CBSE Math Revision Start revising
Themed maths · February

Women in maths: mathematician cards for CBSE Class 10

A ready-to-teach lesson for February: three ‘mathematician cards’, each built on maths that carries a woman mathematician’s name or that she is known for. A 5-minute starter, a 35-minute main activity (one card per task), an extension and full worked answers. No calculator.

Level
CBSE Class 10 (Class 9 can try most of it)
Time
40 minutes, plus a 10-minute extension
Topics
Real numbers: primes and Euclid’s division lemma; Areas related to circles: sectors; Coordinate geometry: plotting a curve; Algebraic proof
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: task A11 minCard 1: Sophie Germain primes
Main: task B12 minCard 2: Nightingale’s rose diagram
Main: task C12 minCard 3: the witch of Agnesi
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths.

  1. Is 2 × 29 + 1 a prime number?
  2. Write 95 as a product of primes.
  3. Find the area of a sector of radius 7 cm and angle 90°. (Use π = 22/7.)
  4. Find the HCF of 23 and 47.

Main activity (35 minutes)

Task A: Card 1: Sophie Germain primes (11 min)

A prime p is a Sophie Germain prime when 2p + 1 is also prime. For example, 11 is one, because 23 is prime.

  1. Find all the Sophie Germain primes less than 50. How many are there?
  2. Find the smallest prime p for which 2p + 1 is not prime.
  3. Every prime bigger than 3 has the form 6q + 1 or 6q + 5 (Euclid’s division lemma with divisor 6). Show that if p = 6q + 1 then 2p + 1 is a multiple of 3.

Task B: Card 2: Nightingale’s rose diagram (12 min)

Florence Nightingale is known for polar area diagrams (‘rose diagrams’): 12 months drawn as 12 equal sectors of 30°, where the area of each sector shows the number. Use π = 22/7.

  1. Find the area of a 30° sector of radius 14 cm.
  2. Another month needs 4 times the area. What radius should its sector have?
  3. Find the perimeter of the 30° sector of radius 14 cm.

Task C: Card 3: the witch of Agnesi (12 min)

The curve y = 8/(x2 + 4) is one of a family known as the witch of Agnesi, after Maria Gaetana Agnesi.

  1. Copy and complete the table, giving y as a fraction: x = 0, 1, 2, 3, 4. Then plot the points for x = −4 to 4.
  2. Find the values of x for which y = 1/2.
  3. Does the point (2, 1) lie on the curve? Show how you know.

Extension (10 minutes)

For fast finishers, or as homework.

  1. Find all the Sophie Germain primes between 50 and 100.
  2. A rose diagram uses a sector of radius 7 cm for 35 cases. What radius is needed for 140 cases?

For teachers

Teacher notes and full worked answers
  • Print the three tasks as cards and rotate groups between them.
  • The cards name each mathematician only through the maths named after her or that she is known for: invite students to research one of them for homework from a reliable source.
  • Card 1 (c) uses Euclid’s division lemma in the same way as the textbook proofs about odd and even numbers.

Starter

  1. Yes, 59
    • 59 is not divisible by 2, 3, 5 or 7, and 82 = 64 > 59.
  2. 5 × 19
    • 95 = 5 × 19
  3. 38.5 cm2
    • 90/360 × 22/7 × 7 × 7 = ¼ × 154 = 38.5
  4. 1
    • Both are prime.

Task A: Card 1: Sophie Germain primes

  1. 2, 3, 5, 11, 23, 29, 41: seven
    • 2 → 5, 3 → 7, 5 → 11, 11 → 23, 23 → 47, 29 → 59, 41 → 83 are prime.
    • 7 → 15, 13 → 27, 17 → 35, 19 → 39, 31 → 63, 37 → 75, 43 → 87, 47 → 95 are not.
  2. 7, because 15 = 3 × 5
    • 2, 3, 5 give 5, 7, 11; 7 gives 15.
  3. 2p + 1 = 3(4q + 1)
    • 2(6q + 1) + 1 = 12q + 3 = 3(4q + 1)
    • So, for p > 3, 2p + 1 is a multiple of 3 bigger than 3, and not prime.

Task B: Card 2: Nightingale’s rose diagram

  1. 154/3 = 51 1/3 cm2
    • 30/360 × 22/7 × 14 × 14 = 1/12 × 616 = 154/3
  2. 28 cm
    • Area is proportional to r2: 4 times the area needs 2 times the radius, 28 cm.
  3. 106/3 = 35 1/3 cm
    • Arc = 30/360 × 2 × 22/7 × 14 = 22/3.
    • Perimeter = 14 + 14 + 22/3 = 106/3

Task C: Card 3: the witch of Agnesi

  1. 2, 8/5, 1, 8/13, 2/5
    • 8/4 = 2, 8/5, 8/8 = 1, 8/13, 8/20 = 2/5
    • x and −x give the same y.
  2. x = ±2√3
    • x2 + 4 = 16, so x2 = 12 and x = ±√12 = ±2√3.
  3. Yes
    • 8/(22 + 4) = 8/8 = 1, which matches y = 1.

Extension

  1. 53, 83 and 89
    • 53 → 107, 83 → 167, 89 → 179 are prime.
    • 59 → 119 = 7 × 17, 61 → 123, 67 → 135, 71 → 143 = 11 × 13, 73 → 147, 79 → 159, 97 → 195 are not.
  2. 14 cm
    • 140 = 4 × 35, so the area is 4 times as big and the radius 2 times: 14 cm.

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

Practise the topics

National Science Day (India) maths · Pi Day maths · Pi Approximation Day maths · All themed maths

More for lessons: Weekly starters · Worksheet builder · Olympiad and competition maths · National Mathematics Day puzzles