Algebra

Traps in Algebra

• Incomplete inverse operations
  Undo operations in REVERSE order, one at a time, to the whole of each side. Make a list: what was done to x? Undo the last one first. Check by substituting back.
• Sign slip when moving or multiplying terms
  Moving a term across "=" means doing the opposite operation to BOTH sides. And (−)×(−) = (+). Write each step on a new line; circle every minus sign before you expand.
• Leaves out a term of the formula
  Write the full formula before substituting and tick each term as you fill it in.
• Applies the rule for a different situation
  Identify the situation first (angle at centre? opposite angles of a cyclic quadrilateral? reverse bearing?) and write the rule that belongs to it before calculating.
• Careless calculation
  Not a knowledge gap — a checking gap. Re-read the question, estimate the answer first, and check every line before you choose an option.
• Mixes up the laws of indices
  aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ. Check with small numbers: 2² × 2³ = 4 × 8 = 32 = 2⁵.
• Uses only part of the information
  Tick off every number and every condition in the stem as you use it. If one is unticked at the end, the answer is incomplete.
• Ignores the power in variation
  Write the law first (y = kx²), find k from the given pair, then substitute. Doubling x in y ∝ x² multiplies y by 4.
• Stops one step short of the answer
  Before writing the answer, re-read the question's last words (each angle? neither? Ama's share? variance?). Ask: is my number that thing, or a stage on the way to it?
• Confuses direct and inverse variation
  'Varies directly' → y = kxⁿ (y grows with x). 'Varies inversely' → y = k/xⁿ (y shrinks as x grows). Write the equation from the words first.
• Inequality sign flipping errors
  Only multiplying or dividing BOTH sides by a NEGATIVE number reverses the inequality. Test a value to check.
• Determinant formula slips
  For [[a,b],[c,d]], |A| = ad − bc: leading diagonal product MINUS the other diagonal.