Math

• What is the purpose of this guide?

  To help with National five math preparation
• How did the author create this guide?

  By reviewing every past paper for questions
• What is the recommended study method using this guide?

  • Watch the video
  • Pause and try questions
  • Review answers and repeat
• What is the first question from the 2022 paper?

  Evaluate $2 \times \frac{19}{20}$
• What is the common denominator for $1 +$$\frac{3}{4}$?


  20
• How do you simplify $\frac{38}{60}$?


  By dividing by 2
• What is the annual profit increase percentage mentioned?

  3%
• How do you calculate the annual profit by 2025?

  Using the formula with a multiplier
• What is the multiplier for a 3% increase?

  $1.03$
• How many years are between 2021 and 2025?

  4 years
• How many tickets were sold for the show?

  4,850 tickets
• What does 4,850 tickets represent in terms of last year's sales?

  15% more than last year
• How do you find last year's ticket sales?

  Divide by 115% and multiply by 100%
• What is the weight of a PO seed in scientific notation?

  $2.88 \times 10^{-6} \text{ kg}$
• How do you calculate 8% of $3.6 \times 10^{6}$?


  Multiply by 0.08
• What is the simplified form of $\sqrt{40} +$$\sqrt{90}$?


  $9\sqrt{10}$
• What is the expression for $\frac{9}{\sqrt{6}}$ with a rational denominator?


  $\frac{3\sqrt{6}}{2}$
• How do you simplify $\frac{4 \times 3a}{\sqrt{a}}$?


  By dividing the indices
• What is the result of $5 - \frac{1}{2}$?


  $\frac{9}{2}$
• What is the box method for expanding brackets?

  • Draw a box for each set of brackets
  • Multiply each term in one bracket by each term in the other
  • Combine like terms
• What is the factorization of $4x^2 - 25$?


  $(2x - 5)(2x + 5)$
• How do you factorize $2x^2 - x - 10$?


  By splitting the middle term
• What is the final simplified form of $\frac{4x^2 - 25}{2x^2 - x - 10}$?


  $2x +$$5$
• What is the first step in expressing algebraic fractions?

  Find a common denominator
• How do you simplify $\frac{4x + 2}{x + 2} \div (x + 2)$?


  By multiplying by the reciprocal
• What is the result of simplifying $\frac{3}{x - 2} +$$\frac{5}{x + 1}$?


  Combine over a common denominator
• What is the expression for the algebraic fraction mentioned?

  $\frac{x + 2}{5}$
• Why is there no need to expand the bracket in the algebraic fraction?

  It is already simplified
• How do you express an algebraic fraction as a single fraction?

  Multiply the denominators for a common denominator
• What is the common denominator for the fractions in the example?

  $(x - 2)(x + 1)$
• What do you do after finding the common denominator?

  Expand and simplify the numerators
• What is the result of expanding the numerators in the example?

  8x - 7
• What is the final expression for the algebraic fraction?

  $\frac{8x - 7}{(x - 2)(x + 1)}$
• What is the function given in the example?

  $f(x) =$$x^3 - 2$
• What is the value of $f(-3)$?


  $-29$
• How do you find the gradient of a line given two points?

  Use the formula $\frac{y_2 - y_1}{x_2 - x_1}$
• What is the gradient calculated from the points given?

  $-4$
• What is the equation of the line in point-slope form?

  $y - 7 =$$-4(x + 5)$
• What is the rearranged equation of the line?

  $y =$$-4x - 3$
• How do you find the coordinates where a line crosses the x-axis?

  Set $y =$$0$ in the equation