Control Test 3: Functions and relationships; algebra 2; graphs; surface, area and volume Total: 50 marks
Question 1 1.1
1.2
Time: 1 hour
Sibongile goes on a business trip and leaves home at 6 a.m. She returns home at 9 p.m. During her trip, Sibongile spends 40% of her time travelling. Calculate the number of hours Sibongile spent travelling.
Sibongile’s company uses the following formulae to calculate allowances for travel and meals: Allowance ( R ) = 15d + k − 5d
of days away from home and k represents the distance (in km) travelled.
1.2.2 Determine how many kilometres Sibongile would have travelled if she received an allowance of R195 for three days travel.
Question 2 2.1
(2)
_____ 3 where d represents the number
1.2.1 What would Sibongile’s allowance be if she spent four days on a business trip and travelled 740 km?
(2)
(2) [6]
Factorise the following:
2.1.1 x2 − 6x + 5 2.1.2 a2 + 2a − 8 2.1.3 y4 − 16
2.1.4 6x2 + 72x + 120
2.2 Simplify using factorisation: 2.2.1 3 x 2 − 9x − 12
___________ 3x − 12
2.2.2 5 x 2 − 125
________ x + 5
2.3 Solve the following equations: 2.3.1 3(x − 2) = 2x + 1 2.3.2 x2 − 8x = 9 2.4
(2) (2) (2) (3)
(3) (2)
(1) (2)
The base of a triangle is x cm and its perpendicular height is 3 cm less than the base. The area of the triangle is 20 cm 2.
2.4.1 Express the perpendicular height of the triangle in terms of x. 2.4.3 Set up an equation (in terms of x) that expresses this situation. (1)
2.4.2 Write down a formula to calculate the area of a triangle in terms of its base (b) and its perpendicular height (h).
(1) (1)
2.4.4 Solve your equation and find the base and the perpendicular height of the triangle. Show all your calculations and test your answers. Make sure that your answers make practical sense.
(3) [23]
Chapter 17: Programme of Assessment
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