Overview
This lecture provides a comprehensive review of essential math concepts for the ATI TEAS Version 7 exam, covering arithmetic, algebra, geometry, statistics, and units of measurement, including strategies for conversions and interpreting data.
Fractions, Decimals, and Percentages
- A numerator (top number) shows parts considered; denominator (bottom) shows total parts in a fraction.
- Equivalent fractions are different fractions that represent the same value (e.g., 2/8 = 1/4).
- Place value: each digit's position determines its value (ones, tens, hundreds, thousands, tenths, hundredths, etc.).
- Percent means “per 100”; convert fractions to decimals by dividing numerator by denominator.
- To convert decimal to percent, multiply by 100; to convert percent to decimal, divide by 100.
- Simplify percentages/fractions by dividing numerator and denominator by their greatest common factor.
Order of Operations and Number Types
- PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
- Rational numbers can be written as a ratio of two integers; irrational numbers cannot (e.g., π, √2).
- Repeating or terminating decimals are rational; non-repeating, non-terminating are irrational.
Comparing, Ordering, and Operations with Numbers
- Convert all numbers to decimals for easy comparison and ordering.
- Use number lines or stacking method to order numbers from least to greatest.
- Inequality signs: < (less than), > (greater than), = (equal to); the "alligator" eats the larger number.
Algebraic Concepts
- Variable: letter representing an unknown.
- Coefficient: number multiplying a variable.
- Constant: standalone number.
- Term: separate parts of an expression, separated by + or -.
- Inverse operations: addition/subtraction, multiplication/division, used to isolate variables.
- Solve equations and proportions by performing inverse operations on both sides.
Estimation, Measurement, and Unit Conversions
- Metric units: meter, centimeter, millimeter, kilometer for length; gram, kilogram, milligram for weight; liter, milliliter, kiloliter for volume.
- U.S. customary units: inch, foot, yard, mile; ounce, pound; teaspoon, tablespoon, cup, pint, quart, gallon.
- Convert larger to smaller units by multiplying, and smaller to larger by dividing.
- Metric conversions use powers of ten; move the decimal left/right as needed.
Interpreting and Converting Expressions and Word Problems
- Translate phrases (e.g., “four times a number” = 4x, “four less than a number” = x-4).
- Set up and solve word problems by creating and manipulating algebraic equations.
Ratios, Proportions, Percents, and Rates
- Set up ratios as fractions; solve proportion equations using cross-multiplication.
- Percent proportion: is/of = percent/100.
- Rate: comparison of two quantities with different units; unit rate denominator is 1.
Statistics: Mean, Median, Mode, Range, and Data Distribution
- Mean: average; sum numbers, divide by count.
- Median: middle value; if even number, average two middle numbers.
- Mode: most frequent value(s).
- Range: difference between highest and lowest.
- Distributions: symmetric (mean = median), bimodal (two peaks), uniform (all frequencies equal), skewed (tail left or right).
Probability
- Probability = number of favorable outcomes / number of possible outcomes.
- Express probabilities as fractions, decimals, or percentages.
- For independent “and” events, multiply probabilities; for “or” events, add.
Graphs, Variables, and Data Interpretation
- Graph types: Cartesian coordinate (x/y axes), scatter plots (relationship between two variables), line graphs (change over time), bar graphs (compare categories), pie/circle charts (parts of a whole).
- Independent variable: what is changed/input (x-axis); dependent variable: what is measured/output (y-axis).
- Recognize trends: linear, exponential, quadratic.
- Outlier: a data point far from the rest.
- Correlation: positive (both variables increase), negative (one increases as other decreases), none (no pattern).
Geometry: Perimeter, Area, and Volume
- Perimeter: sum of sides for polygons.
- Circumference of a circle: C = πd.
- Area: Rectangle/Square = l×w; Triangle = ½ b×h; Circle = πr²; Parallelogram = b×h; Trapezoid = ½(b₁+b₂)×h.
- Volume: Cube/Rectangular Prism = l×w×h; Cylinder = πr²h; Cone = (πr²h)/3; Sphere = (4/3)πr³; Pyramid = (l×w×h)/3.
Key Terms & Definitions
- Numerator — The top part of a fraction, showing the part being considered.
- Denominator — The bottom part of a fraction, showing the total number of parts.
- Percent — A ratio out of 100.
- Rational Number — Any number expressible as a fraction of two integers.
- Irrational Number — A number that cannot be expressed as a fraction of two integers.
- Variable — A letter representing an unknown value.
- Coefficient — The number multiplying a variable.
- Constant — A fixed value in an expression.
- Term — A single part of an expression, separated by + or -.
- Mean — The average of a data set.
- Median — The middle value in an ordered data set.
- Mode — The value(s) appearing most frequently in a data set.
- Range — The difference between the largest and smallest values.
- Independent Variable — The input or controlled factor in an experiment (x-axis).
- Dependent Variable — The measured or affected outcome (y-axis).
Action Items / Next Steps
- Review metric and customary conversion tables and practice conversions.
- Memorize key formulas for area, perimeter, and volume of shapes.
- Practice setting up equations from word problems.
- Complete additional practice problems on ratios, proportions, percent, and probability.
- Review statistical calculation steps and interpretation of data distributions.