MATH1040/7040
Assignment 1
All questions must be submitted by 3 pm on MONDAY 20 March. Assignments are to be submitted via
assignment submission machine on the 3rd floor of the Priestley Building #67. You need a cover sheet which
will be emailed to you (MATH1040 students only). Do not type your answers. Solutions will be available on
the course Blackboard site the following week. Remember that your assignment must be your own work.
1. Describe your mathematical history, for example, did you like maths at school, what did you find
easy/difficult etc. Also write about what you want to get out of this course. Write at least six (6)
lines.
(2 marks)
2. Answer each of the following questions, showing all working.
2
−39
−38 16
(a) Evaluate
×
×
−
.
−4
39
39
−40
(b) Expand and simplify 3y (5 − y).
(c) Expand and simplify (1 + y) (5y + 2).
−5y
− 2 = −5.
(d) Determine y, if
−2
6
(e) Determine z, if
− 4 = 6.
−3z
0 −3
.
(f ) Determine z, if z= −
7
4
5
2
(g) Determine x if − = 2.
x x
(h) Determine x if 10x − 2 + 5 = −3(4x − 2) − 2.
(3 marks)
(1 mark)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
(2 marks)
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3. The volume of a rectangular-based pyramid is given by the formula V = lwh, where l is the length of
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the base, w is the width of the base, and h is the height of the pyramid.
(a) Find the volume of a rectangular-based pyramid of base length 4 cm, base width 5 cm and height 6
cm.
(1 mark)
(b) Find two possible pairs of values for both length and width of the base of a rectangular-based
pyramid of volume 650 cm3 and height 5 cm.
(2 marks)
4. Insert mathematical operator(s) (that is, +, −, ×, ÷) and/or a set of brackets in each of the following in
order to make the statement true:
(a) 3
5
2=6
(1 mark)
(b) 8
6
7 = 14
(1 mark)
(c) 70 = 2
3
4
5
(1 mark)
5. Evaluate the following:
√
(a) −3 × 68 − 20 ÷ 5 − 42 ÷ 2
(b) 12 + 3 ×
(23
22 )
(2 marks)
32
+
×
53 − (3 + 2)
(2 marks)
Please turn over.
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6. After a particularly tedious MATH1040 lecture, Xavier goes to the pub with his friends Xena and Xenophobe, and drinks beer. He drinks LOTS of beer.
1
1
2
of the first jug, of the second jug, of the third jug and all of the fourth jug.
2
3
3
1
1
His friend Xena drinks of the fifth jug, his other friend Xenophobe drinks of the rest of that
4
2
1
jug, and Xavier drinks of what is left in that jug. Finally, after a drunken argument, they buy a
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sixth jug. Xavier throws 40% of the sixth jug over Xenophobe, he throws 50% of what is left over
Xena, and drinks the rest. Assume each jug holds one litre. How many litres of beer does he drink?
(4 marks)
(a) Xavier drinks
(b) Before Xavier passes out, he has to pay. Each jug costs $12. How much money will it cost him
to pay for all of the beer he drinks (but not for the beer drunk by anyone else, or for the beer he
throws)?
(1 mark)
(c) Assume that a standard drink comprises 10 millilitres of pure alcohol and that beer contains exactly
6% pure alcohol. How many standard drinks has Xavier drunk?
(2 marks)
(d) Xavier’s liver can eliminate pure alcohol at the rate of one standard drink per hour. He has another
MATH1040 lecture 5 hours after he started drinking. What do you think is the probability that he
will stay awake in class? Explain your answer.
(2 marks)
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