## MATH 035 - Intermediate Algebraic Mathematics

Intermediate Algebraic 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: rational numbers, percent with applications, measurement of area and perimeter, right-angled trigonometry, signed numbers and algebraic expressions, linear equations, polynomials, simple factoring, graphing linear equations, exponents, roots and scientific notation.

Hours: 120 (Lecture Hours: 120)

Total Weeks: 20

Prerequisites:
“C“ or higher in MATH026 or MATH09 or equivalent or Intermediate Level Placement on the CCP Math Assessment

Non-Course Prerequisites:
None

Co-requisites:
None

Course Content:
1. Operations with Rational Numbers
It is expected that learners will be able to:
a) write fractions as decimals and decimals as fractions
b) add, subtract, multiply, and divide rational numbers
c) use order of operations
d) graph rational numbers on the number line
e) define absolute value
2. Measurement
It is expected that learners will be able to:
a) use the common metric units for temperature, length, area, volume/capacity, and mass
b) use the common Imperial units for temperature, length, area, volume/capacity, and force
c) convert between and within metric and Imperial units using tables and/or calculators
d) use proportional reasoning for conversions
3. Perimeter, Area, and Volume
It is expected that learners will be able to:
a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures using formulas
b) find areas of the above shapes using formulas
c) find the surface areas of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas
d) find the volumes of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas
e) distinguish between concepts of perimeter and area and their respective units
4. Ratio, Proportion and Percent
It is expected that learners will be able to:
a) read, write, interpret, and compare ratios
b) read, write and identify proportions and use them to solve problems
c) use ratio and proportion to interpret and make scale drawings
d) use ratio and proportion to solve problems involving similar triangles
e) use ratios and proportions to solve problems involving:
i) finding percent when part and whole are known
ii) finding part when percent and whole are known
iii) finding whole when part and percent are known
5. Algebra
It is expected that learners will be able to:
a) explain the use of variables
b) evaluate algebraic expressions using substitution
c) combine like terms and remove parentheses
d) solve first degree equations in one variable
e) translate a problem into an equation
f) use equations to solve problems
g) solve simple formulas for one variable
h) use formulas to solve problems
6. Linear Equations and Graphing
It is expected that learners will be able to:
a) draw a Cartesian co-ordinate system
b) plot and name points in a Cartesian co-ordinate system
c) given an equation in two variables:
i) determine if an ordered pair is a solution
ii) find ordered pairs which are solutions
d) graph equations of the form x = a and y = b,
e) graph linear equations using
i) slope and y-intercept
ii) two intercepts
iii) a table of values
f) relate slope to grade and pitch
g) find x- and y-intercepts
h) determine the equation of a line, y = mx + b, given
i) its graph
ii) its slope and a point on the line
iii) two points on the line
i) solve problems using graphs of linear equations
7. Powers, Roots, and Scientific Notation
It is expected that learners will be able to:
a) read and write numbers expressed as powers
b) evaluate powers with integral exponents
c) apply laws of exponents to simplify expressions
d) express numbers using scientific notation
e) convert between scientific and standard notation
f) determine the square root of a perfect square
g) express a square root as a mixed radical in simplest form (numerical radicands only)
h) approximate square roots of real numbers using a calculator
8. Polynomials
It is expected that learners will be able to:
a) distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)
b) apply the laws of exponents to variable expressions with integral exponents
c) evaluate polynomials by substitution
d) add, subtract, and multiply polynomials in one variable
e) factor polynomials by removing the largest common factor
f) factor binomials of the form a2x2 – b2y2
g) factor trinomials of the form ax2 + bx + c with a = 1 ONLY
h) divide a polynomial by a monomial
9. Trigonometry
It is expected that learners will be able to:
a) name parts of a triangle
b) find missing side of a right triangle using the Pythagorean Theorem
c) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios
d) solve problems using right angle trigonometry

Learning Outcomes:
Students will meet the competencies for ABE Intermediate Level Algebraic Mathematics as stated in the 2014-2015 Articulation Handbook at http://www.aved.gov.bc.ca/abe/docs/handbook.pdf
1. Operations with Rational Numbers
It is expected that learners will be able to:
a) write fractions as decimals and decimals as fractions
b) add, subtract, multiply, and divide rational numbers
c) use order of operations
d) graph rational numbers on the number line
e) define absolute value
2. Measurement
It is expected that learners will be able to:
a) use the common metric units for temperature, length, area, volume/capacity, and mass
b) use the common Imperial units for temperature, length, area, volume/capacity, and force
c) convert between and within metric and Imperial units using tables and/or calculators
d) use proportional reasoning for conversions
3. Perimeter, Area, and Volume
It is expected that learners will be able to:
a) find perimeters of triangles, squares, rectangles, parallelograms, trapezoids, circles and composite figures using formulas
b) find areas of the above shapes using formulas
c) find the surface areas of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas
d) find the volumes of cubes, rectangular solids, right cylinders and cones, spheres, and composite solids using formulas
e) distinguish between concepts of perimeter and area and their respective units
4. Ratio, Proportion and Percent
It is expected that learners will be able to:
a) read, write, interpret, and compare ratios
b) read, write and identify proportions and use them to solve problems
c) use ratio and proportion to interpret and make scale drawings
d) use ratio and proportion to solve problems involving similar triangles
e) use ratios and proportions to solve problems involving:
i) finding percent when part and whole are known
ii) finding part when percent and whole are known
iii) finding whole when part and percent are known
5. Algebra
It is expected that learners will be able to:
a) explain the use of variables
b) evaluate algebraic expressions using substitution
c) combine like terms and remove parentheses
d) solve first degree equations in one variable
e) translate a problem into an equation
f) use equations to solve problems
g) solve simple formulas for one variable
h) use formulas to solve problems
6. Linear Equations and Graphing
It is expected that learners will be able to:
a) draw a Cartesian co-ordinate system
b) plot and name points in a Cartesian co-ordinate system
c) given an equation in two variables:
i) determine if an ordered pair is a solution
ii) find ordered pairs which are solutions
d) graph equations of the form x = a and y = b,
e) graph linear equations using
i) slope and y-intercept
ii) two intercepts
iii) a table of values
f) relate slope to grade and pitch
g) find x- and y-intercepts
h) determine the equation of a line, y = mx + b, given
i) its graph
ii) its slope and a point on the line
iii) two points on the line
i) solve problems using graphs of linear equations
7. Powers, Roots, and Scientific Notation
It is expected that learners will be able to:
a) read and write numbers expressed as powers
b) evaluate powers with integral exponents
c) apply laws of exponents to simplify expressions
d) express numbers using scientific notation
e) convert between scientific and standard notation
f) determine the square root of a perfect square
g) express a square root as a mixed radical in simplest form (numerical radicands only)
h) approximate square roots of real numbers using a calculator
8. Polynomials
It is expected that learners will be able to:
a) distinguish between monomials, binomials, trinomials and other polynomials (in one variable only)
b) apply the laws of exponents to variable expressions with integral exponents
c) evaluate polynomials by substitution
d) add, subtract, and multiply polynomials in one variable
e) factor polynomials by removing the largest common factor
f) factor binomials of the form a2x2 – b2y2
g) factor trinomials of the form ax2 + bx + c with a = 1 ONLY
h) divide a polynomial by a monomial
9. Trigonometry
It is expected that learners will be able to:
a) name parts of a triangle
b) find missing side of a right triangle using the Pythagorean Theorem
c) find the measure of an unknown side or angle of a right triangle using sine, cosine, or tangent ratios
d) solve problems using right angle trigonometry