Expressions, Formulae and Equations | Year 7 Mathematics (Cambridge) PDF Download

Simplifying Expressions

When simplifying expressions, we focus on combining like terms and applying distributive properties to make them more straightforward.
Here’s how it works:

• Combining Like Terms: Terms with the same variable and exponent can be added or subtracted together.
  • Example: 3x + 2x = 5x
  • Example: 4y − 2y + y = 3y
• Distributive Property: This allows us to distribute a number or variable through parentheses.
  • Example: 2(a + b) = 2a + 2b
  • Example: 3(x − 2) = 3x − 6

Solving Equations

Equations are like balances that we need to keep equal. Here’s how we solve them step-by-step:

• Isolating Variables: Move numbers and terms to get the variable alone on one side of the equation.
  • Example: 2x + 3 = 9
    • Subtract 3 from both sides: 2x = 6
    • Divide both sides by 2: x = 3
• Balancing Equations: Whatever operation we do to one side, we must do the same to the other to keep the equation balanced.

Using Formulae

Formulas are essential tools in maths, acting like recipes for solving specific problems:

• Substituting Values: Replace variables in a formula with given numbers to find the result.
  • Example: A = πr² (Area of a circle)
    • If r = 2, then A = π⋅2² = 4π
• Rearranging Formulas: Sometimes we need to solve for a different variable within the formula.
  • Example: V = l × w × h (Volume of a box)
    • Solve for h:

Summary

Mastering the skills of simplifying expressions, solving equations, and using formulas empowers us to tackle complex mathematical problems effectively. These concepts not only build a strong foundation in maths but also lay the groundwork for understanding more advanced mathematical concepts in the future. Regular practice and application of these techniques enhance problem-solving abilities and critical thinking skills.