40 Questions
What is the purpose of the MTH 103 course?
To teach students the skills required in Sciences, Technology and Engineering Professions
What is the recommended way to cite the course material if used as a bibliographic reference?
Course Code: Course Title, National Open University of Nigeria, 2014 at http://www.nou.edu.ng/index.htm#
What is the number of study units in the MTH 103 course?
Eleven
What is required to be included on every physical page of the textbook if it is redistributed in print format?
All of the above
What is the title of the course MTH 103?
Elementary Mathematics III
What is the purpose of the attribution statement when electronically redistributing the textbook?
To give credit to the original authors
Who is responsible for the ideas and opinions expressed in the publication?
The authors
What is the equation of an ellipse in its standard form?
x^2/a^2 + y^2/b^2 = 1
What is the value of a in the equation 9x^2 + 4y^2 = 36?
3
What are the coordinates of the foci of the ellipse 9x^2 + 4y^2 = 36?
F1 (0, 5) and F2 (0, -5)
What is the length of the major axis of the ellipse 9x^2 + 4y^2 = 36?
6
What is the definition of a hyperbola?
A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
What is the value of c in the equation 9x^2 + 4y^2 = 36?
$\sqrt{5}$
What are the x-intercepts of the ellipse 9x^2 + 4y^2 = 36?
(2, 0) and (-2, 0)
What is the length of the minor axis of the ellipse 9x^2 + 4y^2 = 36?
8
What is the center of the circle x2 +y 2 +2x− 6x− 15 = 0?
(-1, 3)
What is the radius of the circle x2 +y 2 +2x− 6x− 15 = 0?
5
What is the equation of the circle with center (− 2, 3) and radius 6?
x2 + y2 + 4x - 6y - 23 = 0
What is the radius of the circle with center (-3,4) which passes through the point (2,5)?
√26
What is the equation of the circle with center (-3,4) which passes through the point (2,5)?
x2 + y2 + 6x - 8y - 1 = 0
What is the method used to find the radius of the circle with center (-3,4) which passes through the point (2,5)?
The distance formula between two points
What is the equation of the circle with center (h, k) and radius r?
(x - h)² + (y - k)² = r²
What is the method used to find the equation of the circle with center (h, k) and radius r?
Using the formula (x - h)² + (y - k)² = r²
What is the formula for the vector product of two vectors a = a1 i + a2 j + a3 k and b = b1 i + b2 j + b3 k?
(a2 b3 - a3 b2) i - (a1 b3 - a3 b1) j + (a1 b2 - a2 b1) k
What is the vector product of a = 2i + 2j - k and b = 3i - 6j + 2k?
10i - 10j + 20k
What is the meaning of the concept of Locus in geometry?
A set of points that satisfy a certain condition or description
What is the algebraic expression of the Locus of points at a distance of 3 from the point (0, 0)?
x^2 + y^2 = 9
What is the geometric representation of the equation x^2 + y^2 = 9?
A circle with centre at (0, 0) and radius of 3
What is the objective of the unit on Loci?
To learn the concept of straight line
What is the equation of the Locus of a point that satisfies the condition of being at a distance of 3 from the point (0, 0)?
x^2 + y^2 = 9
What is the vector product of a = 3i + 2j - k and b = 2i + 3j - k?
7i - 7j + 13k
What is the equation of a circle with center at (h, k) and radius r?
$(x - h)^2 + (y - k)^2 = r^2$
What is the length of the hypotenuse of the right triangle in the Pythagoras theorem?
$ ceil{(x - h)^2 + (y - k)^2}$
What is the condition for a second degree equation to represent a circle?
The coefficients of x^2 and y^2 are identical
What is the center of the circle with equation x^2 + y^2 + 8x + 6y = 0?
(-4, -3)
What is the radius of the circle with equation x^2 + y^2 + 8x + 6y = 0?
5
What is the equation of a circle with center at (-g, -f) and radius r?
x^2 + y^2 + 2gx + 2fy + c = 0
What is the value of c in the equation x^2 + y^2 + 2gx + 2fy + c = 0?
g^2 + f^2 - r^2
What is the center of the circle with equation x^2 + y^2 - 4x + 2y - 4 = 0?
(2, -1)
Study Notes
Course Introduction
- The course is designed to teach students how mathematics is used to solve problems in the scientific world.
- The course aims to equip students with the skills required to attain proficiency in sciences, technology, and engineering professions.
Mathematics in Problem-Solving
- The course is structured to expose students to the skills required to solve scientific problems.
Course Objectives
- There are eleven study units in the course, each with its objectives.
- The course aims to teach students the basics of mathematics required to solve scientific problems.
Vector Product of Two Vectors
- The vector product of two vectors a and b is given by the formula: a x b = (a2b3 - a3b2)i - (a1b3 - a3b1)j + (a1b2 - a2b1)k
- Examples of vector product calculations are provided.
Loci
- Loci is a concept that combines algebraic expressions with geometric interpretations.
- The concept of loci involves finding the algebraic expression of a locus given its condition or description.
- Examples of loci include the equation of a circle, which is given by the formula: x2 + y2 = 9.
Coordinate Geometry (Circle)
- The equation of a circle is given by the formula: (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius.
- The equation of a circle can be derived from the Pythagorean theorem.
- Examples of finding the center and radius of a circle are provided.
Coordinate Geometry (Circle) - General Equation
- The general equation of a circle is given by the formula: x2 + y2 + 2gx + 2fy + c = 0, where the center is (-g, -f) and the radius is r = √(g2 + f2 - c).
- Examples of finding the center and radius of a circle using the general equation are provided.
Ellipse and Hyperbola
- The equation of an ellipse is given by the formula: x2/a2 + y2/b2 = 1, where a and b are the lengths of the semi-axes.
- The equation of a hyperbola is given by the formula: x2/a2 - y2/b2 = 1, where a and b are the lengths of the semi-axes.
- Examples of finding the points of intersection of a circle with a line and the length of the major and minor axes are provided.
- The concept of hyperbola is defined as a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
This publication outlines the terms of use and attribution for academic content, including proper citation and credit to the National Open University of Nigeria.
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