Quiz in Basic Mathematics

Evaluate yourself with our basic math problems for engineering. Each problem are carefully selected so that every item in this quiz can be answered by basic principle if not by common sense.
 

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

 

Problem
Calculate the acute angle between two intersecting surfaces whose equations are as follows:
$$2x - 4y - z = -5$$

$$3x + 4y + 5z = -6$$

A.   62.4° C.   42.6°
B.   64.2° D.   46.2°

 

Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?

A.   0.5 C.   1.5
B.   1.0 D.   2.0

 

Answer Key

Problem
The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

A.   9 C.   15
B.   12 D.   18

 

Problem
There are 7 arithmetic means between 3 and 35. What is the sum of all the terms?

A.   133 C.   665
B.   608 D.   171

 

Problem
A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water.

A.   30 kph C.   40 kph
B.   50 kph D.   20 kph

 

Problem
What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?

A.   $4x + 3y = 0$ C.   $3x + 4y = 0$
B.   $3x - 4y = 0$ D.   $4x - 3y = 0$

 

Problem
What is the radius of the circle $x^2 + y^2 - 6x = 0$?

A.   6 C.   4
B.   9 D.   3

 

Problem
When the polynomial $x^4 + bx^3 + 5x^2 + dx + 6$ is divided by $x - 2$ the remainder is 16. When it is divided by $x + 1$ the remainder is 10. Find the value of constant $d$.

A.   7 C.   -5
B.   -7 D.   5

 

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