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Math Concepts Mastery Guide

This study guide covers key concepts like comparing numbers, fractions, decimals, percents, and scientific notation. It also includes simplifying expressions, properties of math operations, solving problems with fractions, decimals, percents, integers, and graphing on a coordinate plane. Master these essential skills for success in math.

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Math Concepts Mastery Guide

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  1. Mid-Term Study Guide

  2. SOL 7.1 • I must be able to: • Compare ( <, >, =) • Order (least to greatest) • Fractions • Decimals • Percents • Scientific Notation

  3. 7.1 Notes • Change all numbers to decimals to compare and order • To turn to decimals: • Fractions: divide top number by bottom number (1/4 = 1 ÷4 = 0.25) • Percents: move decimal 2 places to the left (15% = .15) • Scientific Notation: Move decimal to the right based on the exponent (ex: 2.67 x 104 = 26,700)

  4. SOL 7.1 Sample Problems

  5. SOL 7.2 • I must be able to: Simplify expressions with exponents, using order of operations

  6. 7.2 Notes PEMDAS P - Parenthesis E - Exponents M/D - Multiplication and Division from left to right A/S - Addition and Subtraction from left to right

  7. SOL 7.2 Sample Problems

  8. SOL 7.3 • I must be able to: Identify and apply (use) the following properties: Commutative (Add and Mult) Associative (Add and Mult) Identity (Add and Mult) Inverse (Add and Mult) Distributive Multiplicative Property of Zero

  9. SOL 7.3 Notes * Commutative Property of addition: a + b = b + a of multiplication: a x b = b x a * Associative Property of addition: a + (b+c) = (a+b) +c of multiplication: a x (b x c) = (a x b) x c **same order**

  10. SOL 7.3 Notes * Identity Property: of addition: a + 0 = a of multiplication: a x 1 = a * Inverse Property: of addition: a + (-a) = 0 of multiplication: a x 1/a = 1

  11. SOL 7.3 Notes * Distributive Property: a(b+c) = ab + ac • Multiplicative Property of Zero: a x 0 = 0

  12. SOL 7.3 Sample Problems

  13. SOL 7.4 • I will be able to: • Solve problems with fractions, decimals, and percents • Solve problems involving tips, discounts, sales tax, and simple interest

  14. SOL 7.4 Notes • Tips, Discounts, and Sales Tax • Change percent to decimal (15% = .15) • Multiply • Add or Subtract as needed Ex: $45.00 with a 10% discount 45.00 x .10 = 4.50 45.00 - 4.50 = 40.50

  15. SOL 7.4 Notes continued • Interest = prt • P = principal ($) • R = rate (%) • T = time in years Ex: $1000 in a savings account with 5% interest for 2 years $1,000 x .05 x 2 = $100 interest

  16. SOL 7.4 Sample Problems

  17. SOL 7.5 • I will be able to: • Add • Subtract • Multiply • Divide Using Integers

  18. SOL 7.5 Notes • Adding Integers If signs are the same, add the numbers and keep the sign Ex: -4 + -4 = -8 If signs are different, subtract the numbers and keep the sign of the highest number Ex: -5 + 3 = -2

  19. SOL 7.5 Notes • Subtracting Integers • Change to Addition • Change the sign of the second number Ex: 7 - (-4) = 7 + + 4 = 11

  20. SOL 7.5 Notes • Multiplying and Dividing Integers • If signs are the same, the answer is positive • If signs are different, the answer is negative Ex: 5 x -4 = -20 -5 x -4 = -20

  21. SOL 7.5 Sample Problems

  22. SOL 7.12 • I will be able to: • Identify ordered pairs • Identify quadrants • Graph ordered pairs On the coordinate plane

  23. SOL 7.12 Notes • The coordinate plane is divided into four quadrants

  24. SOL 7.12 Notes • Ordered pairs are written (3, 4) with the x-coordinate first, and then the y-coordinate. • The x-axis is horizontal (left to right) with positive values to the right and negative values to the left • The y-axis is vertical (up and down) with positive values up and negative values down.

  25. SOL 7.12 Sample Problems

  26. SOL 7.16 • I will be able to: Create and solve problems using Measures of Central Tendency Mean Median Mode and the range

  27. SOL 7.16 Notes • Mean - average - add the numbers then divide by the number of data (should not be used when there is an outlier) • Median - middle number - must be ordered least to greatest • Mode - number most often used • Range - highest number minus the lowest number

  28. SOL 7.16 Sample Problems

  29. SOL 7.17 • I will be able to: • Collect • Analyze • Display • Interpret data using: • Frequency tables • Line plots • Histograms • Stem-and-leaf plots • Box-and-whisker plots • Scatterplots

  30. SOL 7.17 Sample Problems

  31. SOL 7.18 • I will be able to: make inferences, conjectures, and predictions based on data.

  32. SOL 7.18 Sample Problems

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