Maths

• Simplifying algebraic expressions


  1. Step 1: Collect like terms

  2. Step 2: Simplify the expression
• Substitution


  Replacing a variable with a given value
• Changing the subject of a formula

  Rearrange the formula to make the desired variable the subject
• Solving Equations


  1. Step 1: 4x - 4 = 28

  2. Step 2: 4x = 28 + 4

  3. Step 3: x = 8
• Solving Equations with Brackets

  1. Step 1: 12(x-2) = 13 - 2(x+3)

  2. Step 2: 12x - 24 = 13 - 2x - 6

  3. Step 3: 14x - 245 = -3

  4. Step 4: 14x = 242

  5. Step 5: x = 17
• y


  A variable that represents the dependent value in an equation
• x


  A variable that represents the independent value in an equation
• Enlarging Shapes by a Positive Scale Factor

  1. Step 1: Draw a straight line from the enlargement point to each point on the original shape

  2. Step 2: Count the number of squares between the enlargement point and each point

  3. Step 3: Multiply that number by the scale factor

  4. Step 4: From the enlargement point, count the new number of squares and place the new point
• Bearing


  The direction from one point to another, measured clockwise from north
• Finding Bearings


  1. Step 1: Always write the bearing in 3 figures

  2. Step 2: Always measure from the north line

  3. Step 3: Always measure clockwise
• Finding Back Bearings


  1. Step 1: Find the bearing from B to A

  2. Step 2: Add 180° to the bearing to get the back bearing
• Using Pythagoras' Theorem


  1. Step 1: Identify the sides of the right-angled triangle

  2. Step 2: Use the formula a^2 + b^2 = c^2 to find the missing side
• Hypotenuse


  The side opposite the right angle in a right-angled triangle
• Opposite


  The side opposite the angle being considered in a right-angled triangle
• Adjacent


  The side next to the angle being considered in a right-angled triangle
• Using Trigonometry


  1. Step 1: Identify which 2 sides are involved

  2. Step 2: Use the appropriate trigonometric ratio (sin, cos, tan) to find the missing side or angle
• Using a Tree Diagram


  1. Step 1: Draw a tree diagram to show all possible outcomes

  2. Step 2: Use the tree diagram to calculate probabilities of different events, especially for independent events
• Dependent Events


  Events where the probability of one event occurring depends on the outcome of another event