
1!+!
A = ( )4172
1!!
A = 34
*************************************************************
************
Find the area of each trapezoid. Round answers to nearest hundredth.
1.
A = _____________
3in
5in 4in
h = 4
6in
8in
4in
7
2.
A = _____________
3.
A = _____________
4. The pool in the back of the YMCA is
in the shape of a trapezoid. Use the
diagram to find the area of the pool.
a) 225 square ft
b) 300 square ft
c) 450 square ft
d) 600 square ft
e) 900 square ft
5. A trapezoid shaped playground has
an area of 54 yd2. Find the height of
the playground if the sum of the
bases equals 12 yd.
a) 4.5 yd
b) 9 yd
c) 66 yd
d) 324 yd
e) 648 yd
Area of Circles *************************************************************
************
To find the area (A) of any circle, multiply π times the radius squared.
A = π × radius 2
A = π × 2r
A = 3.14 × ( )23
A = 3.14 × 9
A = 28.26
*************************************************************
************
Find the area of each circle. Round answers to nearest hundredth.
5.3ft
2.8ft
3.7ft
12m 16m
10m 2.9ft
r = 3
YMCA
10ft
20ft 30ft
8
1.
A = _____________
2.
A = _____________
3.
A = _____________
4. Jarvis Industries created a
circular garden this year. The
radius is 12feet. They want to
cover it with bark chips. One bag
covers 50 ft 2 . How many bags
will they need?
a) 3 b) 5 c) 10 d) 75 e) 144
5. Vinnie’s Pizzeria has an 8in
small pizza, 12in medium, and
16in large. Which has more
pizza 4 smalls, 2 mediums, or
1 large?
a) Smalls
b) Mediums
c) Large d) All the same
e) Not enough information
Perimeter of Squares *************************************************************
************
To find the perimeter (P) of any square, multiply 4 times its side.
P = 4 × side
s = 6 P = 4 × s
P = 4 × 6
P = 24
s = 6
*************************************************************
************
Find the perimeter of each square.
1. 2. 3.
r = 5in r = 1.2m
r = 7.25ft
9
s = 25 cm
P = _________ s = 22
1m
s = 17.6 cm P = _________
P = _________
4. If a square has a perimeter of
900 feet, what is the length of
each side?
a) 30 b) 90 c) 100 d) 225 e) 450
5. Jen’s backyard is in the shape
of a square. What’s the perimeter,
if the length of the side is 12.5ft?
a) 25ft b) 50ft c) 125.5ft d) 156.25ft e) 200ft
6. Which of the following
expressions would be used to
determine the perimeter of the
picture frame?
a) 2(30) + 2(40)
b) 4(40-30) c) 4(40) d) 2 + (30×40)
e) 30 + 40
Perimeter of Rectangle *************************************************************
************
To find the Perimeter (P) of any rectangle, multiply 2 times the sum of
its length and its width.
P = 2 × length + 2 × width
w = 4 P = 2 × 8 + 2 × 4
P = 16 + 8
l = 8 P = 24
40m
30m
10
*************************************************************
************
Find the perimeter of each rectangle. Round answers to nearest tenth.
1. 2. 3. w =6in
w = 25yd
l = 12in l = 3.5ft
P = _________ l = 55yd
w = 1.4ft P = _________
P = _________
4. Robert is placing weather
stripping around the front door of
his house. The door is 7feet by
4.5feet. How many feet of
weather stripping will he need?
a) 18 b) 23 c) 48 d) 63 e) 98
5. Which of the following
expression would be used to
determine the perimeter of the
frame of the mirror?
a) 2(24÷12)
b) (24+12) × (24+12)
c) 2(24) + 2(12)
d) (24×12) – (24+12)
e) 2 + (24×12)
Perimeter of Triangles *************************************************************
************
To find the Perimeter (P) of any triangle, add all sides together.
24 in
12in.
11
9
3=s
P = side1+ side
2+ side
3
P = 321sss ++
P = 7+ 8+ 9
A = 24
*************************************************************
************
Find the perimeter of each triangle.
1.
P = _________
2.
P = _________
3.
P = _________
4. Kaizy was fencing in her
triangular garden. Two sides
measured 14 feet and the third
side was 3 yards. How much
fencing in feet does she need?
a) 17 b) 23 c) 34 d) 37 e) 52
5. Mark needs to make a
triangular poster for his math
project. The perimeter needs to
be 72 inches. The sum of two
sides of the poster was 38 inches.
What is the length of the third
side?
a) 17in b) 23in c) 34in d) 37in e) 52in
Circumference of a Circle *************************************************************
************
82=s 7
1=s
12ft
8ft 6ft
55in 35in
22in
15m
15m 15m
12
To find the circumference (C) of any circle, multiply π times the
diameter.
C = π × diameter
C = π × d
C = 3.14 × 5
C = 15.7
*************************************************************
************
Find the Circumference of each circle. Round answers to nearest
hundredth.
1
d = 24mm
C = _________
2.
d = 6.8cm
C = _________
r =2
1d 2r
= d
3.
r = 4ft
C = _________
4. Lacey wants to install a fence
around her circular pool. The
radius of the pool is 9feet.
Approximately, how many feet of
fencing material will she need?
a) 10 b) 29 c) 57 d) 89 e) 255
5. The circumference of the
circular logo on the state flag is
314 cm. Find the radius in cm?
a) 3.14 b) 10 c) 31.4 d) 50
d = 5
13
e) 100 Volume of a Cube
*************************************************************
************
To find the volume (V) of any cube, multiply edge × edge × edge.
V = edge 3
V = 4 3
V = 4 × 4 × 4
V = 64
*************************************************************
************
Find the Volume of each cube. Round answers to nearest hundredth.
1.
V= _____________
2.
V= _____________
3.
V= _____________
4. What is the volume of a sugar
cube that measures 1cm on each
side?
a) 1cm 3
b) 10m 3
c) 100cm 3
d) 1000cm 3
e) 10000mm 3
5. Woodbury Toy Company
makes wooden cube blocks that
have 4in edges. How many
blocks can be packaged in a
cube-shaped shipping box
measuring 20 inches on each
edge?
e = 4
e = 2.3ft e = 8in e=
2
1 ft
14
a) 500 b) 125 c) 100 d) 64 e) 25
15
Volume of a Rectangular Solid *************************************************************
************
To find the volume (V) of any rectangular solid, multiply
length × width × height.
V = l × w × h
V = 10 × 3 × 5
V = 150
*************************************************************
************
Find the Volume of each solid. Round answers to nearest hundredth.
1.
V= _____________
2.
V= _____________
3.
V= _____________
4. Mason is making ice cubes for
his mother’s birthday party. Each
of the 12 compartments is 4cm
long, 3cm wide, and 2cm high.
Which expression could be used
to find the total volume of the
tray?
a) 2(4 + 3 + 2)
b) 3
1(4 × 3 × 2)
c) 12(4 × 3 × 2)
d) 4 × 3 × 2
e) 3.14(4 + 3 + 2)
5. The volume of a rectangular
pool is 1350yd 3 . Find the depth
of the pool given the length is
30yds and the width is 45feet.
a) 1 yd b) 3yd c) 9yd
l = 10 w = 3
h = 5
2.1cm
0.4cm 5cm
3
1yd
12yd
42
1yd
15in
11in 24in
16
d) 12yd e) 18yd
Volume of a Square Pyramid *************************************************************
************
To find the volume (V) of any square pyramid, multiply
3
1×(base edge) 2 × height.
V = 3
1 × e 2 × h
V = 3
1 × 5 2 × 9
V = 3
1 × 25 × 9
V = 75
*************************************************************
************
Find the Volume of each pyramid. Round answers to nearest hundredth.
1.
V= _____________
2.
V= _____________
3.
V= _____________
The Great Pyramid of Giza in Cairo, Egypt is the oldest and largest of
the three pyramids. The base edge measures about 756.2ft and the
original height was about 480.97ft. It is believed to be 4,569 years old.
Through erosion and the loss of pyramidion (capstone-upper most piece)
the current height is 455ft.
e = 5
h = 9
e = 5
e = 16m
h = 18m h = 1.2in
e = 5.4in
h = 54
3ft
e = 7ft
17
4. Find the current volume of the
Great Pyramid in feet. Round to
nearest whole number.
5. What is the difference between
the volumes of the original and
current pyramid? Round to
nearest whole number.
Volume of a Cylinder *************************************************************
************
To find the volume (V) of any cylinder, multiply
π × radius 2 × height.
V = 3.14 × r 2 × h
V = 3.14 × 5 2 × 6
V = 3.14 × 25 × 6
V = 471
*************************************************************
************
Find the Volume of each cylinder. Round answers to nearest hundredth.
1.
V= _____________
2.
V= _____________
3.
V= _____________
4.
What is the difference between
the volumes of the 2 cylinder
tubes? Round all answers to the
nearest whole number.
a) 88in 3
b) 351in 3
h = 6
r =5
r = 12cm
h = 22cm
h = 3.25in
r = 5.5in
h = 104
1yd
d = 8yd
r = 4in r = 6in
h = 8in h = 10in
18
c) 729in 3
d) 1080in 3
e) 25,398in 3
5. A tuna fish can has an
approximate volume of 201cm 3 .
Find the diameter, if the height of
the can is 4cm.
a) 4cm
b) 8cm
c) 16cm
d) 20cm
e) 32cm
Volume of a Cone *************************************************************
************
To find the volume (V) of any cone, multiply
3
1× π × radius 2 × height
V = 3
1 × π× r 2 × h
V = 3
1 × 3.14 × 4 2 × 10
V = 3
1 × 3.14 × 16 × 10
V = 167.47
*************************************************************
************
Find the Volume of each cone. Round answers to nearest hundredth.
1.
V= _____________
2.
V= _____________
3.
TUNA
r = 4
h = 10
r = 6in
h = 16in
h = 1yd
r = 34 yd
19
V= _____________
4. In art class Mary created a
3-dimensional cone shaped
piece. If the area of the circular
base measures 28.26in 2 and the
height is 1 foot. What is the
volume?
a) 9.42in 3
b) 29.58in 3
c) 113.04in 3
d) 354.95in 3
e) 835.90in 3
5. A pile of sand is in the shape
of a cone. The pile is 4 yards high
and the diameter of the pile is 18
feet. How many cubic yards of
sand are in the pile?
a) 4,069.44 b) 1,356.48 c) 339.12 d) 301.44 e) 37.68
The Distance Formula *************************************************************
************
To find the distance between 2 points ( ) ( )2211
,,, yxyx substitute values into
D = ( ) ( )212
2
12yyxx !+!
Find the distance between (2,1) and (6,4) 6
2
2
1
=
=
x
x
4
1
2
1
=
=
y
y
D = ( ) ( )22
2426 !+!
D = ( ) ( )22
24 +
D = 416 +
D = 20
D = 4.47
*************************************************************
************
Find the distance. Round answers to nearest hundredth.
1. (3,10) and (1,8) 2. (0,0) and (5,10)
h = 55m
d = 30m
20
3. (2,1) and (4,0) 4. (-2,-2) and (4,-1)
5. Point S is located at (-5, 2)
and point T is located at (0, -3).
To the nearest whole unit, what’s
the distance between points S &
T.
a) 0 b) 5 c) 7 d) 10 e) 20
6. The 4 vertices of a square are
placed on the coordinate grid.
A(-3, -3);B(-3, 3);C(3, 3);D(3, -3).
Find the distance of its diagonal
to the nearest whole unit.
a) 3 b) 6 c) 9 d) 11 e) 13
The Slope Formula *************************************************************
************
To find the slope using coordinate points ( ) ( )2211
,,, yxyx substitute values
into the formula:
Slope = 12
12
xx
yy
!
!
Find the slope (2,1) and (6,2) 21=x 6
2=x 1
1=y 2
2=y
Slope = 12
12
xx
yy
!
! =
26
12
!
! =
4
1
*************************************************************
************
Use the formula to find the slope of each line
1. (3, 4) and (6, 8) 2. (1, 1) and (2, 5)
21
3. (-2, 5) and (3, -1) 4. (0, 0) and (-5, -3)
5. Which of the following
expressions represents the
slope of the line above.
a) 3
4
!
b) 4
3!
c) 43
34
+!
+!
d) )3(4
)3(4
!!
!!
e) 34
34
+
!
6. Which value represents the
slope of a line that would be
parallel to the given line above?
a) -3 b) -1 c) 0 d) 1 e) 4
The Pythagorean Relationship *************************************************************
************
In a right triangle, the square of the length of the hypotenuse (the longest
side) is equal to the sum of the squares of the lengths of the legs (the
shorter sides).
a 2 + b 2 = c 2
4 2 + 3 2 = 5 2
16 + 9 = 25
(-3,-3)
(4,4)
b = 3 c = 5
a = 4
22
*************************************************************
************
Use the Pythagorean Relationship to find the unknown measurement.
Round to the nearest hundredth.
1.
c = _____________
2.
b = ________________
3.
a = ________________
4. Jon hiked 8 mi south and 6 mi
west. Which expression can be
used to find the straight line
distance in miles that Jon is from
his start?
a) 2268 +=d
b) 2268 !=d
c) ( )2
68+=d
d) 2268 !=d
e) 2268 +=d
5. Each side of a baseball
diamond is 90ft long. Find the
distance it is from 2nd base to
home plate in yards. Round to
nearest whole number.
a) 360 b) 180 c) 127 d) 60 e) 42
Mean & Median *************************************************************
************
To find the mean (average) add the numbers & divide by total number in the
set.
mean n
xxxn
+++=
...21
x’s are the given data set and
n is the total number in the set.
1) Find the sum of data
2) Count number in set
3) Divide
Find the mean of the given set:
2,5,4,4,6,1,3
Find sum: (3+5+5+4+6+2+3) = 28 Count total number in the set n = 7
a = 10
b = 20 a = 12
c = 18 b = 27
c = 45
1st
2nd
3rd
HOME
23
Divide: 28 ÷ 7 Mean = 4
------------------------------------------------------
---
To find the median first put the numbers in ascending order and find the middle
number. If there are two middle numbers, then find the mean (average) of them.
Example #1
Set: 6, 9, 1, 4, 5, 6, 5
1, 4, 5, 5, 6, 6, 9
median = 5
Example #2
Set: 3, 4, 6, 7, 4, 2
2, 3, 4, 4, 6, 7
two middle numbers are 4 & 6
mean (4 +6) =10 ÷2 = 5
median = 5
*************************************************************
************ 1. Set: 16, 12, 11, 10, 9, 12, 15, 10, 13 2. Set: 22, 25, 33, 31, 28, 33, 30, 30
Mean:_________ Mean:_________
Median:_______ Median:_______
Questions 3 & 4 refer to the table.
Store Haircut Color
Kute Kuts $30.00 $50.00
Maley’s Design $35.00 $65.00
Hair Extravaganza $32.00 $55.00
Happy Scissors $30.00 $48.00
Cut-O-Rama $30.00 $55.00
Scissor Hands Salon $32.00 $52.00
3. What is the mean price of haircuts
at the 6 stores in the table?
a) $32.00
b) $30.00
c) $31.00
d) $31.50
e) $32.50
4. Find the median price of a color at
the 6 stores in the table?
a) $55.00
b) $53.50
c) $50.00
d) $52.50
e) $48.00
Simple Interest *************************************************************
************
To find the interest multiply principal × rate × time.
i = p × r × t
24
You borrow $2,500 from New England Bank for a time period of 4 years.
The current rate is 12%.
a) How much interest will you
pay in the 4 year period?
i = p × r × t
= 2500 × 0.12 × 4
= 1200
You will pay $1,200 interest.
b) How much interest will you
pay if the time period is only 3
years?
i = p × r × t
= 2500 × 0.12 × 3
= 900
You will pay only $900 interest.
*************************************************************
************
Complete the table. Time is represented in years.
principal rate time interest
$500 15% 2
$2,200 7% 1.5
$15,000 5% 5
$5,500 14% 3.5
1. How much interest is earned on
$800 in 4 years in a savings
account that pays a 2% rate?
a) $6.4 b) $64 c) $640 d) $6,400 e) not enough information
2. You borrow $12,500 from the
bank to buy a car. The rate is 6%
and the term of the loan is 2 yrs.
What is the total amount you will
pay back?
a) $1,500 b) $4,250 c) $7,775 d) $14,000 e) $21,250
Distance *************************************************************
************
25
To find the distance multiply rate × time.
d = r × t
An airplane travels 300 miles/hour and flies for 2 hours. Find the distance.
d = r × t
= 300 × 2
= 600 The airplane flew 600 miles.
*************************************************************
************
To find the rate use: To find the time use:
t
dr =
r
dt =
*************************************************************
************
Complete the table. Time needs to be represented in hours.
Round answers to the nearest tenth.
distance rate (mph) time
7.1 mph 42min
6miles 50min
8miles 6 mph
10miles 1hr 40min
1. A train travels at an average
speed of 150 miles per hour. At
this rate, how many hours will it
take the train travel 900 miles?
a) 150 b) 100 c) 90 d) 6 e) 1
2. Kim ran 3 mi. in 362
1minutes.
What was her rate?
a) 4.93 mph
b) 7.23 mph
c) 10.5 mph
d) 12.2 mph
e) 13.4 mph
26
Total Cost *************************************************************
************
To find total cost multiply the (number of units) × (price per unit).
Sara bought a 15lb. pumpkin for her niece. Pumpkins are $0.33 per pound.
How much did Sara pay for the pumpkin?
number of units = 15lbs. price per lb. = $0.33
15 × .33 = $4.95
Sara paid $4.95 for the pumpkin.
*************************************************************
************
Complete the table. Round answers to nearest hundredth.
number of units price per unit total cost
180 $0.02
68 $44.50
4 $123
6024 $0.15
1. A 5lb of potatoes sells for
$2.49. Which expression could be
used to find the cost of one potato
if there are 15 in the bag?
a) $2.49÷5
b) $2.49×15
c) $2.49÷15
d) $2.49 + 5(15)
e) 15÷$2.49
2. Lori ordered thirty 54” curtains
to put up at church. Estimate the
total cost if each curtain costs
$25.99.
a) $246 b) $320 c) $624 d) $780 e) $940
27
28
