Calculator Techniques for LET

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

What do we need?

Using CALC and SHIFT + CALC button The 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

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

d. 2 cot θ d. sec 2θ d. sin θ

Using CALC and SHIFT + CALC button Sample Problems: Simplify: sin x – sin x cos2 x a. sin3 x b. cos3 x c. tan3 x d. cos2 x sin x Evaluate: (1 – sin x) / cos x a. cos x / (1 + sin x) c. sin x / (1 + sin x)

b. cos x / (1 – sin x) d. sin x / (1 – sin x)

Evaluate: (sin2 x + 4sin x + 3)/ cos2 x a. (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

b. 1

c. 2

d. 3

b. 2

c. 3

d. 4

Evaluate : a. 0

Evaluate : a. 1

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 6 th 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, 080b. -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

Sample Problems: f(t) = 3t f(t) = 3 + cos(t)

dt

Matrix (Use mode + 6) Determine the determinant, cofactor, adjoint and inverse of the matrices below 1.

1 4

2 5

2.

1 0 3

4 -2 1

7 1 -2

3.

0 1 3

-1 0 -1

5 2 4

Questions and Answers

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