\MATHS 081\GENERAL\CALC.TEX
Printed on April 11, 2002
Some information about calculators
We strongly recommend that all Maths 081 students own a scientific calculator. A calculator
will be needed for many of the weekly exercise sheets, as well as for the Maths 081 tests.
Here is some information on the type of calculator you should have, and a brief guide on
how to use your calculator.
1
The type of calculator you should have.
Almost any scientific calculator will be sufficient for your needs. The functions which your
calculator should be able to perform are listed on the next page.
• If you don’t already own a suitable calculator, you can buy one for as little as $26.
Some shops which sell calculators are The Melbourne University Bookroom, Target,
Office Works, Tandy and some news–agencies.
• Some suitable calculators which are commonly available (and which have all the functions which you will need for the Maths 081 course) include
– the Casio fx-82TL, (approximately $27 at Target),
– the Casio fx-82SX,
– the Casio fx-100s, and
– the Sharp EL-531LH.
Note:
• Your calculator does NOT need to be programmable.
• In the Maths 081 tests, you are NOT ALLOWED to use a calculator which
– can plot graphs of functions;
– can do symbolic integration or differentiation;
– can do matrix operations; or
– can store large amounts of information.
For example, in the Maths 081 tests you CANNOT use a graphing–calculator, or an
electronic dictionary.
• Many students will already own a calculator. If any student is unsure about
whether their calculator is suitable for the Maths 081 tests, then they should show
their calculator to Cheryl or Bell during the first few weeks of the course.
1
1.1
Some important functions
Your calculator should have the following buttons on it:
sin ,
cos ,
tan ,
log ,
ln and
xy .
Elsewhere on your calculator you should be able to find
π, n!, sin−1 , cos−1 , tan−1 , ex , as well as a memory.
Other functions that are useful (but not essential) are
• a cb (for fraction calculations).
n
• Cr (for combinations).
2
Basic help on how to use your calculator
A calculator is very easy to use. For example, to calculate 4 + 3, just press the following
keys on your calculator:
4
+
3
=
The answer 7 should appear on your screen.
These days there are two main types of calculators.
• Most new calculators use Direct Algebraic Logic (D.A.L.) or V.P.A.M. This is a system
where you can enter expressions in their true order; for example, to calculate sin 90◦ ,
we press the following keys:
sin 90 =
(Make sure that your calculator is in the “degrees mode”).
You should get the answer 1.
• In contrast, with older calculators you have to enter expression in a different way. For
example, to calculate sin 90◦ we press the keys:
90 sin
Provided that your calculator is in the “degrees mode”, you should get the answer 1.
Work out which type of calculator you have by trying to find sin 90◦ as shown above.
2
2.1
Using brackets
It will be useful to know how to use brackets on your calculator. As a simple example, try
calculating 7 × (2 + 3) by using the brackets on your calculator:
×
7
(
2
+
3
)
=
You should get the answer 35.
2.2
Using your calculator’s memory
Almost every calculator has a memory, which is the ability to remember a number and recall
it on demand. The actual keys that must be pressed to do this depends on the brand of
calculator. The example given below shows how to use the memory of most Casio calculators
and the new Sharp calculators.
In the following example, we calculate x + 1, 7x − 1 and x/2 where x = 3.942798.
Sharp
Casio
Store 3.942798 in memory
3.942798 STO M+
3.942798 SHIFT MR
Calculate x + 1
RCL M+ + 1 =
MR + 1 =
Calculate 7x − 1
7 × RCL M+ − 1 =
7 × MR − 1 =
RCL M+ ÷ 2 =
MR ÷ 2 =
Calculate x/2
Notice that we only need to type in the number 3.942798 once.
2.3
Fractions
Provided that your calculator has a a cb key then your calculator can work with fractions
for you!
For example to simplify
1 1
+ , we can press the following buttons:
2 3
1
a cb
Try it; you should get the answer
2
+
1
5
.
6
3
a cb
3
=
3
Exercises
1. Use your calculator to give a decimal equivalent (to 3 decimal places) of the following
expressions:
(a) 2 × 7 + 3
(d) 7 × 2 + 3
(g) 112 × 763
1 + 10
(j)
5
7+3+2+1
(m)
4
(b) 2 × (7 + 3)
(e) 1.4 × 3.6
(h) 3.1623 × 3.1623
(c)
(f)
(i)
(7 + 3) × 2
3.14/3
1/2 + 3/7
(k)
(l)
−10 + 2.79
1 + 10/5
2. Without first simplifying, use your calculator to evaluate (to 3 decimal places):
(a)
((1 + 2.1) × 3 + 7) × 8
1
2
(b)
3+4
7
+
(c)
7
8
1+
1
1 + 1+1 1
1
3. Calculate
(a) (1 + 2)2
(d) (1 + 2 + 3 + 4 + 5)2
(b) (1 + 2 + 3)2
(c)
2
(e) (1 + 2 + 3 + 4 + 5 + 6)
(1 + 2 + 3 + 4)2
(b) 13 + 23 + 33
(c)
3
3
3
3
3
(e) 1 + 2 + 3 + 4 + 5 + 63
13 + 23 + 33 + 43
4. Calculate
(a) 13 + 23
(d) 13 + 23 + 33 + 43 + 53
Compare your answers with those in question ??. Can you see a pattern?
5. Use your calculator to evaluate the following numbers to 3 decimal places.
(a)
π
√
(b)
2
√
1+ 5
2
(c)
6. Use your calculator to evaluate the following numbers to 3 decimal places.
(a) 4 × 1 − 13 + 15 − 17 + 19 −
(b) 1 +
(c) 1 +
1
1 + 1 + 1+1+1
1
11
+
1
13
−
1
15
+
1
17
−
1
19
+
1
21
−
1
23
+
1
25
1
1+1
1
1+
1
1+
1
1
1+ 1
(d) Compare the above answers with those obtained in question ??.
4
7. Evaluate the following to 3 decimal places:
(a)
(2.1)3
(d) (2.3)
(g)
4
9
107.9
(b)
(e)
√
3
8
(c)
(2.7)3.2
(f)
(h) log10 3
√
5
8
1
π
8. If your calculator has a a cb button then use this button to simplify
(a)
1
2
+
1
3
(b)
12
79
+
6
11
(c)
1
7
+ 19 +
1
6
(d) 4 × ( 23 + 14 )
9. Let x = 2.394789. Put this value of x into the memory of your calculator. Hence use
your calculator to find
(a)
2x + 1
(b) 3x + 2
(c)
4x + 9
10. Put your calculator in degrees mode and calculate the following to 3 decimal places:
(a)
sin 30◦
(d) sin−1 0.5
(b) cos 45◦
(c)
tan 60◦
cos−1 1
(f)
tan−1 1
(e)
11. Put your calculator in radians mode and calculate the following to 3 decimal places:
(a)
sin π6
(d) sin−1 0.5
(b) cos π4
(e)
cos−1 1
5
(c)
tan π3
(f)
tan−1 1
3.1
Answers
1. (a)
17
(b)
20
(c)
20
(d)
17
(e)
5.04
(f)
1.047
(g)
85456
(h)
10.000
(i)
0.929
(j)
2.2
(k)
3
(l)
−7.21
(m) 3.25
2. (a)
130.4
(b)
1.714
(c)
1.667
3. (a)
9
(b)
36
(c)
100
(d)
225
(e)
441
4. (a)
9
(b)
36
(c)
100
(d)
225
(e)
441
The pattern is, for any positive integer n, we have
(1 + 2 + . . . + n)2 = 13 + 23 + . . . + n3
5. (a)
3.142
(b)
1.414
(c)
1.618
6. (a)
3.218 (believe it or not, if you continued the pattern then you would eventually get π).
√
(b) 1.417 (believe it or not, if you continued the pattern then you would eventually get 2).
(c)
1.6 (believe it or not, if you continued the pattern then you would eventually get
7. (a)
9.261
(b)
2
(c)
1.516
(f)
0.318
(g)
79432823.47
(h)
0.477
8. (a)
5
6
(b)
606
869
(c)
53
126
9. (a)
5.789578
(b)
9.184367
(c)
18.579156
10. (a)
0.5
(b)
0.707
(c)
1.732
(d)
30◦
(e)
0◦
(f)
45◦
11. (a)
0.5
(b)
0.707
(c)
1.732
0.524
(e)
0
(f)
0.785
(d)
6
(d)
1.448
(d)
3 23
(e)
24.008
√
1+ 5
2
).