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Themed maths

End-of-year maths quiz for IB Maths

A five-round team quiz on the whole year for the last lesson of term: five questions in each round, getting harder, with every answer worked out. Read it aloud, print it, or play it on the projector as a Jeopardy board with team scores.

Level
IB Maths SL and HL (AA and AI)
Time
40 minutes, plus a 5-minute extension
Topics
Number and algebra; Functions; Geometry and trigonometry; Statistics and probability; Calculus
Equipment
No GDC needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: round 17 minNumber and algebra
Main: round 27 minFunctions
Main: round 37 minGeometry and trigonometry
Main: round 47 minStatistics and probability
Main: round 57 minCalculus
Extension5 minFast finishers or homework

Starter (5 minutes)

Warm-up while teams get settled.

  1. Work out 6 × 7.
  2. Work out √81.

Main activity (35 minutes)

Play it on the projector

Opens these five rounds on our Jeopardy board for teams (teacher sign-in): pick a round and a points value, reveal the answer, award the points.

Round 1: Number and algebra (7 min)

Five questions, getting harder.

  1. Evaluate log3 81.
  2. u1 = 5 and d = 3. Find u20.
  3. Find the sum to infinity of 8 + 4 + 2 + …
  4. Solve 2x + 1 = 32.
  5. Find the coefficient of x3 in (2 + x)5.

Round 2: Functions (7 min)

Five questions, getting harder.

  1. f(x) = 2x + 3. Find f−1(11).
  2. Write down the vertex of y = (x − 2)2 + 5.
  3. Write down the vertical asymptote of y = 3/(x − 4).
  4. f(x) = x2 and g(x) = x + 1. Find (f ∘ g)(2).
  5. Solve e2x = 7, giving an exact answer.

Round 3: Geometry and trigonometry (7 min)

Five questions, getting harder.

  1. Write down the exact value of cos 60°.
  2. Find the arc length of a sector of radius 6 cm and angle π/3.
  3. Find the distance between (1, 2, 3) and (3, 5, 9).
  4. Solve sin x = 1/2 for 0 ≤ x ≤ π.
  5. Find the area of a triangle with sides 8 cm and 5 cm and an included angle of 30°.

Round 4: Statistics and probability (7 min)

Five questions, getting harder.

  1. Find the mean of 3, 7, 8, 10, 12.
  2. A and B are independent with P(A) = 0.3 and P(B) = 0.5. Find P(A ∩ B).
  3. X ~ B(10, 0.2). Find E(X).
  4. X ~ N(50, 42). Find P(X > 50).
  5. P(A) = 0.6, P(B) = 0.5 and P(A ∪ B) = 0.8. Find P(A ∩ B).

Round 5: Calculus (7 min)

Five questions, getting harder.

  1. Differentiate x4.
  2. Find ∫ 6x2 dx.
  3. Find the gradient of y = x2 − 3x at x = 5.
  4. Evaluate ∫02 3x2 dx.
  5. Find the gradient of y = xex at x = 0.

Extension (5 minutes)

If two teams are level at the end.

  1. Tie-break, closest wins: how many seconds are there in a week?

For teachers

Teacher notes and full worked answers
  • How to run it: teams of three or four with a mini whiteboard. Read each question out (or use ‘Play it on the projector’ above for a Jeopardy board with team scores). Questions get harder through each round: 1 point for question 1 up to 5 points for question 5, or use the board’s 100 to 500.
  • Tie-break: every team writes one estimate; the closest wins.

Starter

  1. 42
    • 6 × 7 = 42
  2. 9
    • 9 × 9 = 81

Round 1: Number and algebra

  1. 4
    • 34 = 81
  2. 62
    • 5 + 19 × 3
  3. 16
    • 8/(1 − ½)
  4. x = 4
    • x + 1 = 5
  5. 40
    • 5C3 × 22 = 10 × 4

Round 2: Functions

  1. 4
    • 2x + 3 = 11
  2. (2, 5)
    • Vertex form
  3. x = 4
    • The denominator is zero at x = 4.
  4. 9
    • g(2) = 3 and f(3) = 9
  5. x = ½ ln 7
    • 2x = ln 7

Round 3: Geometry and trigonometry

  1. 1/2
    • Standard value
  2. 2π cm
    • rθ = 6 × π/3
  3. 7
    • √(4 + 9 + 36) = 7
  4. π/6 and 5π/6
    • sin is positive in the first and second quadrants.
  5. 10 cm2
    • ½ × 8 × 5 × sin 30° = 10

Round 4: Statistics and probability

  1. 8
    • 40 ÷ 5
  2. 0.15
    • 0.3 × 0.5
  3. 2
    • np = 2
  4. 0.5
    • 50 is the mean, and the curve is symmetric.
  5. 0.3
    • 0.6 + 0.5 − 0.8

Round 5: Calculus

  1. 4x3
    • Power rule
  2. 2x3 + C
    • Add 1 to the power and divide by it.
  3. 7
    • 2x − 3 = 7
  4. 8
    • [x3]02 = 8
  5. 1
    • Product rule: ex + xex = 1 at x = 0

Extension

  1. 604 800
    • 60 × 60 × 24 × 7 = 604 800

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

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