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Calculator Techniques for Mathematics Using CASIO Calculators
Mathematics is one of the most extensive subjects in board exams.It is very eclectic I must say. Mathematics is one of the subjects with the highest components in Engineering Board Examinations having 1/3 of the total percentage of the coverage or in some cases, more than that. In line with your major fields, mathematics is one of the hardest parts in Engineering Board Examinations. It becomes hard because subjects that you have taken in College for 3 or more semesters are compressed. So, how do you aid this?
Topics Included Under Mathematics in Engineering Board Exams
 Algebra
 Trigonometry
 Plane and Solid Analytic Geometry
 Plane and Solid Mensuration
 Differential Calculus
 Integral Calculus
 Differential Equations
 Advanced Engineering Mathematics
 Engineering Economy
Mathematics should be the scoring section in your exam and requires the smallest amount of effort. Unfortunately, it turns out to be the opposite. Many are struggling to get high scores in the Mathematics section in the board exam. The proven reasons are the lack of techniques and intellectual strategies in solving difficult questions.
Most of the solutions to questions in Engineering board exams are quite long. Doing the conventional way of solving will lead to running out of time. Remember that Engineering Board Exams are limited in time. That is why knowing the calculator techniques will greatly save your time and stamina, give you time to review your answers, and let you achieve your desired score.
Caution: Make sure you input correct values in your calculator!
The following tricks shown using the calculator are supported with the conventional way of solving them. If you have problems encountered with the Casio Calculator, refer to the user's manual for a complete list of functions. Here are the most important calculator techniques in mathematics that you should know.
NOTE: These calculator features may not be available in lowquality calculators. I highly encourage you to use scientific calculators produced by large calculator companies like Casio and Sharp.
Algebra
Problem 1: Nth Term of an Arithmetic Progression
Find the 26th term of the arithmetic progression 5, 9, 13, 17...
SOLUTION 1: Conventional Solution
a_{n}=a_{1}+(n1)d
a_{26}=5+(261)(4)
a_{26}=105
SOLUTION 2: Calculator Technique
1. Press "MODE" button.
2. Choose “3: STAT”.
3. Choose “2: A+BX”.
X
 Y


1
 5

2
 9

4. SHIFTSTAT
5. Choose “5: Reg".
6. Choose “5: ŷ”.
7. Input 26 beside ŷ. It should look like 26ŷ. The answer should be 105.
Problem 2: Geometric Progression
The 6th term of a geometric progression is 4096 and the 10th term is 1,048,576. What is the 4th term?
SOLUTION 1: Conventional Solution
The formula for geometric progression is a_{n}= a_{1}r^{n1}. From the given values, we can make 2 equations having 2 unknowns.
Two equations, two unknowns...
Equation 1:
a_{6}=a_{1}r^{61}
4096=a_{1}r^{5}
Equation 2:
a_{10}=a_{1}r^{101}
1,048,576=a_{1}r^{9}
Using any method to solve two equations and two unknowns, it must result to these two answers...
a_{1}=4
r=4
Substituting these values..
a_{4}=a_{1}r^{41}
a_{4}=4(4)^{3}
a_{4}=256
SOLUTION 2: Calculator Technique
 Press "MODE" button.
 Choose “3: STAT”.
 Choose “6: A*B^X”.
X
 Y


6
 4096

10
 1,048,576

4. SHIFTSTAT
5. Choose “5: Reg”.
6. Choose “5: ŷ”.Then input the value of the desired nth term. In this problem, it should be 4ŷ.The answer in your calculator should be 256.
Problem 3: Sum of a Sequence
How many terms of the sequence 2, 4, 6... must be taken so that the sum is 3660?
Solution 1: Conventional Solution
S_{n}=3660
a_{1}=2
Substituting the given values to the equation...
S_{n}=(n/2)[2a_{1}+(n1)(d)]
3660=(n/2)[2(2)+(n1)(2)]
n=60
Solution 2: Calculator Technique
1. Press "MODE" button.
2. Choose “3: STAT”.
3. Choose “3: _+cX^2”.
X
 Y


0
 0

1
 2

2
 2+4

4. Press AC.
5. SHIFTSTAT
6. Choose “5: Reg”.
7. Choose “4: x_{1}”.
8. Put the value of the given sum. It should be 3660x_{1}. Enter and the answer should be 60.
Problem 4: HandClock Problems
At what time between 2PM to 3PM will the hands of the clock be at right angle?
Solution 1: Calculator Technique
1. Press "MODE" button.
2. Choose "3: STAT".
3. Choose "2: A+BX".
X
 Y


2
 30(2)

3
 330 + [30(2)]

4. Press AC.
5. SHIFTSTAT.
6. Choose "5: Reg".
7. Choose "4: x".
8. Input 90 beside x. It should look like this 90x. Press Enter. The answer should be 2:27:16.36 PM
Problem 5: HandClock Problems
What is the angle between the hands of the clock at 2:35:16 in radians?
Solution 1: Calculator Technique
1. Press MODE.
2. Choose "3: STAT".
3. Choose "2: A+BX".
X
 Y


2
 30(2)

3
 330 + (60)

4. Press AC.
5. SHIFTSTAT.
6. Choose "5: Reg".
7. Choose "5: ŷ".
8. Input 2:35:16 beside ŷ. Press Enter. The answer should be 133.97 deg. Convert it to radians. The final answer is 2.338 radians.
Trigonometry
Problem 6: 2 Unknown Sides of a Triangle
A triangle has a base of 10 m and angles 35° and 64° respectively. Find the length of the other two sides.
Illustration of the Problem
Solution 2: Calculator Technique
1. Press MODE.
2. Choose "5: EQN".
3. Choose "1: a_{n}X + b_{n}Y = c_{n}".
ax
 by
 c


cos(64)
 cos(35)
 10

sin(64)
 sin(35)
 0

Problem 7: 3 Circles Tangent to Each Other
Three circles are mutually tangent to one another externally. Connecting the 3 centers form a triangle whose sides are 16 cm, 20 cm and 24 cm. What is the area of the smallest circle in cm^{2}.
Illustration of the Problem
Solution 1: Conventional Solution
X + Y = 16 ← eq. 1
X + Z = 20 ← eq. 2
Y + Z = 24 ← eq. 3
Solving manually, you'll arrive with the answers.
X = 6 cm
Y = 10 cm
Z = 14 cm
Solution 2: Calculator Technique
1. Press MODE.
2. Choose "5: EQN".
3. Choose "2: a_{n}X + b_{n}Y + c_{n}Z= d_{n}".
1
 1
 0
 16


1
 0
 1
 20

0
 1
 1
 24

Plane and Solid Analytical Geometry
Problem 8: Equation of a Parabola
A parabola has its axis parallel to the yaxis and passes through (4, 5), (2, 11) and (4, 21). What is the equation of the parabola?
Solution 1: Calculator Technique
1. Press MODE.
2. Choose "3: STAT".
3. Choose "3: _+cX^{2}".
X
 Y


4
 5

2
 11

4
 21

4. Press "AC".
5. Press "SHIFT 1 5 1". Store at A.
6. Press "SHIFT 1 5 2". Store at B
7. Press "SHIFT 1 5 3". Store at C.
The final answer will be in the form A+BX+CX^{2}.
The final answer is 5  2x + 0.5x^{2}.
Problem 9: Applications of Parabola
When the load is uniformly distributed horizontally, the cable of a suspension bridge hangs in a parabolic arc. If the bridge is 300ft long, the towers 60ft high and the cable 20ft above the roadbed at the center, find the distance from the roadbed 50ft from the center.
Solution 1: Calculator Technique
1. Press the "MODE" button.
2. Choose "3: STAT".
3. Choose "3: _+cX^{2}".
X
 Y


150
 60

0
 20

150
 60

4. Press "AC".
5. SHIFTSTAT
6. Choose "5: Reg".
7. Choose "6: y". Place 50 beside y. The answer is 24.44 feet.
Plane Geometry and Solid Mensuration
Problem 10: Volume of Water in a Sphere
A sphere of radius 15cm contains water at a height of 24cm. Find the volume of water inside the sphere.
Solution 1: Calculator Technique
1. Press the "MODE" button.
2. Choose "3: STAT".
3. Choose "3: _+cX^{2}".
X
 Y


0
 0

15
 pi(15)^2

30
 0

4. Press "AC".
5. Press "SHIFT 1 5 1". Store at A.
6. Press "SHIFT 1 5 2". Store at B
7. Press "SHIFT 1 5 3". Store at C.
8. Go back to mode 1.
9. Get the integral in a form A+BX+CX^{2}. Evaluate from 0 to 24.
V = 4032π cm3
Calculus
Problem 11: Evaluating Limits
Evaluate the limit of (x^{2} + x 12)/(2x^{2}  7x +3) as x approaches 3.
Solution 1: Calculator Technique
1. Input the given equation in your calculator.
2. Press "CALC".
3. Input 3.000001 or 2.999999
The final answer is 1.4.
Engineering Economy
Problem 12: Compound Interest
At what interest rate, compounded quarterly, will an investment double in 5 years?
Solution 1: Calculator Technique
1. Assume money = Y = 1.
2. Press "MODE" button.
3. Choose "3: STAT".
4. Choose "A*B^X".
X
 Y


0
 1

20
 2

5. Press "AC" button.
6. Press "SHIFT 1 5 2".
7. Subtract the result by 1 and multiply by 4 (51).
The answer is 14.05 %.
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