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Themed maths

Christmas maths escape room for A Level Maths

The elves have locked the workshop, and the presents are stuck inside. Teams solve six locks in order; each code is needed for the next. Printable clue cards, a teacher answer key and a bonus lock for the fastest team.

Level
A Level Maths (Year 12 and Year 13)
Time
41 minutes, plus a 10-minute extension
Topics
Algebra and functions: indices and the factor theorem; The binomial expansion; Integration; Sequences and series
Equipment
No calculator needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: lock 16 minThe wrapping room
Main: lock 26 minThe list
Main: lock 36 minThe chimney
Main: lock 46 minThe tinsel
Main: lock 56 minThe factor lock
Main: lock 66 minThe workshop door
Extension10 minFast finishers or homework

Starter (5 minutes)

Warm-up before the locks: quick questions on the board.

  1. Evaluate 271/3.
  2. Differentiate x4.
  3. Evaluate log2 8.

Main activity (36 minutes)

Lock 1: The wrapping room (6 min)

The first lock shows an index equation.

  1. Solve 2x − 1 = 64. This is code 1.

Lock 2: The list (6 min)

The second lock shows a binomial expansion.

  1. Find the coefficient of x2 in (1 + 2x)n, where n = code 1. This is code 2.

Lock 3: The chimney (6 min)

The third lock shows an integral.

  1. Find the positive value of a for which ∫0a 3x2 dx = code 2 − 20. This is code 3.

Lock 4: The tinsel (6 min)

Each strand of tinsel is half as long as the one before.

  1. A geometric series has first term code 3 and common ratio 1/2. Find its sum to infinity. This is code 4.

Lock 5: The factor lock (6 min)

The lock shows f(x) = x3 − 2x + 5.

  1. Find the remainder when f(x) is divided by (x − c), where c = code 4 ÷ 4. This is code 5.

Lock 6: The workshop door (6 min)

The last lock.

  1. Find the sum of the first n terms of 2 + 5 + 8 + …, where n = code 5. It opens the door.

Extension (10 minutes)

Bonus lock for the fastest team.

  1. A toy rocket’s height is h = 20t − 5t2 metres after t seconds. Find its greatest height.

For teachers

Teacher notes and full worked answers
  • How to run it: print the student sheet and cut out the six lock cards. Give each team lock 1. When a team brings you the right code, give them the next card (the answer key is in the answers PDF). The first team to open lock 6 escapes. Teams can also have every card at once and race through them in order.
  • Each code is used in the next lock, so check every code before the team moves on: one slip early on breaks the chain.

Starter

  1. 3
    • 33 = 27
  2. 4x3
    • Bring down the power.
  3. 3
    • 23 = 8

Lock 1: The wrapping room

  1. 7
    • 64 = 26, so x − 1 = 6

Lock 2: The list

  1. 84
    • 7C2 × 22 = 21 × 4 = 84

Lock 3: The chimney

  1. 4
    • [x3]0a = a3 = 64

Lock 4: The tinsel

  1. 8
    • 4 / (1 − 1/2) = 8

Lock 5: The factor lock

  1. 9
    • c = 2
    • f(2) = 8 − 4 + 5 = 9

Lock 6: The workshop door

  1. 126
    • S9 = 9/2 × (2 × 2 + 8 × 3) = 9/2 × 28 = 126

Extension

  1. 20 m
    • dh/dt = 20 − 10t = 0 at t = 2
    • h = 40 − 20 = 20

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

Practise the topics

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