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Themed maths

Summer maths escape room for IB Maths

The beach hut is locked, and the keys are in a box with six locks. 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
IB Maths SL and HL (AA and AI)
Time
41 minutes, plus a 10-minute extension
Topics
Sequences and series; Exponential equations; Integration; The binomial distribution
Equipment
No GDC needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: lock 16 minThe shells
Main: lock 26 minThe tide
Main: lock 36 minThe sand
Main: lock 46 minThe windbreak
Main: lock 56 minThe coin
Main: lock 66 minThe beach hut
Extension10 minFast finishers or homework

Starter (5 minutes)

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

  1. Evaluate ln e3.
  2. Find the gradient of y = x3 at x = 2.
  3. Evaluate 34.

Main activity (36 minutes)

Lock 1: The shells (6 min)

A geometric sequence starts 2, 6, 18, …

  1. Find its 6th term. This is code 1.

Lock 2: The tide (6 min)

The second lock shows an exponential equation.

  1. Solve 3x = code 1 ÷ 2. This is code 2.

Lock 3: The sand (6 min)

The third lock shows an integral.

  1. Evaluate ∫0b 2x dx, where b = code 2. This is code 3.

Lock 4: The windbreak (6 min)

A right-angled triangle has hypotenuse √(code 3) and one shorter side 3.

  1. Find the other shorter side. This is code 4.

Lock 5: The coin (6 min)

X ~ B(n, 1/2), where n = code 4.

  1. Write P(X = 2) as a fraction a/b in its lowest terms. Code 5 is a + b.

Lock 6: The beach hut (6 min)

The last lock.

  1. Find the term of the arithmetic sequence 100, 93, 86, … whose position is code 5. It opens the hut.

Extension (10 minutes)

Bonus lock for the fastest team.

  1. Find the sum to infinity of 30 + 10 + 10/3 + …

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
    • ln and e undo each other.
  2. 12
    • 3x2 = 12
  3. 81
    • 3 × 3 × 3 × 3 = 81

Lock 1: The shells

  1. 486
    • u6 = 2 × 35 = 486

Lock 2: The tide

  1. 5
    • 3x = 243 = 35

Lock 3: The sand

  1. 25
    • [x2]05 = 25

Lock 4: The windbreak

  1. 4
    • √(25 − 9) = 4

Lock 5: The coin

  1. P = 3/8, so code 11
    • 4C2 × (1/2)4 = 6/16 = 3/8
    • 3 + 8 = 11

Lock 6: The beach hut

  1. 30
    • u11 = 100 − 10 × 7 = 30

Extension

  1. 45
    • r = 1/3
    • 30 / (1 − 1/3) = 45

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

Practise the topics

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