Basic Algebra Review

Is this course right for you?
Although we named this course Basic Algebra Review, this is actually designed for those who already completed their Algebra subject in engineering curriculum, hence, review. Problems presented in later topics are not really for beginners and solutions presented here assumed that you already earned the credits of College Algebra from your university.

Beginners however are also welcome to join, but never consider this course as a substitute to the long standing and thoroughly tested university program. Don't forget that your professor is the one holding the authority of the subject. Whenever contradiction arises between my teaching and that of your professor, do not follow me, listen to your professor. You may consider this course, however, as a supplement material to the already rich Algebra materials handed to you in your school.
 

Situation
The solid pole shown in the figure is loaded with a vertical load P = 25 kN and lateral load H = 0.95 kN. The pole is 3 m high, 300 mm diameter and weighs 22 kN/m3.
 

2012-may-design-pole-under-combined-loadings.png

 

Problem
The area of a park on a map is 600 mm2. If the scale of the map is 1 to 40,000 determine the true area of the park in hectares (1 hectare = 104 m2).

A.   112 C.   96
B.   84 D.   120

 

Situation
The three-hinged arch shown below is loaded with symmetrically placed concentrated loads as shown in the figure below.
 

2015-may-design-three-hinged-arch-given.png

 

The loads are as follows:
$$P_1 = 90 ~ \text{kN} \qquad P_2 = 240 ~ \text{kN}$$
 

The dimensions are:
$$H = 8 ~ \text{m} \qquad S = 4 ~ \text{kN}$$
 

Calculate the following:
 

1.   The horizontal reaction at A.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

2.   The total reaction at B.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

3.   The vertical reaction at C.

A.   0 C.   330 kN
B.   285 kN D.   436 kN

 

Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A.   0.2027 C.   0.2270
B.   0.2207 D.   0.2072

 

Problem
Determine the radius of curvature of the curve $x = y^3$ at point (1, 1).

A.   5.27 C.   5.56
B.   5.65 D.   5.72

 

Problem
Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.

A.   15π C.   169π
B.   13π D.   225π

 

Problem
The first three terms of a geometric progression are 2x, 4x + 14 and 20x - 14. Find the sum of the first ten terms.

A.   413,633 C.   489,335
B.   498,533 D.   431,336

 

Problem
A 50-m steel tape that is is 0.02 m too long was used to measure the distance between two points A and B. If the measured distance was 160.42 m, calculate the correct distance between A and B.

A.   160.356 m C.   160.844 m
B.   160.484 m D.   160.563 m

 

Problem
A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.

A.   5 C.   3
B.   -3 D.   -5

 

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