B.C.'s Energy College

MATH 030 - Intermediate Mathematics

Intermediate Math reviews the fundamental arithmetic skill to introduce beginning algebra and problem-solving in preparation for more advanced work in mathematics and the sciences. Units of work include: percent with applications, measurement of area and perimeter, practical geometric construction, right-angled trigonometry, signed numbers and algebraic expressions, linear equations, polynomials, simple factoring, graphing linear equations, and scientific notation.

Hours: 120 (Lecture Hours: 6)

Total Weeks: 20

Prerequisites:

MATH 020 (Fundamental Mathematics) or demonstrated skill at Grade 9 level; OR permission of instructor.

Non-Course Prerequisites: None

Co-Requisites: None

Course Content:
1. Estimating Skills/Calculator Use.
- using a scientific calculator to calculate, solve, and check problems involving adding, subtracting, multiplying and dividing whole numbers, fractions, and decimals
2. Measurement
- metric and imperial units for temperature, length, area, volume/capacity, mass, force
- converting between and within metric and imperial units using tables and/or calculators
- reading and recording measurements with common measuring tools
- estimating in metric and imperial units of measurement
3. Perimeter, Area, and Volume
- calculating perimeters, areas, surfaces, and volumes of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figure by measuring and using formulas
- distinguishing between concepts of perimeter and area and their respective units
4. Ratio and Proportion
- reading, writing, interpreting, and comparing ratios and proportions and using them to solve problems and make scale drawings
5. Percent
- using ratios and proportions to solve percent problems
6. Geometry
- naming and drawing points, lines, rays, segments, angles, triangles, quadrilaterals, other common polygons, and circles
- constructing with a compass and straight edge:
a) the perpendicular bisector of a line segment
b) the bisector of an angle
c) a copy of an angle
d) parallel lines
e) 45, and 60 angles
- classifying and distinguishing among acute, rights, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles; and describe the angle relationships created when parallel lines are cut by a transversal
- measuring angles with a protractor
- classifying triangles according to sides and angles
- identifying similar and congruent figures
7. Statistics
- conducting a survey; tabulating data; calculating median, mean, mode, and range; and graphing the data
- interpolating and extrapolating from the information provided
8. Signed (Rational) Numbers
- adding, subtracting, multiplying, and dividing signed (rational) numbers
9. Algebra
- simplifying expressions and evaluating algebraic expressions using substitution
- translating a problem into an equation
- using equations and formulas to solve problems
10. Problems, Roots, and Scientific Notation
- reading and writing numbers expressed as powers
- calculating powers with integral exponent
- using the rules of exponents to calculate products and quotients of powers with the same base
- using the rules of exponents to calculate the powers of powers
- converting between scientific and standard notation
- reading and writing numbers expressed as roots
- calculating using roots
11. Polynomials
- multiplying and dividing polynomials by a monomial
- removing common factors from polynomials
12. Trigonometry
- finding the missing side of a right triangle using the Pythagorean Theorem
- finding the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios
- solving problems using right angle trigonometry
13. Graphing
- drawing, plotting, and naming points using a Cartesian co-ordinate system
- determining if an ordered pair is a solution
- finding ordered pairs solutions
- creating a table of values
- graphing linear equations
- determining the slope of a line given two points on the line and relating slope to grade and pitch
- finding x and y intercepts

- solving problems using graphs of linear equations

Learning Outcomes:
The learners will be able to:
1. Estimating Skills/Calculator Use.
- use a scientific calculator to calculate and solve problems involving adding, subtracting, multiplying and dividing whole numbers, fractions, and decimals
- estimate and validate answers and solutions to problems that are reasonable in the context of the given questions
2. Measurement
- use the common metric units for temperature, length, area, volume/capacity, and mass
- use the common imperial units for temperature, length, area, volume/capacity, and force
- convert between and within metric and imperial units using tables and/or calculators
- demonstrate reading & recording of measurements with common measuring tools (e.g. thermometer, ruler, measuring tape, triple beam balance, bathroom scale, stop watch, vernier caliper, micrometer)
- describe and apply precision, accuracy and tolerance
- estimate in metric and imperial units of measurement
3. Perimeter, Area, and Volume
- solve perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures by measuring and using formulas
- solve areas of the above shapes by measuring and using formulas
- solve the surface of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by measuring and using formulas
- solve the volumes of cubes, rectangular solids, cylinders, cones, spheres, and composite solids by measuring and using formulas
- distinguish between concepts of perimeter and area and their respective units
4. Ratio and Proportion
- read, write, interpret, and compare ratios
- read, write, and identify proportions and use them to solve problems
- apply ratio and proportion to interpret and make scale drawings
- apply proportions to solve problems involving similar triangles
5. Percent
- use ratios and proportions to solve percent problems
a) finding % when part and whole are known
b) finding part when % and whole are known
c) finding whole when part and % are known
6. Geometry
- name and draw points, lines, rays, segments and angles
- name and draw triangles, quadrilaterals, other common polygons, and circles
- construct with a compass and straight edge:
a) the perpendicular bisector of a line segment
b) the bisector of an angle
c) a copy of an angle
d) parallel lines
e) 45, and 60 angles
- classify and distinguish among acute, rights, obtuse, straight, reflex, complementary and supplementary, and vertically opposite angles
- describe the angle relationships created when parallel lines are cut by a transversal
- measure angles with a protractor
- classify triangles according to sides and angles
- identify similar and congruent figures
7. Statistics
- conduct a survey to collect data
- tabulate the data
- calculate median, mean, mode, and range
- graph the data
- interpolate and extrapolate from the information provided
8. Signed (Rational) Numbers
- perform addition, subtraction, multiplication, and division on signed (rational) numbers
a) by demonstrating order of operations with signed (rational) numbers
b) by graphing signed (rational) numbers on the number line
c) by defining absolute value
9. Algebra
- explain the use of variables
- evaluate algebraic expressions using substitution
- combine like terms and remove parentheses
- solve first degree equations in one variable
- translate a problem into an equation
- use equations to solve problems
- solve simple formulas for one variable
- use formulas to solve problems
10. Problems, Roots, and Scientific Notation
- demonstrate reading and writing of numbers expressed as powers
- calculate powers with integral exponent
- apply the rules of exponents to calculate products and quotients of powers with the same base
- apply the rules of exponents to calculate the powers of powers
- express numbers using scientific notation
- convert between scientific and standard notation
- demonstrate reading and writing of numbers expressed as roots
- calculate using roots
11. Polynomials
- demonstrate multiplication and division of polynomials by a monomial
- illustrate removal of common factors from polynomials
12. Trigonometry
- name the parts of a right triangle
- find the missing side of a right triangle using the Pythagorean Theorem
- find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios
- solve problems using right angle trigonometry
13. Graphing
- draw a Cartesian co-ordinate system
- plot and name points in a Cartesian co-ordinate system
- given an equation in two variable:
a) determine if an ordered pair is a solution
b) find ordered pairs solutions
c) create a table of values
- graph linear equations
- determine the slope of a line given two points on the line
- demonstrate the relationship of slope to grade and pitch
- find x and y intercepts

- solve problems using graphs of linear equations