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  • GED Mathematical Reasoning Formulas

    All Mathematics Formulas a GED Math Test Taker Must Know!

    Created by: Effortless Math Education www.EffortlessMath.com

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 1

    Taking the GED with only a few weeks or even few days to study?

    First and foremost, you should understand that the 2019 GEDยฎ Mathematical Reasoning

    test contains a formula sheet, which displays formulas relating to geometric

    measurement and certain algebra concepts. Formulas are provided to test-takers so

    that they may focus on application, rather than the memorization, of formulas.

    However, the test does not provide a list of all basic formulas that will be required to

    know for the test. This means that you will need to be able to recall many math

    formulas on the GED.

    Below you will find the 2019 GEDยฎ Mathematics Formula Sheet followed by a complete

    list of all Math formulas you MUST have learned before test day, as well as some

    explanations for how to use them and what they mean. Keep this list around for a quick

    reminder when you forget one of the formulas.

    Review them all, then take a look at the math topics to begin applying them!

    Good luck!

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 2

    GED Mathematical Reasoning Formula Sheet

    Area of a: Square ๐ด = ๐‘ 2 Rectangle ๐ด = ๐‘™๐‘ค

    Parallelogram ๐ด = ๐‘โ„Ž

    Triangle ๐ด =

    1

    2 ๐‘โ„Ž

    Trapezoid ๐ด =

    1

    2 โ„Ž(๐‘1 + ๐‘2)

    Circle

    Surface Area and Volume of a:

    Rectangular ๐‘†๐ด = 2๐‘™๐‘ค + 2๐‘™โ„Ž + 2๐‘คโ„Ž ๐‘‰ = ๐‘™๐‘คโ„Ž

    Right Prism ๐‘†๐ด = ๐‘โ„Ž + 2๐ต ๐‘‰ = ๐ตโ„Ž

    Cylinder ๐‘†๐ด = 2๐œ‹๐‘Ÿโ„Ž + 2๐œ‹๐‘Ÿ2 ๐‘‰ = ๐œ‹๐‘Ÿ2โ„Ž

    Pyramid ๐‘†๐ด =

    1

    2 ๐‘๐‘  + ๐ต ๐‘‰ =

    1

    3 ๐ตโ„Ž

    Cone ๐‘†๐ด = ๐œ‹๐‘Ÿ + ๐œ‹๐‘Ÿ2 ๐‘‰ =

    1

    3 ๐œ‹๐‘Ÿ2โ„Ž

    Sphere ๐‘†๐ด = 4๐œ‹๐‘Ÿ2 ๐‘‰ =

    4

    3 ๐œ‹๐‘Ÿ3

    (๐‘ = perimeter of base ๐ต; ๐œ‹ = 3.14)

    Algebra Slope of a line ๐‘š =

    ๐‘ฆ2 โˆ’ ๐‘ฆ1 ๐‘ฅ2 โˆ’ ๐‘ฅ1

    Slope-intercept form of the equation of a line ๐‘ฆ = ๐‘š๐‘ฅ + ๐‘

    Point-slope form of the Equation of a line ๐‘ฆ โˆ’ ๐‘ฆ1 = ๐‘š(๐‘ฅ โˆ’ ๐‘ฅ1)

    Standard form of a Quadratic equation ๐‘ฆ = ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘

    Quadratic formula ๐‘ฅ =

    โˆ’๐‘ ยฑ โˆš๐‘2 โˆ’ 4๐‘Ž๐‘

    2๐‘Ž

    Pythagorean theorem ๐‘Ž2 + ๐‘2 = ๐‘2

    Simple interest ๐ผ = ๐‘๐‘Ÿ๐‘ก (๐ผ = interest, ๐‘ = principal, ๐‘Ÿ = rate, ๐‘ก = time)

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 3

    A Quick Review and the List of all GED Mathematics Formulas

    Place Value

    The value of the place, or position, of a digit in a number. Example: In 456, the 5 is in โ€œtensโ€ position.

    Fractions

    A number expressed in the form ๐‘Ž

    ๐‘

    Adding and Subtracting with the same denominator: ๐‘Ž

    ๐‘ +

    ๐‘

    ๐‘ =

    ๐‘Ž + ๐‘

    ๐‘

    ๐‘Ž

    ๐‘ โˆ’

    ๐‘

    ๐‘ =

    ๐‘Ž โˆ’ ๐‘

    ๐‘

    Adding and Subtracting with the different denominator: ๐‘Ž

    ๐‘ +

    ๐‘

    ๐‘‘ =

    ๐‘Ž๐‘‘ + ๐‘๐‘

    ๐‘๐‘‘

    ๐‘Ž

    ๐‘ โˆ’

    ๐‘

    ๐‘‘ =

    ๐‘Ž๐‘‘โˆ’ ๐‘๐‘

    ๐‘๐‘‘

    Multiplying and Dividing Fractions: ๐‘Ž

    ๐‘ ร—

    ๐‘

    ๐‘‘ =

    ๐‘Ž ร— ๐‘

    ๐‘ ร— d

    ๐‘Ž

    ๐‘ รท

    ๐‘

    ๐‘‘ =

    ๐‘Ž

    ๐‘ ๐‘

    ๐‘‘

    = ๐‘Ž๐‘‘

    ๐‘๐‘

    Comparing Numbers Signs Equal to = Less than < Greater than > Greater than or equal โ‰ฅ Less than or equal โ‰ค

    Rounding Putting a number up or down to the nearest whole number or the nearest hundred, etc. Example: 64 rounded to the nearest ten is 60, because 64 is closer to 60 than to 70.

    Whole Number The numbers {0, 1, 2, 3, โ€ฆ }

    Mixed Numbers A number composed of a whole number and fraction

    Example: 2 2

    3

    Converting between improper fractions and mixed numbers:

    a ๐‘

    ๐‘ = a +

    ๐‘

    ๐‘ =

    ๐‘Ž๐‘+ ๐‘

    ๐‘

    Estimates Find a number close to the exact answer.

    Decimals Is a fraction written in a special form. For example, instead of

    writing 1

    2 you can write 0.5.

    Factoring Numbers Factor a number means to break it up into numbers that can be multiplied together to get the original number. Example: 12 = 2 ร— 2 ร— 3

    Divisibility Rules Divisibility means that you are able to divide a number evenly. Example: 24 is divisible by 6, because 24 รท 6 = 4

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 4

    Greatest Common Factor Multiply common prime factors Example: 200 = 2 ร— 2 ร— 2 ร— 5 ร— 5 60 = 2 ร— 2 ร— 3 ร— 5 GCF (200, 60) = 2 ร— 2 ร— 5 = 20

    Least Common Multiple Check multiples of the largest number Example: LCM (200, 60): 200 (no), 400 (no), 600 (yes!)

    Integers {โ€ฆ , โˆ’3, โˆ’2, โˆ’1, 0, 1, 2, 3, โ€ฆ } Includes: zero, counting numbers, and the negative of the counting numbers

    Real Numbers All numbers that are on number line. Integers plus fractions, decimals, and irrationals

    (โˆš2, โˆš3, ๐œ‹, etc.)

    Order of Operations

    PEMDAS (parentheses / exponents / multiply / divide / add / subtract)

    Absolute Value Refers to the distance of a number from 0, the distances are positive as absolute value of a number cannot be negative. |โˆ’22| = 22

    |๐‘ฅ| = { ๐‘ฅ ๐‘“๐‘œ๐‘Ÿ ๐‘ฅ โ‰ฅ 0

    โˆ’๐‘ฅ ๐‘“๐‘œ๐‘Ÿ ๐‘ฅ < 0

    |๐‘ฅ| < ๐‘› โ‡’ โˆ’๐‘› < ๐‘ฅ < ๐‘› |๐‘ฅ| > ๐‘› โ‡’ ๐‘ฅ < โˆ’๐‘› or ๐‘ฅ > ๐‘›

    Ratios A ratio is a comparison of two numbers by division.

    Example: 3: 5, or 3

    5

    Percentages use the following formula to find part, whole, or percent

    ๐‘๐‘Ž๐‘Ÿ๐‘ก = percent

    100 ร— ๐‘คโ„Ž๐‘œ๐‘™๐‘’

    Proportional Ratios A proportion means that two ratios are equal. It can be written in two ways: ๐‘Ž

    ๐‘ =

    ๐‘

    ๐‘‘ , ๐‘Ž: ๐‘ = ๐‘: ๐‘‘

    Discount Multiply the regular price by the rate of discount Selling price = original price โ€“ discount

    Percent of Change ๐‘๐‘’๐‘ค ๐‘‰๐‘Ž๐‘™๐‘ข๐‘’โˆ’๐‘‚๐‘™๐‘‘ ๐‘‰๐‘Ž๐‘™๐‘ข๐‘’

    ๐‘‚๐‘™๐‘‘ ๐‘‰๐‘Ž๐‘™๐‘ข๐‘’ ร— 100%

    Markup Markup = selling price โ€“ cost Markup rate = markup divided by the cost

    Expressions and Variables A variable is a letter that represents unspecified numbers. One may use a variable in the same manner as all other numbers:

    Tax To find tax, multiply the tax rate to the taxable amount (income, property value, etc.)

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 5

    Addition 2 + ๐‘Ž 2 plus ๐‘Ž

    Subtraction ๐‘ฆ โ€“ 3 ๐‘ฆ minus 3

    Division 4

    ๐‘ฅ

    4 divided by ๐‘ฅ

    Multiplication 5๐‘Ž 5 times ๐‘Ž

    Distributive Property ๐‘Ž(๐‘ + ๐‘) = ๐‘Ž๐‘ + ๐‘Ž๐‘

    Polynomial ๐‘ƒ(๐‘ฅ) = ๐‘Ž0๐‘ฅ

    ๐‘› + ๐‘Ž1๐‘ฅ ๐‘›โˆ’1 + โ‹ฏ +

    ๐‘Ž๐‘›โˆ’2๐‘ฅ 2 + ๐‘Ž๐‘›โˆ’1๐‘ฅ + ๐‘Ž๐‘›

    Systems of Equations Two or more equations working

    together. example: { โˆ’2๐‘ฅ + 2๐‘ฆ = 4 โˆ’2๐‘ฅ + ๐‘ฆ = 3

    Equations The values of two mathematical expressions are equal. ๐‘Ž๐‘ฅ + ๐‘ = ๐‘

    Inequalities Says that two values are not equal ๐‘Ž โ‰  ๐‘ a not equal to b ๐‘Ž < ๐‘ a less than b ๐‘Ž > ๐‘ a greater than b ๐‘Ž โ‰ฅ ๐‘ a greater than or equal b ๐‘Ž โ‰ค ๐‘ a less than or equal b

    Lines (Linear Functions) Consider the line that goes through points ๐ด(๐‘ฅ1, ๐‘ฆ1) and ๐ต(๐‘ฅ2, ๐‘ฆ2). Distance from ๐‘จ(๐‘ฅ1, ๐‘ฆ1) to ๐‘ฉ(๐‘ฅ2, ๐‘ฆ2):

    โˆš(๐‘ฅ1 โˆ’ ๐‘ฅ2) 2 + (๐‘ฆ1 โˆ’ ๐‘ฆ2)

    2

    Mid-point of the segment AB:

    M ( ๐‘ฅ1+๐‘ฅ2

    2 ,

    ๐‘ฆ1+๐‘ฆ2

    2 )

    Slope of the line:

    ๐‘ฆ 2

    โˆ’ ๐‘ฆ 1

    ๐‘ฅ2 โˆ’ ๐‘ฅ1 =

    ๐‘Ÿ๐‘–๐‘ ๐‘’

    run

    Solving Systems of Equations by Substitution Consider the system of equations ๐‘ฅ โˆ’ ๐‘ฆ = 1, โˆ’2๐‘ฅ + ๐‘ฆ = 6 Substitute ๐‘ฅ = 1 โˆ’ ๐‘ฆ in the second equation โˆ’2(1 โˆ’ ๐‘ฆ) + ๐‘ฆ = 5 ๐‘ฆ = 2 Substitute ๐‘ฆ = 2 in ๐‘ฅ = 1 + ๐‘ฆ ๐‘ฅ = 1 + 2 = 3

    Solving Systems of Equations by Elimination Example:

    ๐‘ฅ + 2๐‘ฆ = 6 + โˆ’ ๐‘ฅ + ๐‘ฆ = 3

    3๐‘ฆ = 9 ๐‘ฆ = 3

    ๐‘ฅ + 6 = 6 ๐‘ฅ = 0

  • GED Mathematical Reasoning Formulas

    www.EffortlessMath.com 6

    Point-slope form:

    Given the slope m and a point (๐‘ฅ1, ๐‘ฆ1) on the line, the equation of the line is

    (๐‘ฆ โˆ’ ๐‘ฆ1) = ๐‘š(๐‘ฅ โˆ’ ๐‘ฅ1).

    Slope-intercept form: given the slope m and the y- intercept ๐‘, then the equation of the line is:

    ๐‘ฆ = ๐‘š๐‘ฅ + ๐‘.

    Scienti

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