3rd Form Revision for EOY 2

• Quadrants


  • Quadrant I: (+, +)
  • Quadrant II: (-, +)
  • Quadrant III: (-, -)
  • Quadrant IV: (+, -)
• Plotting Graphs of Linear Functions

  1. Explicit Functions: y=mx+c

  2. Implicit Functions: Rearrange to y=mx+c
• Gradient (m)


  The slope of the line, shows how steep the line is
• 1. intercept (c)


  Where the line crosses the y-axis
• Finding the Linear Function

  Given gradient and a point, use y=mx+c to find the equation
• Midpoint of a Line Segment


  (x1+x2/2, y1+y2/2)
• Properties of Parallel and Perpendicular Lines

  • Parallel Lines: Same gradient
  • Perpendicular Lines: Gradients multiply to -1
• Constructing Triangles from Given Information

  Use ruler and compass to draw triangles based on side lengths and angles
• Standard Compass Constructions on Line Segments

  Bisect lines, create perpendiculars, construct angles
• Solving Geometric Problems Using Bearings


  Measure and draw angles clockwise from north using a protractor
• Ratio Problems


  Simplify ratios, solve proportion problems
• Converting Fractions to Percentages and Vice Versa

  1. Fraction to Percentage: Multiply by 100

  2. Percentage to Fraction: Divide by 100 and simplify
• Non-Calculator Percentage Increases and Decreases

  Find 10% and multiply
• Using Multiplying Factors for Harder Percentage Problems

  1. 30% increase: Multiply by 1.3

  2. 30% decrease: Multiply by 0.7
• Reverse Percentage Problems


  Find original amount before percentage change
• Compound Interest and Depreciation


  Use formula A=P(1+r/n)^nt
• Straight-Line Graphs to Model Situations

  Use linear equations to represent real-life situations
• Drawing Graphs to Represent Rates of Change


  Plot graphs based on data to show how one quantity changes over time
• Travel Graphs


  Use distance-time graphs to solve problems related to speed and travel time
• Measures of Central Tendency


  • Mean
  • Median
  • Mode
  • Range
• Interquartile Range


  Range of the middle 50% of the data
• Cumulative Frequency Diagrams and Histograms

  1. Cumulative Frequency Diagrams: Plot cumulative totals

  2. Histograms: Show frequency of data within intervals
• Solving Simultaneous Equations


  1. By Inspection

  2. By Elimination

  3. Graphically
• Solving Linear Inequalities


  1. Solve similar to equations, flip inequality when multiplying/dividing by negative

  2. Represent solutions on number line
• Linear Inequalities in Two Variables

  Graph the inequality and shade the solution region
• Simple Quadratic Inequalities


  Solve by finding critical points and testing intervals
• Corresponding Angles


  Equal angles on the same side of a transversal
• Alternate Angles


  Equal angles on opposite sides of a transversal
• Angles in Triangles and Quadrilaterals

  • Triangle angles sum to 180°
  • Quadrilateral angles sum to 360°
• Revision and Feedback