Number

Traps in Number

• 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.
• Calculates a different quantity
  Name the quantity and its unit before you start (remainder; horizontal distance; cm²). After calculating, check your number is that quantity and not a neighbour.
• 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.
• 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.
• Leaves out a term of the formula
  Write the full formula before substituting and tick each term as you fill it in.
• Uses the wrong base for a percentage
  Ask: "percentage OF what?" The original is 100%. After a 20% cut you have 80%, so original = new ÷ 0.8. For an increase, multiply by 1 + rate.
• 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?
• Writes an amount with the wrong unit
  A percentage is a ratio × 100. An amount in cedis only becomes a % after dividing by the original amount.
• Inverts a relationship
  Say the rule with its direction (angle at centre = TWICE the angle at the circumference; (x − 1) = 0 gives x = +1). Check your answer against a simple case.
• Treats one part of a ratio as the total
  In a : b, total parts = a + b. One part = amount ÷ (a + b). Then multiply by the part you need.
• Gives the other person's share
  Write the ratio with names above the numbers (Kofi : Ama = 4 : 5) and circle whose share is asked for before calculating.
• Repeats a given value as the answer
  If your answer equals a number in the question, check whether the rule really leaves it unchanged. Most rules transform the given value.
• Ignores place value in number bases
  Each place is a power of the base: …2², 2¹, 2⁰. Multiply each digit by its place value and add.
• Gives the new amount as a percentage instead of the change
  Percentage change = change ÷ original × 100. Find the change first (SP − CP), then divide by the original (CP).
• Mixes up the roles of the quantities
  Label each symbol with its meaning (a = first term, d = common difference; in y = mx + c, m = gradient, c = intercept) before substituting.
• Is off by one in counting
  For the nth term there are n − 1 gaps between the 1st and nth terms. For quartiles, use the (n + 1)/4 and 3(n + 1)/4 positions and count carefully.
• Uses n instead of (n−1) in progressions
  The 1st term already includes a, so you add d only (n−1) times: Tₙ = a + (n−1)d; GP: Tₙ = arⁿ⁻¹. Check with n = 1.
• Multiplies the bases
  The base never changes when you use index laws — only the power does. 2³ × 2⁴ is 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁷.
• Confuses AP and GP
  Test: subtract consecutive terms (AP if constant) and divide them (GP if constant).
• 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.
• Adds surds by adding the numbers inside
  Only LIKE surds add: 2√3 + 5√3 = 7√3. Simplify each surd first by taking out square factors (√12 = 2√3). Test: √9 + √16 = 7, but √25 = 5.
• 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.
• Uses the wrong operation
  Write the rule in words first (bearing back = bearing ± 180°; IQR = Q₃ − Q₁), then substitute. Estimate: does the size of the answer make sense?