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Calculator Techniques in Mathematics Using Casio FX-991ESPLUS

Updated on July 18, 2017
JR Cuevas profile image

John Ray is a Civil Engineering student at Mapua Institute of Technology Laguna (MITL). He is an aspiring blogger from the Philippines.

Mathematics is one of the most extensive subjects in board exams.It is very eclectic. Mathematics. It 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.

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 of board exams. The proven reason is the lack of techniques and 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, help you review your answers, and makes you achieve your desired score.

Source

Here are the most important calculator techniques in mathematics that you should know.
NOTE: These calculator features may not be available in low-quality calculators. I highly encourage you to use scientific calculators produced by large calculator companies.

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(CASIO) Scientific Calculator (FX-991ESPLUS)
(CASIO) Scientific Calculator (FX-991ESPLUS)

FX-991ESPLUS is one the best scientific calculators that you can use in board examinations. Buy one now!

 

I. Algebra

Nth Term of an Arithmetic Progression

Find the 26th term of the arithmetic progression 5, 9, 13, 17...

Conventional Solution

Arithmetic Progression
Arithmetic Progression

Calculator Technique

1. Press "MODE" button.

2. Choose “3: STAT”.

3. Choose “2: A+BX”.

X
Y
1
5
2
9
Input these values.

4. SHIFT-STAT

5. Choose “5: Reg".

6. Choose “5: ŷ”.

7. Input 26 beside ŷ. It should look like 26ŷ. The answer should be 105.

Geometric Progression

The 6th term of a geometric progression is 4096 and the 10th term is 1,048,576. What is the 4th term?

Conventional Solution

The formula for geometric progression is an= a1rn-1. From the given values, we can make 2 equations having 2 unknowns.

Calculator Technique

  1. Press "MODE" button.
  2. Choose “3: STAT”.
  3. Choose “6: A*B^X”.

X
Y
6
4096
10
1,048,576
Input values

4. SHIFT-STAT
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.

Sum of a Sequence

How many terms of the sequence 2, 4, 6... must be taken so that the sum is 3660?

Conventional Solution

Calculator Technique

1. Press "MODE" button.

2. Choose “3: STAT”.

3. Choose “3: _+cX^2”.

X
Y
0
0
1
2
2
2+4
Input values

4. Press AC.

5. SHIFT-STAT

6. Choose “5: Reg”.

7. Choose “4: x1”.

8. Put the value of the given sum. It should be 3660x1. Enter and the answer should be 60.

Hand-Clock Problems

At what time between 2PM to 3PM will the hands of the clock be at right angle?

Calculator Technique

1. Press "MODE" button.

2. Choose "3: STAT".

3. Choose "2: A+BX".

X
Y
2
-30(2)
3
330 + [-30(2)]
Under the X column, input the two values of time. Take note that -30 and 330 here is constant. Multiply -30 by the first time. Then, add the product to 330.

4. Press AC.

5. SHIFT-STAT.

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

Hand-Clock Problems

What is the angle between the hands of the clock at 2:35:16 in radians?

1. Press MODE.

2. Choose "3: STAT".

3. Choose "2: A+BX".

X
Y
2
-30(2)
3
330 + (-60)

4. Press AC.

5. SHIFT-STAT.

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.

II. Trigonometry

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.

Conventional Solution

Calculator Technique

1. Press MODE.

2. Choose "5: EQN".

3. Choose "1: anX + bnY = cn".

ax
by
c
cos(64)
cos(35)
10
sin(64)
-sin(35)
0
After putting these values, press the Enter button and you'll get the same answer.

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 cm2.

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

Calculator Technique

1. Press MODE.

2. Choose "5: EQN".

3. Choose "2: anX + bnY + cnZ= dn".

1
1
0
16
1
0
1
20
0
1
1
24
Press Enter and the answers must be the same with the conventional way.

III. Plane and Solid Analytic Geometry

Equation of a Parabola

A parabola has its axis parallel to the y-axis and passes through (4, 5), (-2, 11) and (-4, 21). What is the equation of the parabola?

Calculator Technique

1. Press MODE.

2. Choose "3: STAT".

3. Choose "3: _+cX2".

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+CX2.

The final answer is 5 - 2x + 0.5x2.

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.

Calculator Technique

1. Press the "MODE" button.

2. Choose "3: STAT".

3. Choose "3: _+cX2".

Calculator Technique

X
Y
-150
60
0
20
150
60

4. Press "AC".

5. SHIFT-STAT

6. Choose "5: Reg".

7. Choose "6: y". Place 50 beside y. The answer is 24.44 feet.

IV. Plane Geometry and Solid Mensuration

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.

Calculator Technique

1. Press the "MODE" button.

2. Choose "3: STAT".

3. Choose "3: _+cX2".

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+CX2. Evaluate from 0 to 24.

V = 4032π cm3

V. Calculus

Evaluating Limits

Evaluate the limit of (x2 + x -12)/(2x2 - 7x +3) as x approaches 3.

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.

VI. Engineering Economy

Compound Interest

At what interest rate, compounded quarterly, will an investment double in 5 years?

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 (5-1).

The answer is 14.05 %.

I'll Add More Calculator Techniques

What mathematics part is your weakness?

See results

© 2017 John Ray De la Cruz Cuevas

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    • JR Cuevas profile image
      Author

      John Ray De la Cruz Cuevas 4 months ago from Santa Rosa, Philippines

      No, I don't.I'm still a college student. We are just taught of the different calculator techniques in school. :)

    • pen promulgates profile image

      Imran Khan 4 months ago from Mumbai, India

      Wow, so technical. Do you teach?