Math Exam Prep for AIT Version 7

Mar 4, 2025

Mindmap

Lecture Notes: AIT's Version 7 Math Portion Exam Prep

Fractions

  • Numerator: Number above the fraction line; represents parts of the whole.
    • Example: In ( \frac{3}{4} ), 3 is the numerator.
  • Denominator: Number below the fraction line; represents how many equal parts the whole is divided into.
    • Example: In ( \frac{3}{4} ), 4 is the denominator.
  • Equivalent Fractions: Different fractions representing the same value once simplified.
    • Example: ( \frac{2}{8} = \frac{1}{4} ) by dividing both numerator and denominator by 2.

Place Values and Decimals

  • Basic Place Values: Ones, tens, hundreds, and thousands.
    • Example: In 1,234:
      • 4 is in the ones place.
      • 3 in the tens place represents 30.
      • 2 in the hundreds place represents 200.
      • 1 in the thousands place represents 1,000.
  • Decimals: Extend to the right of the decimal point.
    • Example: 0.2 as ( \frac{2}{10} ).

Percentages

  • Definition: Represents parts per hundred.
    • Example: 90% means 90 out of 100.
  • Conversion to Fractions and Decimals:
    • Percent to fraction: Simplify ( \frac{90}{100} = \frac{9}{10} ).
    • Percent to decimal: Move decimal two places left (e.g., 25% = 0.25).

Order of Operations (PEMDAS)

  • Sequence: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
  • Example: Solve (4 + (3 \times 2) - (8 / 2)).
    • Perform operations within parentheses first, then move left to right through multiplication/division, and addition/subtraction.

Rational and Irrational Numbers

  • Rational Numbers: Can be expressed as a fraction of two integers.
    • Example: 3.75 as ( \frac{375}{100} ).
  • Irrational Numbers: Cannot be expressed as a simple fraction.
    • Examples: ( \pi, e, \sqrt{2} ).

Comparing Rational Numbers

  • Methods: Use number lines or stacking to order from least to greatest.
  • Inequalities: Use symbols (<, >, =) to compare values.

Algebra Basics

  • Expressions: Terms, coefficients, variables, and constants.
    • Example: In (15x + 5), 15 is the coefficient, x is the variable, and 5 is the constant.
  • Solving Equations: Use inverse operations to isolate variables.
  • Proportions: Cross-multiply to solve.

Estimation and Measurement

  • Length, Weight, Capacity: Use metric system conversions.
    • Example: 1 meter approx. height of a doorknob.

Word Problems

  • Translate words into algebraic expressions.
    • Example: "Six more than a number" as (x + 6).

Graphical Representation

  • Types: Cartesian coordinates, scatter plots, line, pie/circle, and bar graphs.
  • Use Cases: Choose appropriate graph type based on data.

Statistical Measures

  • Mean: Average of a data set.
  • Median: Middle number when data is ordered.
  • Mode: Most frequently occurring number.
  • Range: Difference between highest and lowest numbers.

Probability

  • Basic Concept: Total number of favorable outcomes divided by total possible outcomes.
    • Example: Probability of rolling a 3 on a die is ( \frac{1}{6} ).

Review of Important Formulas

  • Area and Volume Formulas
    • Rectangle Area: ( length \times width ).
    • Triangle Area: ( \frac{1}{2} \times base \times height ).
    • Circle Circumference: ( \pi \times diameter ).
    • Circle Area: ( \pi \times radius^2 ).
    • Volume for Prisms: ( base_area \times height ).

These notes outline key concepts and methods needed to prepare for the AIT's version 7 math exam, including conversion methods, equation solving, statistical analysis, and graph interpretation.