Course:MATH110/Archive/2010-2011/003/Basic Skills

Even if mathematics is mainly about ideas and concepts, we need to be able to manipulate some of its elements in order to get the job done. By basic skills, we understand some of the technical skills that are usually addressed in elementary and high school. Math 110 students usually have difficulties with those or have never seen some aspects of it. It is one of the goals of Math 110 to have students close this gap and be able to successfully take the UBC basic skills test. Our goal is to get this done by the end of December so that we can move on to our other goals. The December final exam will address this and test you on those basic skills.

Learning Objectives

Properties of functions - group 4

What is a function?
What is the graph of a function?
How to use the graph of a function?
What is the domain of a function?
How to find the domain of a given function?
How to see/use the domain of a function on its graph?

Radical functions - group 18

What they are?
How to graph them?
How to use them?
How to find functions describing circles?

Trigonometric functions - group 11

What they are?
How to graph them?
How to modify them?
How to use them?

Exponential functions - group 5

What they are?
How to graph them?
How to modify them?
How to use them?
How to link them to logarithmic functions?

Logarithmic functions - group 14

What they are?
How to graph them?
How to modify them?
How to use them?
How to link them to exponential functions?

Piecewise functions - group 6

What they are?
How to graph them?
How to modify them?
How to use them?

Absolute-valued functions - group 3

What they are?
How to graph them?
How to modify them?
How to use them?
How to link them with piecewise functions?

Equations - group 7

What is an equation?
How to solve linear equations?
How to solve quadratic equations?
How to solve polynomial equations of degree more than 3?
How to solve equations of square roots?
Where to look for other types of equations?

Inequalities - group 9 and group 10

What is an inequality?
How to represent the solutions of inequalities?
How to solve linear inequalities?
How to solve quadratic inequalities?

Polynomial long division - group 8

How to perform long divisons of polynomials?
How to write the result out? (Whether there is a remainder or not).

Intersections of functions - group 16

How to find intersections of two or more graphs? (Given functions, or given a picture, etc)
What techniques are involved?

Distances and lines - group 2

How to find the distance between two points? (given two points; or a slope and a point; or some other information...)
How to use the distance formula?
What is the equation of a line?
What is the slope of a line?
When are lines parallel or perpendicular?

Operations on graphs of functions - group 13

How to construct new functions by using elementary operations such as:
- addition/subtraction of functions
- multiplication/division of functions
- composition of functions
How to identify the various functions that make up a composite function?
How to translate, scale and reflect graphs of functions?

Trigonometry and the Pythagorean theorem - group 17

How to apply the Pythagorean theorem?
How to write down trigonometric relationships involving the sides and angles of a right triangle?
How does that relate to the trigonometric circle?
How to prove the Pythagorean theorem?

Areas and volumes - group 1

How to compute the area of basic 2D shapes?
How to compute the surface area of basic 3D shapes?
How to compute the volume of basic 3D shapes?

Mathematical writing - group 12

How to construct neat, logical, understandable explanations and solutions?