maths test

Page 1 of 3 FINAL TEST MTH153S _ 2 NOVEMBER 2018

QUESTION 1

Simplify the following expressions:
2(3𝑛𝑛 )−9�3(𝑛𝑛−2) �
a) (3)
3𝑛𝑛 −3(𝑛𝑛−1)

b) 4(2𝑦𝑦 ) − 2(4𝑦𝑦 ) + 2(2𝑦𝑦+1) (3)

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QUESTION 2
Solve the equation: 3𝑒𝑒 2𝑥𝑥 + 5𝑒𝑒 𝑥𝑥 − 2 = 0
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QUESTION 3
a) A rectangle has perimeter 20 m. Express the area of the rectangle as a function
of the length of one of its sides. (4)
b) A closed rectangular box with volume 6 𝑚𝑚3 has length twice the width. Express
the height of the box as a function of the width. (4)
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QUESTION 4
At the surface of the ocean, the water pressure is the same as the air pressure above
the water, 1.05 𝑘𝑘𝑘𝑘/𝑐𝑐𝑐𝑐2 . Below the surface, the water pressure increases by 0.10 𝑘𝑘𝑘𝑘/
𝑐𝑐𝑐𝑐2 for every meter of descent.
(a) Express the water pressure as a function of the depth below the ocean surface.(4)
(b) At what depth is the pressure 7𝑘𝑘𝑘𝑘/𝑐𝑐𝑐𝑐2 ? (4)
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