ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Calculator Techniques for Mathematics Using Casio Calculators

Updated on July 15, 2018
JR Cuevas profile image

JR has a Bachelor of Science in Civil Engineering and specializes in Structural Engineering. He loves to write anything about education.

Mathematics is one of the most illimitable problems in board examinations. 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 and in some cases, more than that. In line with your primary disciplines, mathematics is one of the toughest parts in Engineering Board Examinations. It becomes difficult because subjects that you have taken in College for three or more semesters are concentrated. 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 standard 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 hugely save your time and stamina, give you time to review your answers and let you achieve your desired score.

Calculator Techniques in Math
Calculator Techniques in Math | Source

For every calculator technique solution, there is a conventional method of solving provided. 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 valuable calculator techniques in mathematics that you should know. Note that these calculator features may not be available in low-quality calculators. I highly encourage you to use scientific calculators produced by large calculator companies like Casio and Sharp.

I. 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

an = a1 + (n - 1) d

a26 = 5 + (26 - 1) (4)

a26 = 105

Solution 2: 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 final answer should be 105.

Problem 2: Geometric Progression

In a geometric progression, the term 6th is 4096, and the 10th term is 1048576. What is the value of the 4th term?

Solution 1: Conventional Solution

The formula for geometric progression is an= a1 rn-1. From the given values, we can make 2 equations having 2 unknowns.

Equation 1:

a6 = a1 r6-1

4096 = a1 r5

Equation 2:

a10 = a1 r10-1

1,048,576 = a1 r9

Using any method to solve two equations and two unknowns, it must result to these two answers.

a1 = 4

r = 4

Substituting these values,

a4 = a1 r4-1

a4 = 4 (4)3

a4 = 256

Solution 2: 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 final 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

Sn = 3660

a1 = 2

Substituting the given values to the equation...

Sn = (n/2)[2a1+(n-1)(d)]

3660 = (n/2)[2(2)+(n-1)(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
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.

Problem 4: Hand-Clock Problems

At what time between 2 PM till 3 PM will the hands of the clock be at the 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)]
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

Problem 5: Hand-Clock 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. 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

Problem 6: Two 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.

Calculator Technique for Unknown Sides of a Triangle
Calculator Technique for Unknown Sides of a Triangle | Source
Solution 1: Conventional Solution
Solution 1: Conventional Solution | Source

Solution 2: 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.

Problem 7: Three 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?

Calculator Techniques for Circles Tangent to Each Other
Calculator Techniques for Circles Tangent to Each Other | Source

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: 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 Analytical Geometry

Problem 8: 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?

Solution 1: 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.

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 300 ft long, the tower is 60 ft. high, and the cable is 20 ft. above the roadbed at the center, find the distance from the roadbed 50 ft. from the center.

Solution 1: Calculator Technique

1. Press the "MODE" button.

2. Choose "3: STAT".

3. Choose "3: ±cX2".

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

Problem 10: Volume of Water in a Sphere

A sphere of radius 15 cm. contains water at a height of 24 cm. Find the volume of water inside the sphere.

Solution 1: 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

Problem 11: Evaluating Limits

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

Solution 1: Calculator Technique

1. Input the given equation into your calculator.

2. Press "CALC".

3. Input 3.000001 or 2.999999

The final answer is 1.4.

VI. 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 (5-1).

The answer is 14.05 %.

Casio fx-115ES PLUS Engineering/Scientific Calculator
Casio fx-115ES PLUS Engineering/Scientific Calculator

Casio and Sharp calculators are good calculators in solving different calculator techniques.

 

I'll Add More Calculator Techniques

What mathematics part is your weakness?

See results

© 2017 John Ray

Comments

    0 of 8192 characters used
    Post Comment

    • JR Cuevas profile imageAUTHOR

      John Ray 

      13 months ago from 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 

      13 months ago from Mumbai, India

      Wow, so technical. Do you teach?

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)