Mathematics is a complicated problem that can come in many forms. It is one of the most significant subjects in civil engineering board examinations. It has 1/3 of the total percentage of the coverage, and sometimes it is more than that.
Civil engineering board exams are challenging, but mathematics is one of the most difficult elements. It becomes difficult because the subjects you took in college for multiple semesters are in one place. How do you plan to help with this?
You should put Mathematics in your exam’s scoring section, and it requires the least effort. Unfortunately, it’s the other way around. Many people are battling to get good scores in the Mathematics section of the board exam.
The reason is that there are no practical techniques or strategies for solving hard questions. Knowing the calculator techniques will save time and help you review your answers. This way, you can get your desired score.
This article will show you ways to solve math problems faster using calculator tricks. We also give you tips for studying for the board exam.
Calculator Tricks and Techniques
There’s a common way to solve every calculator technique solution. Refer to the user’s manual if you have concerns with the Casio Calculator or any other calculator you use. Here are the most useful techniques for using calculators in mathematics.
Note: These calculator features may not be available in low-quality calculators. I recommend using scientific calculators produced by large companies like Casio, Canon, and Sharp.
Problem #1: Sum of a Sequence in Arithmetic Progression
Find the sum of 1 + 2 + 3 +…………98 + 99 + 100.
The solution in a conventional way:
Using the formula provided below, compute the sum of the sequence manually by the method of substitution.
Sn = n2 (α1 + αn)
S100 = (100/2)(1 + 100)
S100 = 5050
Therefore, the sum of the sequence is 5050.
Using calculator:
Mode 1 > Shift > input x= 1100X = 5050
Therefore, the sum of the sequence is 5050.
For a more detailed explanation, you can watch this video with Engr. Padilla in our Youtube channel, the Padilla Review Center Online TV.
Video here: Calculator Tricks: Arithmetic Progression
Problem #2: Nth term for Arithmetic Progression
Find the 50th term of the arithmetic progression of 3, 7,11, 15…
The solution in a conventional way:
Using the formula provided below, compute the 50th term manually by the method of substitution.
αn = α1 + (n – 1) d
α50 = 3 + (50 – 1) (4)
α50 = 199
Therefore, the 50th term is 199.
Using the calculator:
Press MODE > (3) STAT > (2) A+Bx where B is d, and A+Bx is α1
Show a linear table, where X will be the n and Y is αn
| X | Y |
| 1 | 3 |
| 2 | 7 |
| 3 | 11 |
| 4 | 15 |
After you input click AC. Don’t be wary because the data you input is already stored.
Type the 50 (the term that you need to find), then click Shift STAT > (5) REG > (5) y = 199
Therefore, the 50th term is 199.
For a more detailed explanation, you can watch this video with Engr. Padilla in our Youtube channel, the Padilla Review Center Online TV.
Video here: Calculator Tricks: Arithmetic Progression
Problem #3: Simultaneous Reciprocal Equations
Find the value of x, y, and z:
1x + 1y = 142
1y + 1z = 131
1x + 1z = 120
Using calculator tricks:
Let:
A = 1x
B = 1y
C = 1z
Where:
1x + 1y = 142 =======> A +B = 142
1y + 1z = 131 =======> B + C = 131
1x + 1z = 120 =======> A + C = 120
Press MODE > (5) EQN > (2) Anx + Bny + Cnz = dn
Input the value like this table:
| A | B | C | d |
| 1 | 1 | 0 | 1/42 |
| 0 | 1 | 1 | 1/31 |
| 1 | 0 | 1 | 1/20 |
Answer shows x,y,z where; X is A, Y is B and Z is C.
A = 541/26040
B = 79/26040
C = 761/26040
Substitute the value of A, B, and C in this equation:
A = 1x ====> x = 1/A = 26040/541
B = 1y ====> y = 1/B = 26040/79
C = 1z ====> z = 1/C = 26040/761
Therefore, the value of x is 26040/541, y is 26040/79, and z is 26040/761.
For a more detailed explanation, you can watch this video with Engr. Padilla in our Youtube channel, the Padilla Review Center Online TV.
Video here: Calculator Tricks for Reciprocal Simultaneous Equations
Problem #4: Geometric Progression
Find the 20th term of the geometric progression of 2, 6, 18, 54,…
Using conventional way:
αn = α1 rn-1
α20 = (2)(3)(20 – 1)
α20 = 2324522934
Therefore, the α20 or 20th term of this geometric progression is 2324522934.
Using the calculator trick:
Press MODE > (3) STAT > (6) A*B^x where x is n, B is the common ratio(r), and AB is α1
| X | Y |
| 1 | 2 |
| 2 | 6 |
| 3 | 18 |
| 4 | 54 |
After you input click AC. Don’t be wary because the data you input is already stored.
Type the 20 (the term that you need to find),
then click Shift STAT > (5) REG > (5) y = 2324522934.
Therefore, the 20th term of this geometric progression is 2324522934.
For a more detailed explanation, you can watch this video with Engr. Padilla in our Youtube channel, the Padilla Review Center Online TV.
Video here: Calculator Techniques: Geometric Progression
Problem #5: Purpose of Colon for Trigonometric Identities
If tan X sin X + cos X is equal in what equation below?
a.) sin X
b.) cos X
c.) sec X
d.) csc X
Using calculator trick:
sin X
cos X
sec X = 1/cos X
csc X = 1/sin X
Type the first equation tan X sin X + cos X, the press ALPHA : (colon). Then type the next equation, and put the colon in the middle of every equation.
tan X sin X + cos X: sin X: cos X: 1/cos X: 1/sin X
After you input all, press CALC > X? > Input any value of X.
Let X = 5,
tan X sin X + cos X = 1.0038
sin X = 0.0872
cos X = 0.9962
sec X = 1/cos X = 1.0038
csc X = 1/sin X = 11.474
Therefore, tan X sin X + cos X is equal to sec X.
For a more detailed explanation, you can watch this video with Engr. Padilla in our Youtube channel, the Padilla Review Center Online TV.
Insert Video here: Calculator Tricks: Purpose of Colon
The Bottomline:
These calculator tricks and techniques are made to make you take your exam faster with accurate results. With these techniques, you will improve more on analyzing using your brain than just focusing on written solutions that take more of your time. But take note, using the calculator tricks should be done alongside the proper formulas.
To learn more about calculator tricks and techniques you can buy the book by Engr. Perfecto B. Padilla Jr., Calculator Tricks and Techniques. And you can also take the course Calculator Tricks at the Padilla Review Center for more understanding and detailed teaching.