NAT 5 MATHS

• What does Rule 1 state about diameters in circles?

  Diameters create right angle triangles.
• What does Rule 2 state about radii in circles?

  Radii create an isosceles triangle.
• What is a tangent in relation to a curve?

  A tangent is a line that touches the edge of a curve and creates a 90° angle.
• What is the sum of the angles 40° and 90°?

  130°
• If the sum of angles is 180° and two angles are 40° and 90°, what is the third angle?

  The third angle is 50°.
• What is the total of the angles in a triangle?

  180°
• What does the term "cequal" refer to in the context of angles?

  It indicates that angles are equal.
• What is the formula for standard deviation?


  S = √(Σ(x - S)² / N)
• What does the symbol Σ represent in the context of standard deviation?

  Σ represents the sum of all data values.
• In Example 1, what is the standard deviation value given?

  S = 26
• What does the variable x represent in the standard deviation formula?


  x represents the data value.
• What is the mean value denoted by in the standard deviation formula?

  S represents the mean value.
• What is the formula for the volume of a sphere?


  V = \frac{4}{3} \pi r^3
• What is the formula for the volume of a cone?


  V = \frac{1}{3} \pi r^2 h
• What is the formula for the volume of a pyramid?


  V = \frac{1}{3} A h
• What is the formula for the volume of a cube?

  V = l^3
• What is the formula for the volume of a cuboid?


  V = l \times w \times h
• What is the formula for the volume of a cylinder?

  V = \pi r^2 h
• What is a common factor in algebra?

  A common factor is a number that divides two or more numbers without leaving a remainder.
• What is the difference of squares formula?

  The difference of squares formula is a² - b² = (a - b)(a + b).
• What is the quadratic formula?

  x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
• What is the purpose of solving simultaneous equations?

  The purpose is to find the values of variables that satisfy all equations simultaneously.
• How do you solve simultaneous equations using substitution?

  Substitute one variable into the other equation to find the values of both variables.
• What is the time conversion for 18 hours and 24 minutes into hours?

  18.4 hours
• How do you convert minutes into hours?

  Divide the number of minutes by 60.
• What is the time conversion for 3 hours and 43 minutes into hours?

  1. 72 hours
• What are the types of equations in simultaneous equations?

  • Linear equations
  • Non-linear equations
  • Quadratic equations
• What are the steps to solve a quadratic equation using the quadratic formula?


  1. Identify coefficients a, b, and c.
  2. Substitute values into the formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
  3. Simplify to find the values of x.
• What are the types of factoring methods in algebra?

  • Common factor
  • Difference of squares
  • Trinomials
• What are the formulas for the volumes of different shapes?

  • Sphere: \(V = \frac{4}{3} \pi r^3\)
  • Cone: \(V = \frac{1}{3} \pi r^2 h\)
  • Pyramid: \(V = \frac{1}{3} A h\)
  • Cube: \(V = l^3\)
  • Cuboid: \(V = l \times w \times h\)
  • Cylinder: \(V = \pi r^2 h\)
• What are the key components of standard deviation?

  • Mean value (S)
  • Data values (x)
  • Total number of values (N)
  • Sum of squared differences (Σ)