Problem
A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?

A.   0.168 C.   0.681
B.   0.618 D.   0.816

 

Probability Problems Involving Coins

When you toss a coin, the outcome can either be head or tail. If the coin is so balanced that these two outcomes are equally likely to occur, then the probability that the outcome is head is 1/2, and the probability that the outcome is tail is also 1/2.
 

5-peso-coin-bsp.png

 

Example
A coin is tossed three times. What is the probability that the head will appear only once?
 

01 Area of a right triangle of known median bisecting the hypotenuse

Problem
The median of a right triangle drawn to the hypotenuse is 3 cm long and makes an angle of 60° with it. Find the area of the triangle.

A.   7.97 cm2 C.   8.79 cm2
B.   8.97 cm2 D.   7.79 cm2

 

How long will P2.5M amounts to P4.5M at 8% compounded quarterly?

Problem
By the conditions of a will, the sum of P2.5M is left to a girl to be held in a trust fund by her guardian until it amounts to P4.5M. When will the girl receive the money if the fund is invested at 8% compounded quarterly?

A.   7 years C.   7.42 years
B.   6.8 years D.   7.25 years

 

Length of hypotenuse of a right triangle of known area in the xy-plane

Problem
For triangle BOA, B is on the y-axis, O is the origin, and A is on the x-axis. Point C(5, 2) is on the line AB. Find the length of AB if the area of the triangle is 36 unit2.

A.   24.31 units C.   13.42 units
B.   18.30 units D.   10.80 units

 

The Straight Line

Definition
Straight line is the locus or path of a point that moves without changing its direction.
 

straight-line-01.jpg

 

General Equation
The general equation of the straight line is given by

$ax + by + c = 0$

 

Volume of regular tetrahedron of given length of edges

Problem
Determine the volume of a regular tetrahedron of edge 2 ft.

A.   1.54 ft3 C.   1.34 ft3
B.   1.01 ft3 D.   0.943 ft3

 

Problem 02 - Semi-Elliptical Arch in a Stone Bridge

Problem
A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.
 

A.   1.41 m C.   1.56 m
B.   1.63 m D.   1.73 m

 

Curvature and Radius of Curvature

Curvature and Radius of Curvature in xy-Plane | Derivation of Formula | Differential Calculus

Curvature (symbol, $\kappa$) is the mathematical expression of how much a curve actually curved. It is the measure of the average change in direction of the curve per unit of arc. Imagine a particle to move along the circle from point 1 to point 2, the higher the number of $\kappa$, the more quickly the particle changes in direction. This quick change in direction is apparent in smaller circles.
 

Circle of Curvature

 

Pages

Subscribe to MATHalino RSS