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GED Math Test Overview

Four Main Topic Areas:

1. Basic Math

Number operations, decimals, fractions, percentages, ratios, proportions, statistics, probability

2. Geometry

Area, perimeter, volume, coordinate geometry, basic geometric shapes

3. Basic Algebra

Linear equations, polynomials, factoring, rational expressions, quadratics

4. Graphs and Functions

Coordinate plane, graphing lines, slope, functions, interpreting graphs

1. Basic Math

Topics Covered:

Place Value and Rounding
Number Line and Negatives
Order of Operations (PEMDAS)
Roots and Exponents
Fractions
Decimals

Ratios and Proportions
Rates
Percent
Measures of Central Tendency
Probability and Combinations

Practice Problems:

The problems in this section start with core ideas and gradually get more challenging.

1. Convert 0.125 to a percentage.

2. Express $\frac{3}{8}$ as a decimal.

3. Round 847.2691 to the nearest hundredth.

4. Order these fractions from smallest to largest: $\frac{2}{5}$, $\frac{3}{7}$, $\frac{1}{3}$, $\frac{5}{8}$

5. Calculate $\frac{2}{3} + \frac{5}{12}$

6. If 18 out of 24 students passed a test, what percentage of students passed?

7. A recipe calls for 2.5 cups of flour to make 8 servings. How much flour is needed for 12 servings?

8. A sweater originally costs $85. If it's marked down 30%, what is the sale price?

9. Find the mean of this data set: {12, 8, 15, 9, 11, 14, 7, 13}

10. A jar contains 5 red balls, 8 blue balls, and 7 green balls. What is the probability of randomly selecting a blue ball?

11. How many different ways can you arrange 4 people in a line for a photo?

12. Sarah invests $2,400 at 3.5% simple interest for 2 years. How much interest will she earn?

2. Geometry

Topics Covered:

2-Dimensional Figures
Area and Perimeter
3-Dimensional Figures

Surface Area and Volume
Coordinate Geometry
Pythagorean Theorem

Practice Problems:

The problems in this section start with core ideas and gradually get more challenging.

1. Find the perimeter of a rectangle with length 12 cm and width 8 cm.

2. What is the area of a square with side length 9 inches?

3. Calculate the area of a triangle with base 16 feet and height 10 feet.

4. Find the circumference of a circle with radius 7 meters. Use $\pi = 3.14$

5. What is the volume of a rectangular box measuring 5 in × 8 in × 12 in?

6. A right triangle has legs measuring 6 cm and 8 cm. Find the length of the hypotenuse.

7. Calculate the area of a circle with diameter 18 feet. Use $\pi = 3.14$

8. Find the volume of a cylinder with radius 4 inches and height 15 inches. Use $\pi = 3.14$

9. A trapezoid has parallel sides of 14 cm and 22 cm, with a height of 8 cm. What is its area?

10. What is the surface area of a cube with edge length 6 feet?

3. Basic Algebra

Topics Covered:

Polynomials
Multiplying Polynomials
Factoring Polynomials
Rational Expressions

Equations and Inequalities
Systems of Equations
Quadratic Equations
Translating Word Problems

Practice Problems:

The problems in this section start with core ideas and gradually get more challenging.

1. Simplify: $4x + 7x - 2x$

2. Solve for $x$: $2x + 9 = 25$

3. Evaluate $3x^2 - 5x + 1$ when $x = 4$

4. Solve the inequality: $5x - 8 < 27$

5. Multiply: $(x + 6)(x - 3)$

6. Factor completely: $x^2 + 8x + 15$

7. Simplify: $\frac{x^8}{x^3}$

8. Solve by factoring: $x^2 - 9x + 20 = 0$

9. A phone plan costs $35 per month plus $0.15 per text message. Write an equation for the total monthly cost $C$ if you send $t$ text messages.

10. Use the quadratic formula to solve: $2x^2 + 7x + 4 = 0$

4. Graphs and Functions

Topics Covered:

Graphing
Line Equations

Slope
Functions

Practice Problems:

The problems in this section start with core ideas and gradually get more challenging.

1. What is the slope of a line passing through points (2, 5) and (6, 13)?

2. Find the $y$-intercept of the line $y = -3x + 8$.

3. Write the equation of a line with slope $m = 4$ passing through point (1, 7).

4. If $f(x) = 2x^2 + 5x - 3$, find $f(3)$.

5. What is the slope of a line perpendicular to $y = \frac{2}{5}x - 1$?

6. Find the $x$ and $y$ intercepts of the line $4x - 3y = 12$.

7. Determine if the relation $\{(1,3), (2,5), (3,7), (1,9)\}$ represents a function. Explain why or why not.

8. For what values of $x$ is $y = \sqrt{x + 4}$ defined as a real number?

9. Write the equation of a line parallel to $2x + 5y = 15$ that passes through point (-2, 4).

10. If $g(x) = x^3 - 2x + 1$, find the value of $g(-2)$.

GED Math Formula Reference Sheet

These formulas are provided on the actual GED test. Familiarize yourself with them!

Area Formulas

Square: $A = s^2$

Rectangle: $A = lw$

Parallelogram: $A = bh$

Triangle: $A = \frac{1}{2}bh$

Trapezoid: $A = \frac{1}{2}h(b_1 + b_2)$

Circle: $A = \pi r^2$

Perimeter Formulas

Square: $P = 4s$

Rectangle: $P = 2l + 2w$

Triangle: $P = s_1 + s_2 + s_3$

Circle (Circumference): $C = 2\pi r$ OR $C = \pi d$; $\pi \approx 3.14$

Surface Area and Volume Formulas

Rectangular Prism:
$SA = 2lw + 2lh + 2wh$
$V = lwh$

Right Prism:
$SA = ph + 2B$
$V = Bh$

Cylinder:
$SA = 2\pi rh + 2\pi r^2$
$V = \pi r^2 h$

Pyramid:
$SA = \frac{1}{2}ps + B$
$V = \frac{1}{3}Bh$

Cone:
$SA = \pi rs + \pi r^2$
$V = \frac{1}{3}\pi r^2 h$

Sphere:
$SA = 4\pi r^2$
$V = \frac{4}{3}\pi r^3$

($p$ = perimeter of base with area $B$; $\pi \approx 3.14$)

Statistics

Mean: The mean (average) is the sum of all values divided by how many values there are: $\text{Mean} = \dfrac{\text{sum of values}}{\text{n}}$.

Mode: The mode is the value(s) that appear most often in a data set. A set may have no mode, one mode, or multiple modes.

Median: The median is the middle value when the data are ordered. For an even number of values, the median is the mean of the two middle values.

Range: The range measures spread and is calculated as the difference between the largest and smallest values: $\text{Range} = \text{max} - \text{min}$.

Probability & Counting

Probability (basic): $P(A) = \dfrac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$

Complement rule: $P(A') = 1 - P(A)$

Addition rule: $P(A\text{ or }B) = P(A) + P(B) - P(A\text{ and }B)$ (if mutually exclusive, add directly)

Multiplication (independent): $P(A\text{ and }B) = P(A)\times P(B)$

Combinations: $\displaystyle {n \choose r} = \frac{n!}{r!(n-r)!}$ — unordered selections

Factorial: $n! = n\times(n-1)\times\dots\times1$

Algebra

Slope of a line: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Slope-intercept form: $y = mx + b$

Point-slope form: $y - y_1 = m(x - x_1)$

Standard form of quadratic: $y = ax^2 + bx + c$

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Pythagorean theorem: $a^2 + b^2 = c^2$

Money Formulas

Sales tax: tax amount = price × tax rate

Side note: sometimes the question asks for the tax amount; other times it asks for the final price (price + tax).

Discount: discount amount = price × discount rate

Side note: check whether the problem wants the discount amount or the sale price (price − discount).

Simple interest: $I = Prt$
($I$ = interest, $P$ = principal, $r$ = rate, $t$ = time)

Tip: Tip amount = bill × tip rate (add to bill for total)

Commission: Commission = sales × commission rate

Total cost: total cost = (number of units) × (price per unit)

Distance, Rate & Time

Distance: $d = rt$

Rate (speed): $r = \dfrac{d}{t}$

Time: $t = \dfrac{d}{r}$

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