This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Section B 1.a) Step 1: Calculate the time duration. The train starts at 9:30 am and travels until 12:00 noon. Time duration = 12:00 noon - 9:30 am = 2 hours 30 minutes. Step 2: Convert the time duration to hours. 2 hours 30 minutes = 2 + (30)/(60) hours = 2 + 0.5 hours = 2.5 hours Step 3: Calculate the distance covered. Given speed = 4 km/hr. Distance = Speed × Time Distance = 4 km/hr × 2.5 hours = 10 km The distance covered by the train is 10 km. 1.b) Three properties of a rectangle: • Opposite sides are equal in length and parallel. • All four interior angles are right angles (90^). • The diagonals bisect each other and are equal in length. Three properties of a square: • All four sides are equal in length. • All four interior angles are right angles (90^). • Opposite sides are parallel. 2.a) Step 1: Convert all weights to kilograms (kg). Maize: 115.2 kg Beans: 242 kg Rice: 142000 g 142000 g × 1 kg1000 g = 142 kg Step 2: Calculate the total weight. Total weight = Weight of maize + Weight of beans + Weight of rice Total weight = 115.2 kg + 242 kg + 142 kg = 499.2 kg The total weight is 499.2 kg. 2.b) Step 1: Convert seconds to minutes. There are 60 seconds in 1 minute. 60 seconds = 1 minute Step 2: Convert minutes to hours. There are 60 minutes in 1 hour. 1 minute = (1)/(60) hour Therefore, 60 seconds is equal to (1)/(60) hour. 3.a) Step 1: Convert all volumes to the same unit (cm³). Given volume 1: 2 litres 2 litres × 1000 cm^31 litre = 2000 cm^3 Given volume 2: 800 cm³ Step 2: Calculate the total volume. Total volume = 2000 cm³ + 800 cm³ = 2800 cm³ Step 3: Divide the total volume among 7 traders. Volume per trader = Total volumeNumber of traders Volume per trader = 2800 cm^37 = 400 cm^3 Each trader receives 400 cm^3. 3.b) Three properties of a cube: • It has 6 faces, and all faces are squares of equal size. • It has 12 edges, and all edges are of equal length. • It has 8 vertices (corners). 4. Step 1: Ensure all dimensions are in the same unit (meters). Length = 80 m Width = 30 cm 30 cm × 1 m100 cm = 0.3 m Depth = 8 m Step 2: Calculate the volume of the water in the pool. The pool is a cuboid, so its volume is given by Length × Width × Depth. Volume = 80 m × 0.3 m × 8 m = 24 m^2 × 8 m = 192 m^3 The volume of the water in the pool is 192 m^3. 5.a) Step 1: Calculate the area of the rectangle. Length = 8(1)/(2) m = 8.5 m Width = 3(1)/(2) m = 3.5 m Area of rectangle = Length × Width Area_rectangle = 8.5 m × 3.5 m = 29.75 m^2 Step 2: Calculate the area of the right-angled triangle. Base = 16 cm Height = 18 cm Area of triangle = (1)/(2) × Base × Height Area_triangle = (1)/(2) × 16 cm × 18 cm = 8 cm × 18 cm = 144 cm^2 The area of the rectangle is 29.75 m^2 and the area of the triangle is 144 cm^2. 5.b) Step 1: Convert mixed fractions to improper fractions. 1(3)/(4) = (1 × 4 + 3)/(4) = (7)/(4) 1(1)/(2) = (1 × 2 + 1)/(2) = (3)/(2) 2(1)/(3) = (2 × 3 + 1)/(3) = (7)/(3) Step 2: Find a common denominator for 4, 2, and 3. The least common multiple (LCM) is 12. (7)/(4) = (7 × 3)/(4 × 3) = (21)/(12) (3)/(2) = (3 × 6)/(2 × 6) = (18)/(12) (7)/(3) = (7 × 4)/(3 × 4) = (28)/(12) Step 3: Add the fractions. (21)/(12) + (18)/(12) + (28)/(12) = (21 + 18 + 28)/(12) = (67)/(12) Step 4: Convert the improper fraction back to a mixed number. (67)/(12) = 5 with a remainder of 7 5(7)/(12) The simplified expression is 5(7)/(12).