Calculator Technique for Clock Problems in Algebra

Jhun Vert

The following models of CASIO calculator may work with these methods: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus.
 

Before we go to Calculator technique, let us first understand the movements of the hands of our continuously driven clock.
 

For simplicity, let "dial" be the unit of one hand movement and there are 60 dials in the complete circle as shown in the figure.
 

Calculator Techniques for Solving Progression Problems

Jhun Vert

This is the first round for series of posts about optimizing the use of calculator in solving math problems. The calculator techniques I am presenting here has been known to many students who are about to take the engineering board exam. Using it will save you plenty of time and use that time in analyzing more complex problems. The following models of CASIO calculator may work with these methods: fx-570ES, fx-570ES Plus, fx-115ES, fx-115ES Plus, fx-991ES, and fx-991ES Plus.
 

Calculator for Engineering Board Exam

Jhun Vert

Any one who took an engineering board examination will agree with me that scientific calculator is our best friend during the examination. It will speed up our work and will allow us to go through the analysis of the problem. In most cases, solving the equation is not the real issue, it is to write the correct equation that matters. If we are able to determine the correct equation of a particular situation, the burden of that problem is over. Our next step is obviously to solve for the desired value. It is important to note that the correct answer can only be derived from the correct equation. To determine the correct equation is where should our brain go, not in finding the solution of that equation. You guess it right, we use our best friend, the scientific calculator, to do the task. Don't do manual calculation please, the examiner will not give you bonus points in finding the roots of
 

$9\sin^{3/4} \theta + 4\sin^{3/2} \theta - 12 = 0$

 

manually. Calculator can easily solve for the value of θ fast and accurate than you.
 

02 Trapezoidal lot segregated from triangular land

Situation
A triangular lot ABC have side BC = 400 m and angle B = 50°. The lot is to be segregated by a dividing line DE parallel to BC and 150 m long. The area of segment BCDE is 50,977.4 m2.
 

Part 1: Calculate the area of lot ABC.
A. 62,365 m2
B. 59,319 m2
C. 57,254 m2
D. 76.325 m2
 

Part 2: Calculate the area of lot ADE.
A. 8,342 m2
B. 14,475 m2
C. 6,569 m2
D. 11,546 m2
 

Part 3: Calculate the value of angle C
A. 57°
B. 42°
C. 63°
D. 68°
 

Swimming pool in the shape of two intersecting circles

Situation
A swimming pool is shaped from two intersecting circles 9 m in radius with their centers 9 m apart.
 

Part 1: What is the area common to the two circles?
A. 85.2 m2
B. 63.7 m2
C. 128.7 m2
D. 99.5 m2
 

Part 2: What is the total water surface area?
A. 409.4 m2
B. 524.3 m2
C. 387.3 m2
D. 427.5 m2
 

Part 3: What is the perimeter of the pool, in meters?
A. 63.5 m
B. 75.4 m
C. 82.4 m
D. 96.3 m
 

Depth of water in conical tank in upright and inverted positions

Situation
A closed conical vessel has a base radius of 2 m and is 6 m high. When in upright position, the depth of water in the vessel is 3 m.
 

Part 1: What is the volume of water?
A. 22 m3
B. 25 m3
C. 28 m3
D. 32 m3
 

Part 2: If the vessel is held in inverted position, how deep is the water?
A. 4.53 m
B. 5.74 m
C. 4 m
D. 5 m
 

Part 3: What is the weight of water in quintals. Unit weight of water is 9,800 N/m3.
A. 263.4
B. 195.4
C. 219.7
D. 247.2