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End-of-year maths quiz for CBSE Class 10

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
CBSE Class 10 (Class 9 can try most of it)
Time
40 minutes, plus a 5-minute extension
Topics
Real numbers and polynomials; APs and coordinate geometry; Trigonometry and mensuration; Statistics and probability
Equipment
No calculator. Use π = 22/7 where a question says so.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: round 17 minReal numbers
Main: round 27 minAlgebra
Main: round 37 minAPs and coordinates
Main: round 47 minTrigonometry and mensuration
Main: round 57 minStatistics and probability
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: Real numbers (7 min)

Five questions, getting harder.

  1. Find the HCF of 84 and 126.
  2. Find the LCM of 12 and 18.
  3. Write 7/40 as a decimal.
  4. HCF × LCM of two numbers is 360. One number is 18. Find the other.
  5. Find the largest number that divides 245 and 1029 leaving remainder 5 each time.

Round 2: Algebra (7 min)

Five questions, getting harder.

  1. Solve 5x − 3 = 17.
  2. Find the zeroes of x2 − 9x + 20.
  3. Find the sum of the zeroes of 2x2 − 8x + 5.
  4. Solve x + y = 10 and x − y = 4.
  5. Find the positive value of k for which x2 + kx + 9 = 0 has equal roots.

Round 3: APs and coordinates (7 min)

Five questions, getting harder.

  1. Find the 20th term of the AP 3, 7, 11, …
  2. Find the sum of the first 20 natural numbers.
  3. Find the distance between (2, 3) and (8, 11).
  4. Find the midpoint of (−2, 5) and (6, −1).
  5. Which term of the AP 21, 18, 15, … is −81?

Round 4: Trigonometry and mensuration (7 min)

Five questions, getting harder.

  1. Find sin 30° + cos 60°.
  2. Find tan2 45° + 1.
  3. Find the area of a circle of radius 14 cm. (Use π = 22/7.)
  4. From a point 30 m from the foot of a tower, the angle of elevation of the top is 45°. Find the height.
  5. Find the volume of a cone of radius 3 cm and height 7 cm. (Use π = 22/7.)

Round 5: Statistics and probability (7 min)

Five questions, getting harder.

  1. A die is thrown. Find P(a prime number).
  2. A card is drawn from a pack of 52. Find P(a king).
  3. Find the mean of 4, 6, 8, 10, 12.
  4. Find the mode of 2, 3, 3, 5, 5, 5, 7.
  5. Two dice are thrown. Find P(the total is 8).

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: Real numbers

  1. 42
    • 84 = 22 × 3 × 7, 126 = 2 × 32 × 7
    • HCF = 2 × 3 × 7 = 42
  2. 36
    • 22 × 32 = 36
  3. 0.175
    • 7/40 = 175/1000
  4. 20
    • 360 ÷ 18 = 20
  5. 16
    • It divides 240 and 1024.
    • HCF(240, 1024) = 16

Round 2: Algebra

  1. x = 4
    • 5x = 20
  2. 4 and 5
    • (x − 4)(x − 5)
  3. 4
    • −b/a = 8/2
  4. x = 7, y = 3
    • Add: 2x = 14
  5. k = 6
    • k2 − 36 = 0

Round 3: APs and coordinates

  1. 79
    • 3 + 19 × 4 = 79
  2. 210
    • 20 × 21 ÷ 2
  3. 10
    • √(36 + 64) = 10
  4. (2, 2)
    • ((−2 + 6)/2, (5 − 1)/2)
  5. The 35th
    • 21 − 3(n − 1) = −81
    • n − 1 = 34

Round 4: Trigonometry and mensuration

  1. 1
    • ½ + ½
  2. 2
    • 1 + 1
  3. 616 cm2
    • 22/7 × 196 = 616
  4. 30 m
    • tan 45° = h/30 = 1
  5. 66 cm3
    • ⅓ × 22/7 × 9 × 7 = 66

Round 5: Statistics and probability

  1. 1/2
    • 2, 3, 5: 3 out of 6
  2. 1/13
    • 4/52
  3. 8
    • 40 ÷ 5
  4. 5
    • 5 appears three times.
  5. 5/36
    • (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)

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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