Forming & solving equations

• What is an expression in algebra?

  An expression is an algebraic statement without an equals sign.
• Why do we form expressions in algebra?

  To help express unknown values.
• How can you represent an unknown value in an expression?

  You can represent it by a letter such as x.
• How would you express "2 less than something" in algebra?


  x - 2
• How would you express "double the amount of something" in algebra?

  2x
• How would you express "5 lots of something" in algebra?

  5x
• How would you express "3 more than something" in algebra?


  x + 3
• How would you express "half the amount of something" in algebra?


  \(\frac{1}{2}x\) or \(x/2\)
• Why might you need to use brackets in algebraic expressions?


  To show the correct order of operations.
• How would you express "something add 1 then multiplied by 3" in algebra?

  (x + 1) × 3, which simplifies to 3(x + 1)
• How would you express "something multiplied by 3 then add 1" in algebra?

  (x × 3) + 1, which simplifies to 3x + 1
• What is the benefit of choosing the smallest value to represent a letter in algebra?

  It makes the algebra easier.
• If Adam is 10 years younger than Barry, how would you represent their ages?

  Represent Adam's age as x, then Barry's age is x + 10.
• If Adam's age is half of Barry's age, how would you express their ages?

  If Adam's age is x, then Barry's age is 2x.
• What is an equation?

  An equation is an expression with an equals sign that can be solved.

  
• How do you form an equation from a word problem?

  You first need to form an expression and make it equal to a value or another expression.
• What are alternative words for addition?


  Sum, total, more than, increase, etc.
• What are alternative words for subtraction?

  Difference, less than, decrease, etc.
• What are alternative words for multiplication?

  Product, lots of, times as many, double, triple, etc.
• What are alternative words for division?

  Shared, split, grouped, halved, quartered, etc.
• If Adam is 10 years younger than Barry and their ages sum to 25, how can you find their ages?


  Represent Adam's age as x, then Barry's age is x + 10, and solve the equation \(x + (x + 10) = 25\).
• How would you express that an adult's ticket is double the price of a child's ticket?

  Adult = 2 × Child
• How would you express that a child's ticket is £7 cheaper than an adult's ticket?

  Child = Adult - £7
• How would you express the total cost of 3 children's tickets and 2 adults' tickets is £45?

  3 × Child + 2 × Adult = £45
• What should you do if a question involves area, perimeter, or angles?

  Read the question carefully to decide which one it involves.
• What is a good practice if no diagram is given in a question about shapes?

  Quickly sketch one.
• How do you determine the perimeter of a shape?

  Figure out which sides are equal length and add these together.
• What is true about the sides of a square or rhombus?

  All four sides are equal.
• What is true about the sides of a rectangle or parallelogram?

  Opposite sides are equal.
• What should you do if the question involves area?

  Write down the necessary formula for the area of that shape.
• What should you do if the shape is uncommon?

  You may need to split it up into two or more common shapes.
• What does a regular polygon mean?

  All the sides are equal length.

  
• How do you find the perimeter of a regular pentagon with side length \(2x - 1\)?

  The perimeter is \(5(2x - 1)\).
• What should you use for a circle or part of a circle in calculations?

  Use \(\pi\) throughout rather than multiplying by it.
• What should you do if the question involves angles in a 2D shape?

  Consider the properties of angles within the given shape.
• How many equal angles does an isosceles triangle have?

  Two equal angles.
• How many equal angles does an equilateral triangle have?

  Three equal angles.
• What is true about angles in a parallelogram or rhombus?

  Opposite angles are equal and all four sum to 360°.
• What is true about a kite's angles?

  A kite has one equal pair of opposite angles.
• What is the formula for the sum of the interior angles of a polygon with \(n\) sides?

  The sum is \(180° \times (n - 2)\).