TMSCA Calculator
Resource Packet
TMSCA Calculator is one of those contests that requires some practice on the calculator, knowledge
of a few crucial formulas, and a lot speed and intensity.
In this packet a set of tips and formulas that you will need for the calculator test will be provided.
However, memorizing all of these tips and formulas will not be enough. In this event, plenty of
practice is necessary in order to master the locations of the keys and to develop the speed necessary.
Enjoy!
Tony Liu
Tips
Read and follow the rules carefully! This especially applies to those taking the test for the
very first time. I have seen many people get negative scores because of a few small rules that they
missed. (A common mistake is putting a dot for multiplication instead of an “x”)
This is probably the most important thing to do in TMSCA Calculator: Spend your time
wisely! Although 30 minutes may seem like a lot, still speed through it just as fast as a number sense
test. Flip pages fast, write fast, do everything like you’re being chased.
Fold the page corners before the test starts. This greatly increases the speed that you flip the
page. Doing this can save you up to a minute of valuable time.
Make sure that you set your calculator to Scientific Notation, 2 Decimal Places, and Degree
mode.
Some people suggest having two calculators (with one in normal, non-scientific notation). I
have never really found this to be useful, but some people may find it helpful.
Another common question is, “Where should I position my calculator?” This is almost
entirely dependent on your own preferences. However, I always put my calculator on my right side,
because I am right handed. To input digits I use both my left and right hands, with my pencil still in
my right hand so I can quickly write down the answer when I am through. This would be reversed
for someone that is left-handed.
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Do not be afraid to skip answers! Always remember this: a correct answer gives you 5 points.
An incorrect answer takes away 4 points. Thus if you skip a problem to the next problem that you
actually know how to do, you still gain a net point. This is especially pertinent to the calculator test.
Skipping all the word problems and geometry problems and coming back is a strategy used by some.
(This requires that you are able to finish all the other problems first)
A small thing you can do to save a little bit of time is to press clear as you are writing down
the answer.
Remember some quick ways to access various symbols. Something that comes up often is
the factorial, “!”. The quick way to access this (on the TI 84) is to press MATH, the left arrow, then
4. Also, the fast way to clear RAM is to press 2nd, “+”, 7, 1, 2.
Remember on some of the later problems involving the trigonometric functions to change
to radian form if the problem states.
If you are all done with the problems, don’t just sit there idly. Instead, start from the second
set of pure computation problems and input all of the problems through your calculator again.
Mistakes are very easy to make on this test!
Make sure you know your calculator well and all the various commands. For example, know
how to input scientific notation (something like 6.25 × 1049), roots greater than the cube root, etc.
Don’t get psyched by batteries. This is something that I did, and was not good. Don’t be too
eager to change the batteries—remember that you only need to change them when the “Low battery”
display is shown on your screen. And even if it comes to that during the actual test, you still do not
need to change the batteries. Chances are, even after this display is flashed, you still have a good
hour or so. Changing batteries mid-test is definitely not a good idea.
The last thing is, PRACTICE! (Did I mention that before?) This is the only way that you can
master the positions of the keys. Knowing the locations of the keys alleviates the need to constantly
look down at what you are typing, and can save you about 10 minutes. (Really!) It’s a bit like
keyboarding.
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Formulas and Facts
This section will be focused on formulas and facts (such as conversions) that would be
needed for the word problems and the geometry problems. These problems are important, mainly
because they are used as tiebreakers. Additionally, there are always 22 of these problems.
This means that 110/400 points come from these types of problems.
Thus these problems are important, and should be looked at extensively.
Conversions
Length:
1 ft = 12 in
1 yd = 3 ft = 36 in
1 rod = 5.5 yd = 16.5 ft
1 mi = 320 rods = 1760 yd = 5280 ft = 63360 in
1 in = 2.54 cm
1 mi ≈ 5/8 km
Area:
1 ft = 144 in2
1 yd2 = 9 ft2 = 1296 in2
1 acre = 160 rods2 = 4840 yd2 = 4360 ft2
1 mi2 = 640 acres
2
Volume:
1 ft = 1728 in3
1 yd3 = 27 ft3 = 46656 in3
1 cm3 = 1 mL = .2 tsp
3
Measures:
1 cup = 8 oz
1 pt = 2 cups = 16 oz
1 qt = 2 pt = 4 cups = 32 oz
1 gal = 4 qt = 8 pt = 16 cups = 128 oz = 231 in3
1 peck = 2 gal = 8 qt
1 bushel = 4 pecks = 8 gal = 32 qt
1 oz = .04 g
1 cup = 16 tbsp = 48 tsp
1 tbsp ≈ .5 oz ≈ 15 mL
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Weights:
1 lb = 16 oz
1 ton = 2000 lbs = 32000 oz
1 long ton = 2240 lbs
Note that the ounces (oz) here are weight, while the ounces in the above “Measures” section are fluid
ounces.
Units:
1 dozen = 12 units
1 gross = 12 dozen = 144 units
1 baker’s dozen = 13 units
Temperature:
F = (9/5) C + 32
C = (5/9) (F – 32)
K = C + 273 = (5/9) (F – 32) + 273
Speeds:
1 f/s = 22/15 mi/hr
1 mi/hr = 15/22 f/s
Time:
1 min = 60 s
1 hr = 60 min = 3600 s
1 day = 24 hr = 1440 min = 86400 s
1 year = 365 days ≈ 52 weeks
Know which months have 28, 30, or 31 days:
Month
Number of Days
January
31
February
28
March
31
April
30
May
31
June
30
July
31
August
31
September
30
October
31
November
30
December
31
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Besides these conversions, it is also necessary to know conversion factors. This is in case they ask
you to convert to some obscure units.
Also, the “King Henry Danced Merrily/Gleefully/Laboriously down Center Main” is a helpful
acronym. Remember this means:
Kilo1,000
Hecto100
Deka10
Meter/Gram/Liter Deci1
.1
Centi.01
Milli.001
Geometry
The geometry problems will be either implementing rudimentary trigonometry or testing your
knowledge of geometric formulas. Thus a brief look at trigonometry is given, along with a table of
necessary formulas.
Trigonometry
To the left a diagram is given detailing the
three major trigonometry functions. The
reason trigonometry is useful for finding
an unknown side or angle if you know
some other values, such as angles or side
measurements.
An acronym that some people find useful
in memorizing which trig function goes
with what relationship is this:
SOH-CAH-TOA
This stands for:
SINE/OPPOSITE/HYPOTENUSECOSINE/ADJACENT/HYPOTENUSE
-TANGENT/OPPOSITE/ADJACENT
Additionally, each of these functions has
its inverse, which maps the value given by
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the function back to the degree measure inputted to the function. These would be sin-1θ and
similarly for the other two functions. Also, there are three other trigonometry functions, but these
will generally be unnecessary for TMSCA Calculator.
It is also important to know how to use these functions. Below is an example of a problem that uses
the trigonometry functions. Apply the methods used in the problem below to other problems you
encounter, and you should be able to solve any of them.
In this problem it is asking for the
area of the triangle – thus we need to
find the leg that is missing in order
to find the area by the well known
formula:
In order to find the other leg we may
employ the trigonometric function
tangent, because we have an angle,
an opposite side, and we need to find
the adjacent side.
From this we can set up a ratio where we will be able to find the adjacent side. Thus we have:
From here we have the simple task of plugging the RHS value into the calculator. Wrapping the
problem up we have:
Note also that the problem has the value 25 stated in degrees, so be sure your calculator is in that
form.
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Geometric Formulas
Circles
Here r will denote the radius.
Circumference:
2πr
Area:
πr2
Polygons
Here n will denote the number of sides.
Sum of Interior Angles:
180(n-2)
Sum of Exterior Angles:
360
Diagonals from a vertex:
n-3
Diagonals in a polygon:
n (n-3)/2
Triangles
Here s is semi-perimeter, r is in-radius, A and B are two sides, and C is the angle between them.
Additionally, b is the base, h is the height, and a, b, and c are the sides of a right triangle.
Area:
bh/2
sr
AB sin C/2
Pythagorean Theorem:
a2+b2=c2
Rhombus
Here the d denotes the diagonals.
Area:
(d1d2)/2
bh
Parallelogram
Here theta (θ) is the angle between the two diagonals. (It does not matter which)
Area:
bh
d1d2sin(θ)/2
Square
Here s is the side length and d is the length of the diagonal.
Area:
s2
d2/2
Diagonal:
s√(2)
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Cone
Here “l” is the slant height, “r” is the radius, and “h” is the height. Don’t forget division by three in
the volume formula! I can’t tell you how many times I missed that.
Volume:
πr2h/3
Surface Area:
πr(l+r)
Lateral Surface Area:
πrl
Cylinders
Volume:
Surface Area:
Lateral surface Area:
πr2h
2πr(l+r)
2πrh
Spheres
Here r will denote the radius. Remember that the r term in the volume formula is cubed. I missed that
for about half a year.
Volume:
4πr3/3
Surface Area:
4πr2
Cubes
Here “s” will denote the side length, d the length of the diagonal from one corner of a square on
one side of the cube to the other corner, D the length of the diagonal from one vertex to the vertex
farthest from it.
Volume:
s3
Surface Area:
6s2
Face Diagonal (d):
s√(2)
Long Diagonal (D):
s√(3)
Pyramids
Here “l” will denote the length of the base, “w” the width of the base,” “h” the height of the
pyramid, and “s” the slant height of the pyramid. (This is the “diagonal length” from one base vertex
to the top vertex”)
Volume:
lwh/3
Surface Area:
s(l+w) + lw
Prisms
This refers to prisms in general, so the value of “B”, the area of the base, will be calculated
differently based upon the type of base. Note that many figures are actually prisms, such as cubes
and cylinders. This fact can be exploited.
Volume:
Bh
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Also, interest formulas have been mentioned before.
Simple Interest:
Compound Interest:
PIN
P(1+I)N
Here “P” is the principal or initial value. “I” is the interest rate. “N” is the number of “time periods”
the money goes through. Generally this is a year, but can differ. Compound interest is really just
simple interest, but each time you reach a new time period you calculate the earned interest based on
the money you now have, not the initial value, if that makes any sense.
The final things you may need to know are triangular, pentagonal, and hexagonal numbers.
Triangular Numbers:
Pentagonal Numbers:
Hexagonal Numbers:
n (n+1)/2
n (3n-1)/2
n (2n-1)
Miscellaneous and Conclusion
Some other skills you may have to implement to solve these problems are creating systems of
equations and in being able to convert a word problem into a math problem.
This packet has provided a mostly complete set of information concerning the TMSCA Calculator
Test. I hope that this helps you a lot! Feedback is welcomed and asked for. The test is constantly
evolving, so do not hesitate to contact me if you have any questions or any revisions you wish to
request.
Good luck!
Tony Liu
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