Maths calc

• What is the purpose of the revision guide for achieving a grade 9 in Maths?

  To cover essential topics, key concepts, problem-solving strategies, and critical equations.
• What are the key concepts covered in the Algebra section of the revision notes?

  • Expressions: Combinations of numbers, variables, and operations.
  • Equations: Mathematical statements showing equality.
  • Simplifying Expressions: Combining like terms.
  • Expanding Brackets: Using the distributive property.
  • Factoring: Writing expressions as products.
  • Solving Linear Equations: Isolating the variable.
  • Quadratic Equations: Standard form and factoring.
• What is an example of an expression?


  \(3x + 5\)
• What is an example of an equation?

  \(2x + 3 = 7\)
• What are like terms?

  Terms that have the same variable raised to the same power.
• How do you combine like terms in the expression \(5x + 3x - 2\)?

  Combine to get \(8x - 2\).
• What does the distributive property state?

  Multiply each term inside the bracket by the term outside.
• Expand the expression \(3(x + 4)\) using the distributive property.


  \(3x + 12\)
• What is the process of factoring an expression?

  Writing an expression as a product.
• Factor the expression \(2x + 4\).

  \(2(x + 2)\)
• Solve the linear equation \(3x + 4 = 10\).

  \(x = 2\)
• What is the standard form of a quadratic equation?

  \(ax^2 + bx + c = 0\)
• How do you solve the quadratic equation \(x^2 - 5x + 6 = 0\)?

  Factor to \((x - 2)(x - 3) = 0\) and find \(x = 2\) and \(x = 3\).
• What are the key concepts covered in the Geometry section of the revision notes?

  • Lines and Angles: Complementary and supplementary angles.
  • Types of Triangles: Equilateral, isosceles, and scalene.
  • Pythagorean Theorem: \(a^2 + b^2 = c^2\).
  • Area and Perimeter: Formulas for triangles and rectangles.
• What are complementary angles?

  Two angles that sum to \(90^\circ\).
• What are supplementary angles?

  Two angles that sum to \(180^\circ\).
• What is the Pythagorean Theorem formula?

  \(a^2 + b^2 = c^2\)
• In a triangle with legs \(3\) and \(4\), what is the length of the hypotenuse?

  \(5\)
• What is the area of a triangle with a base of \(6\) and a height of \(4\)?

  \(\text{Area} = 12\)
• What is the perimeter of a rectangle with a length of \(5\) and a width of \(3\)?

  \(P = 16\)
• What are the key concepts covered in the Trigonometry section of the revision notes?

  • Basic Ratios: \(\sin(\theta)\), \(\cos(\theta)\), \(\tan(\theta)\).
  • Using Trigonometric Ratios: Finding sides in right triangles.
  • Finding Angles: Using inverse functions.
• What is the sine ratio in a right triangle?

  \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)
• What is the cosine ratio in a right triangle?

  \(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)
• What is the tangent ratio in a right triangle?

  \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\)
• If the angle \(\theta = 30^\circ\) and the hypotenuse is \(10\), what is the opposite side?

  \(5\)
• If \(\tan(\theta) = \frac{5}{12}\), how do you find \(\theta\)?


  \(\theta = \tan^{-1}\left(\frac{5}{12}\right)\)
• What are the key concepts covered in the Statistics section of the revision notes?

  • Mean: Average value and its formula.
  • Median: Middle value in a sorted list.
  • Mode: Most frequently occurring number.
  • Analyzing Data: Steps to calculate mean, median, mode, and identify trends.
• What is the formula to calculate the mean?

  \(\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}\)
• How do you find the median in a sorted list?

  Identify the middle value; if even, average the two middle values.
• What is the mode in a data set?

  The most frequently occurring number.
• In the data set \(2, 4, 4, 5, 6\), what is the mode?


  \(4\)
• What are the key concepts covered in the Probability section of the revision notes?

  • Probability Formula: \(P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
  • Calculating Probability: Examples and explanations.
  • Independent Events: Definition and formula.
• What is the probability formula?

  \(P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\)
• What is the probability of rolling a \(3\) on a die?

  \(P(3) = \frac{1}{6}\)
• What defines independent events in probability?

  Two events that do not affect each other.
• How do you calculate the probability of two independent events \(A\) and \(B\)?

  \(P(A \text{ and } B) = P(A) \times P(B)\)
• What are the key concepts covered in the Equations and Graphs section of the revision notes?

  • Linear Equation: \(y = mx + c\).
  • Quadratic Equation: \(y = ax^2 + bx + c\) and vertex form.
  • Steps to graph equations: Identify y-intercept, use slope, plot points.
• What is the general form of a linear equation?

  \(y = mx + c\)
• What is the vertex form of a quadratic equation?

  \(y = a(x - h)^2 + k\)
• How do you graph the equation \(y = 2x + 3\)?

  Identify the y-intercept at \(3\) and use the slope \(2\) to find another point.