Calculator Techniques for L.E.T.ENGR. LUIGI CARLO M. DE JESUS

What do we need?

Using CALC and SHIFT + CALC buttonThe CALC button can be use:◦ To check the simplified answers on Algebraic and Trigonometric expressions on

multiple choice questions◦ To avoid using same values in an expression that could cause typing errors◦ To avoid long equations on the calculator display◦ To determine the case 1 and case 2 of partial fraction of an Algebraic expression◦ To evaluate the limits of a certain function as it approaches to a certain value

The SHIFT + CALC button can be use:◦ To solve the unknown automatically

Using CALC and SHIFT + CALC button Sample Problems: What is the value of A in the following equation?   If f(x) = 2x2+2, find the value of f(x+4).

a. 2x2+16x+24 b. 2x2+16 c. 2x2+6x+4 d. 2x2+16x+34

If f(x) = 3x+2 and g(f(x))=x, then g(x) is equal to:a. x-2/3 b. 4x+9 c. 1/3(x-2) d. 3x-2

Using CALC and SHIFT + CALC button Sample Problems: Solve for the value of “A” when sin A = 3.5x and cos A = 5.5x.

a. 32.47° b. 33.68° c. 34.12° d. 35.21°

Find the value of a. 2 sin θ b. 2 cos θ c. 2 tan θ d. 2 cot θ

Simplify the equation sin 2θ (1 + cot 2θ)a. 1 b. sin 2θ c. sin 2θ sec 2θ d. sec 2θ

Simplify the expression sec θ – (sec θ) sin 2θa. cos 2θ b. cos θ c. sin 2θ d. sin θ

Using CALC and SHIFT + CALC button Sample Problems: Simplify: sin x – sin x cos2 x

a. sin3 x b. cos3 xc. tan3 x d. cos2 x sin x

Evaluate: (1 – sin x) / cos xa. cos x / (1 + sin x) b. cos x / (1 – sin x)c. sin x / (1 + sin x) d. sin x / (1 – sin x)

Evaluate: (sin2 x + 4sin x + 3)/ cos2 xa. (3 – sin x)/ (1 – sin x) b. (3 – sin x)/ (1 + sin x)c. (3 + sin x)/ (1 – sin x) d. (3 + sin x)/ (1 + sin x)

Using CALC and SHIFT + CALC button Sample Problems:

Find the value of x: log (x-1)(x-3)= 0.5

a. 5 b. -5 c. 3 d. -3

Evaluate :

a. 0 b. 1 c. 2 d. 3

Evaluate :

a. 1 b. 2 c. 3 d. 4

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Using CALC and SHIFT + CALC button Worker A can finish a job in 3 hours. When working at the same time as Worker B, they can finish the job in 2 hours. How long does it take for Worker B to finish the job if he works alone? 

a. 5 b. 6 c. 7 d. 8

X can finish a certain job in 10 days if Y will help for 6 days. The same work can be done by Y in 12 days if X helps for 6 days. If they work together, how long will it take for them to do the job?

a. 3.75 days b. 8.4 days c. 4 days d. 32.73 days

A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total number of days it took them to finish the job.

a. 10.34 b. 18.45 c. 15.03 d. 20.56

In the expansion of (2x3 – 3/x)12. Find the term that is free of x.

a. 34, 246, 080 b. -34, 642, 080 c. -34, 246, 080 d. 34, 642, 080

Complex Numbers (Use mode + 2) The mode + 2 can be use

◦ To evaluate complex numbers◦ To evaluate case 3 and case 4 of the partial fraction of algebraic expression

Sample Problems: What is the value of A in the following equation?  

Find the rectangular form of e 1 – i

Find the exponential form of i 2 – i

Find the rectangular form of ln( 3 + 4i )Find the rectangular form of log( 6 + 4i )Simplify i1005 + 2 ( i2014 ) – ( i + 2)12

Laplace Transform in LineIO(Use mode + 1 and Shift + mode + 2)

The LineIO (Shift + mode + 2) is used:◦ To speed up the calculations of linear operations such as differential, integral and summation

operations◦ Under integral operations includes the Laplace Transform operations

F(s) = ∫f(t) e-st dtSample Problems:f(t) = 3tf(t) = 3 + cos(t)

Matrix (Use mode + 6) Determine the determinant, cofactor, adjoint and inverse of the matrices below

1. 1 24 5

2. 1 4 70 -2 13 1 -2

3. 0 -1 51 0 23 -1 4

Questions and Answers

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