Mathematics Sample Question Paper

• This is a sample question paper for Mathematics (211).
• The time is 3 hours and the maximum marks are 100.
• Questions 1-16 are multiple-choice questions each worth 1 mark
• Questions 17-26 are each worth 3 marks
• Questions 27-34 are each worth 5 marks
• Questions 35 and 36 are each worth 7 marks

Question 1

• The sum of 2⁰, 3⁰, and 4⁰ is 3

Question 2

• In terms of the power of prime numbers, 360 can be written as 2³ x 3² x 5¹

Question 3

• The highest common factor (HCF) of 12 and 28 is 4

Question 4

• The square root of 0.04 is 0.2

Question 5

• A person took a loan of Rs 1500 from his employer for 3 months at 12% per annum simple interest and the amount to return is Rs 1545

Question 6

• At a book stall, a discount of x% was allowed on each book and a book purchased by a customer for Rs y has a marked price of Rs (100y) / (100 - x)

Question 7

• A wholesaler allows a discount of 20% on the list price to a retailer and the retailer sells at 8% discount on the list price. The profit percent of the retailer is 12%

Question 8

• A man purchased a bundle of cloth, with a list price of Rs 20000, and a sales tax of 10% on it, and he paid Rs 25000 to the shopkeeper. The money he got back was :Rs 3000

Question 9

• In the presented figure, with a transversal PQ intersecting lines AB and CD, a pair of alternate angles is 1 and 4

Question 10

• In triangle ABC, if the bisector of angle A is the same as the median through A, then triangle ABC is isosceles with AB = AC

Question 11

• A circle has area 314 cm², and using π = 3.14, its diameter is 20 cm

Question 12

• A closed right circular cylinder with radius 3.5 m and height 7 m has a total surface area of 231 m²

Question 13

• If tan θ = ¾, then sin θ is ⅗

Question 14

• If sin θ + cos θ = √2 cos θ, the value of tan θ is √2 - 1

Question 15

• Cumulative frequency of a class in a frequency distribution table is the sum of all frequencies up to the class

Question 16

• The cumulative frequency of the last class of a frequency distribution equals the total of all frequencies

Question 17

• Simplify: ⁵√3125 ÷ ⁵√243 = (25√15) / 27

Question 18

• Expand: (x^½ - 1/x^½)² = 4x⁴ - 4x + (1/x²)

Question 19

• Factorize: 1 - x⁴y⁴ = (1 - x²y²)(1 + x²y²) = (1 - xy)(1 + xy)(1 + x²y²)

Question 20

• Express -0.3 as a fraction p/q = - ⅓

Question 21

• A triangle has sides in the ratio 1:1.5:2 and a perimeter of 13.5 cm, the side lengths are 3cm, 4.5cm, and 6cm

Question 22

• Entries in a Savings Account Passbook:
  • 1.7.2002 B/F: Balance Rs 20,000.00.
  • 22.7.2002 By cheque: Deposit Rs 10,000.00, Balance Rs 30,000.00.
  • 30.7.2002 To cheque: Withdrawal Rs 12,000.00, Balance Rs 18,000.00.
  • 20.9.2002 By cheque: Deposit Rs 8,000.00, Balance Rs 26,000.00.
  • 10.10.2002 By cheque: Deposit Rs 10,000.00, Balance Rs 36,000.00.
  • 9.11.2002 By cash: Deposit Rs 8,000.00, Balance Rs 44,000.00.
  • 24.12.2002 To cheque: Withdrawal Rs 33,000.00, Balance Rs 11,000.00.
• The monthly principal on which interest is payable amounts to Rs 145000

Question 23

• In the given figure, where S is any point on QR, it is necessary to prove that PQ + QR + RP > 2PS.
  • PQ + QS > PS
  • PR + SR > PS
  • PQ + QS + PR + SR > 2PS
  • PQ + QR + RP > 2PS

Question 24

• In the given figure, the value of x is 60°
  • 110° + ∠ACB = 180°, so ∠ACB = 70°
  • Also, x + 50° + 70° = 180°
  • x = 60°

Question 25

• A cube with a volume of 1728 cubic cm has a total surface area of 864 cm²
  • If edge of the cube is x cm: x³ = 1728; x = 12
  • Total surface area = 6x² = 6 x 12 x 12 cm² = 864 cm²

Question 26

• Evaluate (cos² 32° + cos² 58°) / (sin² 59° + sin² 31°) = 1
• (cos² 32° + cos² 58°) / (sin² 59° + sin² 31°) = (cos² 32° + cos² (90°-32°)) / (sin² (90°-31°) + sin² 31°)
• = (cos² 32° + sin² 32°) / (cos² 31° + sin² 31°) = 1

Question 27

• The sum of the series + 1/2 + 1/6 + 1/12 + ... + 1/156 = 12/13

Question 28

• 1/(1+x^(b-a)+x^(c-a)) + 1/(1+x^(a-b)+x^(c-b)) + 1/(1+x^(b-c)+x^(a-c)) = 1

Question 29

• Articles are sold at Rs 5 each.
  • First week: 1600 articles were sold.
  • Second week: 1840 articles were sold.
  • Third week: 2024 articles were sold.
• Amount received by the salesman = Rs 3948
  • RS ((12/100) x 1000 x 5) + ((15/100) x 648 x 5)

Question 30

• Medians drawn on equal sides of an isosceles triangle are equal

Question 31

• Instructions to construct triangle ABC with the following: base BC = 4 cm, ∠B = 60°, ∠C = 45°.

Question 32

• A square flower bed is prepared in the centre of a square field, of side 40 m, leaving a gravel path all around the bed. The total cost of laying the flower bed and gravels at the path at the rate of Rs 2.75 and Rs 1.50 per sq. m respectively is Rs 4020. Find the width of the path: the width is equal to 2m

Question 33

• When three coins are tossed:
  • The possible outcomes are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
  • Total number of possible outcomes = 8
  • Favorable outcomes are HHH, HHT, HTH, THH.
  • Required probability = ½

Question 34

• A survey on causes of strikes in factories:
  • Economic: 32%.
  • Political: 28%.
  • Rivalry: 10%.
  • Accidents: 20%.

Question 35

• Parallelograms on equal bases and between the same parallels are equal in area.

Question 36

• A pole PQ is broken at point R by the wind, and its top P strikes the ground at point S at an angle of 30° at a distance of 15 m from the foot Q of the pole. The original height PQ is 25.98 m.