A Level Math Revision Free diagnostic
Themed maths

Spot the mistake relay and maths taboo for A Level Maths

An end-of-term lesson that is fun and still useful: teams race to find the slip in worked solutions built on the most common exam mistakes, then play maths taboo and pictionary with the course’s vocabulary.

Level
A Level Maths (Year 12 and Year 13)
Time
39 minutes, plus a 10-minute extension
Topics
Algebra and functions, the binomial expansion; Integration by parts and R cos(θ − α); The binomial and normal distributions; Proof
Equipment
A calculator is needed for task B.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minRelay, part 1
Main: task B12 minRelay, part 2
Main: task C10 minMaths taboo
Extension10 minFast finishers or homework

Starter (5 minutes)

Spot the slip: each line has one mistake.

  1. Using cos θ ≈ 1 − θ2/2, cos 2θ ≈ 1 − 2θ2/2 = 1 − θ2
  2. The x2 term of (1 + 3x)4 is 6 × 3x2 = 18x2
  3. X ~ B(4, 0.5): P(X > 3) = 1 − P(X ≤ 4) = 0

Main activity (34 minutes)

Task A: Relay, part 1 (12 min)

Each worked solution has exactly one mistake. Find it, then give the correct answer.

  1. Find ∫ xex dx. Working: xex + ex + c.
  2. (6, 5) lies on y = f(x). Find the matching point on y = f(2x). Working: a stretch with scale factor 2 parallel to the x-axis gives (12, 5).
  3. Write 3 cos θ + 4 sin θ as R cos(θ − α). Working: R = 5, tan α = 3/4, α = 36.9°.

Task B: Relay, part 2 (12 min)

Each worked solution has exactly one mistake. Find it, then give the correct answer.

  1. f(x) = 2x and g(x) = x + 3. Find fg(1). Working: g(f(1)) = g(2) = 5.
  2. X ~ N(20, 22). Find P(X < 22). Working: with a continuity correction, P(X < 22.5) = P(Z < 1.25) = 0.894.
  3. f(x) = x3 − 2x − 5. Show that f(x) = 0 has a root between 2 and 3. Working: f(2) = −1 and f(3) = 16.

Task C: Maths taboo (10 min)

Describe the word to your team without saying it or any of the banned words.

  1. Describe INTEGRAL without saying: area, under, curve, anti.
  2. Describe VECTOR without saying: direction, magnitude, arrow, size.
  3. Describe POLYNOMIAL without saying: power, term, degree, quadratic.
  4. Describe FUNCTION without saying: input, output, machine, map.

Extension (10 minutes)

For fast finishers.

  1. Prove that x2 − 6x + 10 > 0 for all real x. Working: squares are always positive, so it is positive.

For teachers

Teacher notes and full worked answers
  • Relay: teams of three. Give each team the first worked solution; when they bring you the mistake and the corrected answer, they get the next one. The first team through all six wins.
  • Every slip here is one of the common mistakes on our Edexcel A Level Examiner Insights page, in a new example of our own. Show the page afterwards so students can see which mistakes cost the most marks.
  • Taboo cards: one student describes the word without saying it or any of the banned words; their team guesses. The sample clue on each card shows that it can be done.
  • Pictionary (no words or numbers allowed on the board, 60 seconds each): asymptote, tangent, normal, vector, point of inflection, radian, box plot, moment.

Starter

  1. 1 − 2θ2
    • Bracket the whole angle: 1 − (2θ)2/2 = 1 − 4θ2/2
  2. 54x2
    • (3x)2 = 9x2, so 6 × 9x2
  3. 1/16
    • P(X > 3) = 1 − P(X ≤ 3) = P(X = 4) = 1/16

Task A: Relay, part 1

  1. xex − ex + c
    • Mistake: a sign. By parts, ∫ u dv = uv − ∫ v du.
    • xex − ∫ ex dx = xex − ex + c
  2. (3, 5)
    • Mistake: f(2x) is a stretch with scale factor ½ parallel to the x-axis.
    • (6 ÷ 2, 5) = (3, 5)
  3. 5 cos(θ − 53.1°)
    • Mistake: the ratio is upside down. R cos α = 3 and R sin α = 4, so tan α = 4/3.
    • α = 53.1°

Task B: Relay, part 2

  1. 8
    • Mistake: fg means do g first, then f.
    • fg(1) = f(g(1)) = f(4) = 8
  2. 0.841
    • Mistake: a continuity correction is only for approximating a discrete distribution.
    • P(Z < 1) = 0.841
  3. Add the conclusion
    • Mistake: no conclusion. f(2) < 0 < f(3) and f is continuous on [2, 3], so there is a change of sign and a root between 2 and 3.

Task C: Maths taboo

  1. Sample clue: ‘Undoes differentiation, like adding up lots of thin strips.’
    • The word is integral. Any clue that avoids the banned words is fine.
  2. Sample clue: ‘Something with both how big and which way, like a velocity.’
    • The word is vector. Any clue that avoids the banned words is fine.
  3. Sample clue: ‘An expression like 3a³ + 2a − 7, with whole-number indices.’
    • The word is polynomial. Any clue that avoids the banned words is fine.
  4. Sample clue: ‘A rule that turns each number you put in into exactly one number.’
    • The word is function. Any clue that avoids the banned words is fine.

Extension

  1. (x − 3)2 + 1 ≥ 1 > 0
    • Mistake: the reasoning is incomplete, and a square can be 0.
    • x2 − 6x + 10 = (x − 3)2 + 1. Since (x − 3)2 ≥ 0, the expression is at least 1, so it is always positive.

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

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