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Mathematics Reference Sheets

Grades 6-8 FCAT mathematics Reference Sheet

Area
KEY
b = base

h = height

l = length

w = width

S.A. = Surface area

d= diameter

r = radius

A = area

C = circumference

V = volume

Use 3.14 or 22/7 for p

 

Triangle

 

A = 1/2 bh

 

 

Rectangle

 

A = lw

 

 

Trapezoid

 

A = 1/2 h(b1 + b2)

 

 

Parallelogram

 

A = bh

 

Circumference
C = pd = 2pr

Circle A = pr2


In a polygon, the sum of the measures of the interior angles is equal to 180(n - 2), where n represents the number of sides.

 

Pythagorean theorem: c2 = a2 + b2



Volume
Total Surface Area

Right Circular Cylinder V = pr2h S.A. = 2prh + 2pr2
       
Rectangular Solid V = lwh S.A. = 2(lw) + 2(hw) + 2(lh)


Conversions
1 yard = 3 feet = 36 inches
1 mile = 1,760 yards = 5,280 feet
1 acre = 43,560 square feet
1 hour = 60 minutes
1 minute = 60 seconds

1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 liter = 1000 milliliters = 1000 cubic centimeters
1 meter = 100 centimeters = 1000 millimeters
1 kilometer = 1000 meters
1 gram = 1000 milligrams
1 kilogram = 1000 grams

1 pound = 16 ounces
1 ton = 2,000 pounds
Metric numbers with four digits are represented without a comma (e.g., 9960 kilometers). For metric number greater than four digits, a space is used instead of a comma (e.g., 12 500 liters).

 

Grades 9-10 FCAT mathematics Reference Sheet

Area
KEY
b = base

h = height

l = length

w = width

= slant height

S.A. = Surface area

d= diameter

r = radius

A = area

C = circumference

V = volume

Use 3.14 or 22/7 for p

 

Triangle

 

A = 1/2 bh

 

 

Rectangle

 

A = lw

 

 

Trapezoid

 

A = 1/2 h(b1 + b2)

 

 

Parallelogram

 

A = bh

 

Circumference
C = pd = 2pr

Circle A = pr2


Volume
Total Surface Area

 

Right Circular Cone

 

V = 1/3 pr2h

 

S.A. = 1/2 (2pr) + pr2 = pr + pr2

 

Square Pyramid V = 1/3 lwh S.A. = 4(1/2 l) + l2 = 2l + l2
       

Sphere V = 4/3 pr3 S.A. = 4pr2
       

Right Circular Cylinder V = pr2h S.A. = 2prh + 2pr2
       
Rectangular Solid V = lwh S.A. = 2(lw) + 2(hw) + 2(lh)


In the following formulas, n represents the number of sides.

In a polygon, the sum of the measures of the interior angles is equal to 180(n - 2).

In a regular polygon, the measure of an interior angle is equal to [180(n - 2)] / n.



Pythagorean theorem: c2 = a2 + b2

Distance between two points P1(x1,y1) and P2 (x2,y2):

y = mx + b

Slope-intercept form of an equation of a line, where m = slope and b = the y-intercept:

Midpoint between two points P1(x1,y1) and P2 (x2,y2):

d = rt

Distance, rate, time formula, where d = distance, r = rate, t = time.

I = prt

Simple interest formula, where p = principal, r = rate, t = time.



Conversions
1 yard = 3 feet = 36 inches
1 mile = 1,760 yards = 5,280 feet
1 acre = 43,560 square feet
1 hour = 60 minutes
1 minute = 60 seconds

1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 liter = 1000 milliliters = 1000 cubic centimeters
1 meter = 100 centimeters = 1000 millimeters
1 kilometer = 1000 meters
1 gram = 1000 milligrams
1 kilogram = 1000 grams

1 pound = 16 ounces
1 ton = 2,000 pounds
Metric numbers with four digits are represented without a comma (e.g., 9960 kilometers). For metric number greater than four digits, a space is used instead of a comma (e.g., 12 500 liters).

 

FCAT MATH REFERENCE SHEET
Name ______________________

DIRECTIONS: Refer to your FCAT Mathematics Reference Sheet to answer each of the following.

  1. Make a drawing of a trapezoid.


  2. Write the formula for the volume of a sphere. ______________
    What is the volume of a sphere with a radius of 3 inches? _________________




  3. Write the formula for the total surface area _____________________ and the volume ________________________ of a right circular cylinder. Use the correct formula to find how many ounces of broth could be held in a cylinder that has a radius of 2 inches and a height of 7 inches if every cubic inch of volume contains one-fourth ounce of broth. Round your answer to the nearest whole number.)




  4. Find the circumference of a circle with a radius of 14 cm. Use the fractional value for pi (p) that is given on your reference sheet.




  5. What is the sum of the interior angles of a regular pentagon? (5 sides)




  6. If the equation of a given line is y = x + 2, what is the slope of the line, and what is its
    y-intercept? Slope _____ y-intercept _____

  7. Write out the Pythagorean Theorem . _______________ The hypotenuse is represented by the letter ____ and the two legs are represented by the letters ____ and ____ . Find the length of the hypotenuse of an isosceles right triangle with legs of 5 units. Round your answer to the nearest hundredth or give the exact square root answer. _________




  8. Write the formula for the distance between two points. _____________________
    Use this formula to find the distance between the points (-1, -1) and (3, 3). ________




  9. Write the formula for simple interest. _________________
    Find the simple interest on a loan of $300 for 8 months at 6% annual interest.




  10. Write the distance, rate, time formula. ________________
    Using this formula, how long does it take you to drive 780 miles at 65 mph? ______




  11. Write the formula for the midpoint between two points. ___________________
    Find the coordinates of the midpoint between the points (8, -3) and (-2. 11). ______




  12. How many inches are in a yard? _____ How many in yard? _____


  13. There are _____ feet in a mile. What part of a mile is 1320 feet? _____



  14. How many cups are in one gallon? _________

  15. How many ounces are in one quart? _________

Find the area of each figure.

16. 17. 18.

 

 

 

Find the volume of each figure.

19. 20.

 

 

 

Used by permission of Cheryl Greenfield, Gibbs high School, 2002.

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8th Grade Math Home > Teacher Resources > Secondary Mathematics Resource Booklet > Mathematics Reference Sheets