Math

• What are some challenging topics in GCSE maths?

  Indices and surds, fractions and percentages, algebra, geometry and trigonometry, statistics and probability
• What is the equation to solve in the first step?

  $3x +$$5 =$$20$
• What is a linear equation?

  • Has one variable, usually $x$
  • Variable raised to the power of 1
  • Consists of two sides separated by an equal sign
  • Contains variable on one side and constants on the other
• In the linear equation $4x +$$7 =$$19$, what are the variable and constant terms?


  Variable: $4x$, Constants: $7$, $19$
• What is the variable in the equation $3x +$$5 =$$20$?


  $x$ is the variable
• What are the constants in the equation $3x +$$5 =$$20$?


  Constants are $3$ and $5$
• What operation should be applied to isolate the variable in $3x +$$5 =$$20$?


  Subtract $5$ from both sides
• What does the addition or subtraction property of equality state?


  You can add or subtract the same number to both sides
• What is the result after isolating the variable term in $3x +$$5 =$$20$?


  $3x =$$15$
• How do you solve for $x$ in $3x =$$15$?


  Divide both sides by $3$
• What is the solution for $x$ in $3x =$$15$?


  $x =$$5$
• What is the multiplication or division property of equality?

  • You can multiply or divide both sides by the same number (except zero)
  • It does not alter the balance of the equation
• How do you solve $\frac{x}{2} =$$7$ for $x$?


  Multiply both sides by $2$
• What is the solution for $x$ in $\frac{x}{4} =$$9$?


  $x =$$36$
• How do you verify a solution in an equation?

  1. Substitute the solution back into the original equation
  2. Calculate to check if both sides are equal
  3. Confirm if the solution is correct
• How do you verify the solution $x =$$5$ for $3x +$$5 =$$20$?


  Substitute $x =$$5$ into the equation
• What does substituting $x =$$5$ into $3x +$$5 =$$20$ show?


  It confirms $20 =$$20$
• What is the solution for $2x +$$6 =$$10$?


  $x =$$2$
• How do you verify the solution $x =$$2$ for $2x +$$6 =$$10$?


  Substitute $x =$$2$ into the equation
• What does substituting $x =$$2$ into $2x +$$6 =$$10$ confirm?


  It confirms the equation holds true
• What is a linear equation?

  • Has one variable, usually $x$
  • Variable raised to the power of 1
  • Consists of two sides separated by an equal sign
  • Contains variable on one side and constants on the other
• What is the equation to solve in the first step?

  $3x +$$5 =$$20$
• What is the equation used to find the value of $y$?


  $2y - 7 =$$13$
• What operation is performed to isolate $y$ in the equation $2y - 7 =$$13$?


  Add 7 to both sides
• What is the result of adding 7 to both sides of $2y - 7 =$$13$?


  $2y =$$20$
• Why do we add 7 to both sides of the equation?

  To eliminate the $-7$ term
• What does the left side of the equation become after adding 7?

  $2y$
• What is the simplified form of the left side after combining like terms?

  $2y$
• What operation is performed to isolate $y$ in the equation $2y =$$20$?


  Divide both sides by 2
• What is the result of dividing both sides of $2y =$$20$ by 2?


  $y =$$10$
• What is the right side of the equation after adding 7 to both sides?

  $20$
• What is the final value of $y$ after solving the equation?


  $10$
• What is the first step to solve for $z$ in the equation $\frac{z}{3} +$$4 =$$10$?


  Subtract 4 from both sides
• What is the original equation used for checking?

  $\frac{z}{3} +$$4 =$$10$
• Why do we subtract 4 from both sides of the equation?

  To keep the equation balanced
• What does the equation become after subtracting 4 from both sides?

  $\frac{z}{3} =$$6$
• What operation is performed to isolate $z$ in the equation $\frac{z}{3} =$$6$?


  Multiply both sides by 3
• What is the result of the operation $10 - 4$ in the equation?


  6
• What is the result of multiplying both sides of $\frac{z}{3} =$$6$ by 3?


  $z =$$18$
• How does the equation $3 \times \frac{z}{3} =$$6 \times 3$ simplify to $z =$$18$?


  Both sides simplify to $z =$$18$