Examination Details

• Subject: Mathematics
• Examining Body: Botswana Examinations Council
• Qualification: Botswana General Certificate of Secondary Education
• Paper: Paper 2
• Centre Number: 511
• Candidate Number: 0563/02
• Date: October/November 2019
• Duration: 2 hours

Instructions

• Write your centre number, candidate number, and name in the designated spaces at the top of the exam paper.
• Answer all questions in the spaces provided on the question paper.
• Show essential workings for each question; absence of this may result in loss of marks.
• No use of staples, paper clips, highlighters, glue, or correction fluid.
• Marks are indicated in brackets ( ) at the end of each question or question part.
• Total available marks: 75.
• If accuracy isn't specified, present answers to three significant figures; answers in degrees are to be given to one decimal place.
• Use calculator value for π or take π as 3.142.

Mathematical Formulae for Papers 1 and 2

Surface Area and Volume of Solids

Names of Solids and Associated Formulas

• Cone
  • Total Surface Area: ext{Total Surface Area} = rac{1}{3} ext{π} r^2 + ext{π} r l
  • Volume: V = rac{1}{3} ext{π} r^2 h
• Pyramid
  • Volume: ext{Volume} = rac{1}{3} ext{Base Area} imes ext{Height}
• Sphere
  • Total Surface Area: A = 4 ext{π} r^2
  • Volume: V = rac{4}{3} ext{π} r^3

Trigonometry

• Sine Rule: rac{a}{ ext{sin(A)}} = rac{b}{ ext{sin(B)}} = rac{c}{ ext{sin(C)}}
• Area of a Triangle: ext{Area} = rac{1}{2} ab ext{sin(C)}

Questions and Answers

Question 1: Multi-Residential Property

• A multi-residential property with four identical houses rented for a total of P13,500 monthly.
  • (a) Calculate the monthly rent for one house.
  • Answer: P3,375.00
  • (b) Each house can be shared by at most two people.
  • (i) Maximum possible number of tenants: 8 people
  • (ii) Monthly rent per sharing tenant: P421.88

Question 2: Potato Crisps Mass Increase

• Mass of a packet of potato crisps = 32.5 g; increased by 6%.
  • Answer: 34.45 g

Question 3: Juice Volume for Catering

• Masego plans to cater for 33 people, expecting each to drink 4 glasses of juice (1 glass = 375 ml).
  • (a) Total volume needed: 49.5 L
  • (b) Juice bought in 7-litre bottles at cost of P64.97 each.
  • (i) Bottles needed: 8 bottles
  • (ii) Total cost: P519.76

Question 4: Matchstick Patterns

• Draw diagram 4 on grid provided.
• Express in terms of n, total matchsticks in diagram n: Total = 3n + 1
• Total matchsticks = 52 gives diagram number: n = 17

Question 5: Restaurant Lunch Costs

• Lunch costs (in Pula): {45, 60, 55, 70, 95, 80, 100, 90, 120, 110, 200}
  • (a) Median cost: P90.00
  • (b) Inter-quartile range: P55.00

Question 6: Area of Triangle STU

• Given sides: ST = 52 mm, TU = 68 mm, Angle STU = 63.7°.
  • Area of triangle STU: 1,226.83 mm^2

Question 7: Endpoint B from Midpoint

• A line segment with endpoints A (-4, -2) and midpoint (5, 3).
  • Endpoint B coordinates: (14, 8)

Question 8: Depth of Water in Tank

• Cylindrical tank radius = 1.5 m, water volume = 6.34 m³.
  • Depth of water = 0.89 m

Question 9: Cone Calculations

• Cone base radius = 7.25 cm, height = 12 cm.
  • (a) Slant height: 13.00 cm
  • (b) Curved surface area: 276.46 cm²

Question 10: Graph and Values Analysis

• Graph of: y = 3x - x^2
  • (a) Turning point coordinates: (1.5, 2.25)
  • (b) Draw graph of function y = -x + 4
  • (c) Values of x such that 3x - x^2 = -x + 4: x = -1 or x = 4

Question 11: Vector Calculations

• Given vectors AB = (9, -10) and BC = (x, y).
  • (a) AC as column vector: (9 + x, -10 + y)
  • (b) AC in terms of EF: …

Question 12: Rotation of Triangle K

• Triangle K vertices given, rotate triangle K 90° anticlockwise about point (-1, 2).

Question 13: Expand and Simplify Expression

• (a) Expand the expression: (x + 7)(x - 3) = x² + 4x - 21
• (b) Equation of line parallel to y = -x + 2 passing through (4, 5): y = -x + 9

Question 14: Symmetry of a Rhombus

• Fully described symmetry: Four lines of symmetry along diagonals and rotational symmetry of order 2.

Question 15: Copper Pipe Calculations

• Pipe with inner diameter = 12.5 cm, outer diameter = 14 cm, length = 24 cm.
  • (a)(i) Inner circle area: 122.72 cm²
  • (ii) Shaded cross-section area: 76.96 cm²
  • (b) Volume of copper in pipe: 1,846.98 cm³
  • (c) Density of copper: 8.92 g/cm³; mass of pipe = 16,426.91 g

Question 16: Solving Equations

• (a) Solve: \frac{y + 3}{y - 1} = \frac{5}{6}; answer: y = 0.00
• (b) Make w the subject of: h = 12 - w^2; answer: w = ext{√}(12-h)

Question 17: Waiting Times Distribution

• Waiting times of people at bus stop as charted.
  • (a) Total number of people = 10
  • (b) Percentage waiting more than 15 minutes = 40%

Question 18: Framework ABCD Calculations

• Framework of beams with lengths and angles specified.
  • (a) Size of angle BCD = 71°
  • (b) Length of BC calculated = 2.07 m
  • (c) Length of perpendicular beam from B to AD calculated = 1.75 m