Calculator and Math Techniques using Casio 991-ES

“A man is like a fraction whose numerator is

what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.”

—Leo Tolstoy

ECE Board Nov. 1993Simplify the ff. equation

a. c. b. d.

Hint: Maglet ng value ng x for the equation then gamitin the same “x” sa mga choices. Kung anu yung same na sagot, that’s the answer.

Answer: a.

Practice:Find x, if

•√2•√3•√5•√7

Hint: used “calc” instead of “shift solve”

Answer: b. √3

Find the value of k so that 4x2+6x+k is a perfect square.

a. 36 c. 9 b. 2.5 d. 2.25

Hint: Quadratic equation. Mode 5-3.

Answer: d. 2.25

EE Board April 1996, March 1998The polynomial x3+4x2-3x+8 is divided by x-5, then the remainder is

a. 175 c. 218 b. 140 d. 200

Hint: Remainder Theorem

Answer: c. 218

ECE Board April 1993Solve for the value of x in the ffequation: x3logx=100x

a. 12 c. 30 b. 8 d. 10

Answer: d. 10

EE Board Oct. 1994One number is 5 less than the other. If their sum is 135, whatare the numbers?

a. 85,50 c. 70,65 b. 80,55 d. 75,60

Answer: c. 70, 65

Arithmetic ProgressionFind the 14th term in the arithmetic sequence: 1,3,5,7

a. 25 c. 29 b. 27 d. 31

Hint: Arithmetic Progression. Mode 3-2 x= nth term y=yung value(term itself)

Answer: b. 27

CE Board May 1995What is the sum of the progression 4,9,14,19 up to the 20th term?

a. 1030 c. 1040 b. 1035 d. 1045

Answer: a. 1030

CE Board May 1993,1994How many terms of the progression 3,5,7…. must be taken in order that their sum will be 2600?

a. 48 c. 50 b. 49 d. 51

Answer: c. 50

EE Board Oct 1991The Fourth term of G.P. is 216 and 6th term is 1944. Find the 8th term ?

a. 17649 c. 16749 b. 17496 d. 17964

Hint: Geometric Progression. Mode 3-6 x= nth term y=yung value(term itself)

Answer: a. 17496

ECE Board April 1998

The sum of the first 10 terms of a geometric progression 2,4,8 is?

a. 1023 c. 225 b. 2046 d. 1596

Answer: b. 2046

What is the sum of the 6+9+12…………..+171?

a. 4956 c. 5198 b. 4389 d. 5462

Answer: a. 4956

Find the polar coordinates of the point (3,-2)

Answer: Ans. r=3.60555, θ=-33.69°

• Find the area of a triangle whose sides are 30,16 and 34 units.

• 240 sq. units• 420 sq. units• 320 sq units• 200 sq. units

Answer: a. 240 sq. units

ECE Board November 1990In a cartesian coordinates, the vertices of a triangle are defined by the following points: (-2,0),(4,0) and (3,3). What is the area?•8 sq. units•9 sq. units•10 sq. units•11 sq. units

Answer: a. 9 sq. units

Practice:EE Board April 1994Given three vertices of a triangle whose coordinates are (1,1), (3,-3) and (5,-3). Find the area of the triangle.•3 sq. units•4 sq. units•5 sq. units•6 sq. units

Answer: b. 4

In a cartesian coordinates, the vertices of a square are: (1,1),(0,8),(4,5) and (3,-4).

•20 sq. units•30 sq. units•25 sq. units•35 sq. units

Answer: c. 25

Find the distance between (4,-3) and (-2,5).

•11•9•10•8

Answer: c. 10

Two sides of triangle measures 6 cm and 8 cm and their included angle is 40°. Find the third side.

•5.144 cm•4.256 cm•5.263 cm•5.645 cm

Answer: a. 5.144 cm

What is the equation of the line that passes thru (4,0) and is parallel to the line x-y-2=0

•x-y+4=0•x+y+4=0•x-y-4=0•x-y=0

Answer: c. x-y-4=0

Evaluate the ff:

•1•0•45.5•10

Hint: use summation sa calculator

Answer: a. 1

Find the value of

•2sinθ •2cosθ•2tanθ•2cotθ

Answer: c. 2tanθ

Practice:Evaluate:

•Sinθ •Cosθ•Tanθ•cotθ

Answer: d. cotθ

If coversed sinθ=0.134, find the value of θ.

•30°•45°•60°•90°

Hint: coverse sinθ = 1 - sinθ

Answer: c. 60°

The sum of two positive numbers is 50. what are the numbers if their product is to be the largest.

•24 & 26•28 & 22•25 & 25•20 & 30

Answer: c. 25 & 25

What is the derivative with respect to x of (x+1)3 - x3?

•3x+6•3x-3•6x-3•6x+3

Hint: use differential function sa calculator.

Answer: d. 6x+3

Find the value of x when the function y=lnx/x is at maximum value

•0•e•1•1/e

Hint: at maximum value, first derivative is zero

Answer: b. e

The function is discontinous at x=?

A. 2B. -2C. either a or bD. neither a nor b

Answer: b. -2

Evaluate A x B.

a. c.

b. d.

What is the integral of (3t-1)3dt?

A. (1/12) (3t-1)4 + CB. (1/12) (3t-4)4 + CC. (1/4) (3t-1)4 + CD. (1/4) (3t-1)3 + C

Hint: use the integral function sa calculator

Answer: a. (1/12) (3t-1)4 + C

PracticeIntegrate: (7x3 + 4x2)dx

•(7x3/3) + (4X2/2) + C•(7x4/4) + (4X2/5) + C•(7x4/4) + (4X3/3) + C•7x4 - (4X/2) + C

Answer: c. (7x4/4) + (4X3/3) + C

Solve 3x(xy-2)dx + (x3 + 2y)dy=0

•x2y – x + y = C•x3y – 3x2 + y2 = C•x2y + x + y2 = C•x3y –x2 + y = C

Answer: b. x3y – 3x2 + y2 = C

Evaluate 2xydx + (y2 – x2)dy=0

•x2 + y2 = Cx•x2 + y2 = C•x2 - y2 = C•x2 + y2 = Cy

Answer: d. x2 + y2 = Cy

Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes tom 96 mg. How many mg will be left after 200 years?•50.2 mg•92.16 mg•76.3 mg•81.2 mg

Hint: use mode 3-5. (e^x function) x=time/years

y= amount

Answer: b. 92.16 mg

PracticeA radioactive substance decreases form 10 grams to 9 grams in two hours. Find its half life.

•10.19 hr•11.49 hr•12.89 hr•13.16 hr

Answer:

Find the Laplace transform of f(t)=cosh(5t).

•5/(s2 – 25)•5s/(s2 – 25)•s/(s2 + 25)•s/(s2 – 25)

Hint: F(s)=

Answer:

End!Thank you!