Download Math Test Study Guide (MPT)

Math Test Study Guide (MPT)
WHAT IS THE MATH PLACEMENT TEST?
The Alexander College’s Mathematics Placement Test (MPT) is an assessment to test equivalent
knowledge of the BC Grade 11 & 12 Mathematics curriculum (Foundations of Mathematics and PreCalculus 11 & 12), which is required for success in university level Mathematics.
The MPT will include questions related to selected BC Math 11 & 12 topics, and may include:
1. Number, Exponents and Radicals
2. Variables, Equations and Inequality
3. Geometry
4. Functions and their Graphs
5. Trigonometry
Students are placed based on their Math Placement Test score:
Math Placement Test Scoring Table
Score
Course
0-25
Math 100
26-35
Math 104/151
The Math Placement Test takes a total of one hour.
Content Description:

Number, Exponents and Radicals
1. Identify and apply properties of the real numbers ( Commutative, Associative and distributive)
2. Arrange fractions, decimals, and percentages in order of size; convert between them and use
them to solve problems
3.
4.
5.
6.
7.
8.
9.
Use absolute value to express distance;
Find union and intersection of two sets;
Use properties of exponents to simplify exponential expressions;
Convert between decimal and scientific notation.
Add/Subtract/ Multiply/divide expressions involving radicals and simplify radical expressions.
Rationalize numerators and denominators of rational expressions containing radicals
Identify a sequence as arithmetic, geometric or other, and find the sum of the first nth terms
and the value of a specific term of an arithmetic and geometric series
10. Use sigma notation to represent series
11. Use sequences and series to solve real-life problems.
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12. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems
13. Use arithmetic operations with fractions, decimals, and integers and use the correct order of
operations in situations where more than one operation is performed

Variables, Equations and Inequality
1. Evaluate algebraic expression for given values of variables;
2. Translate a verbal statement into algebraic language and vice versa;
3. Add / Subtract/ multiply/ divide Polynomials
4. Factor completely: a quadratic trinomial, difference of two squares or the sum or difference of
two cubes
5. Use remainder and factor theorems to find the zeros of polynomials
6. Find the sum, difference, product and quotient of rational expressions in simplest form;
7. Solve rational equations; and word problems involving a rational equation or a proportion
8. Given two points (x1, y1) and ( x2, y2) , find the distance and midpoint between the two points;
slope and equation of a line through the two given points
9. Find the slope (m) and y-intercept (b), given the equation of a line; and find the equation of a
line given the slope (m) and y-intercept (b)
10. Interpret the meaning of intercept and slope of a linear function in a given context;
11. Given a point (x1, y1) and the slope m, find the equation of a line
12. Given the equations of two lines, determine if they are parallel, perpendicular or neither
13. Solve a formula for a specified variable;
14. Solve linear equations and inequalities in one variable including those that involves absolute
value; and graph their solution sets ;
15. Find and use the discriminate to determine the number and type of solutions of quadratic
equations; and know how to solve the equation (by completing the square, by factoring method;
and by using the quadratic formula)
16. Find the axis of symmetry; the x-intercepts and the vertex of a parabola; interpret the meaning
of each of them in a given context; and sketch the graph of the parabola
17. Solve a system of two linear equations in two variables algebraically and graphically recognizing
cases of no solutions or infinitely many solutions.
18. Read, analyze, and solve verbal problems involving ( linear and quadratic) equations and
inequality

Basic Geometry
1. Find measures of angles by using complementary and supplementary relations.
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2. Solve problems involving the measures of angles of triangles; recognize and apply properties of
isosceles and equilateral triangles; recognize and apply properties of congruent and similar
triangles;
3. Apply the Pythagorean Theorem to solve problems involving right triangle in various contexts;
4. Know and apply the angle properties in a circle including the properties of radius, tangent,
chord, arc, and sector in problem solving
5. Use units of appropriate size and type to measure angles, perimeter, area, surface area, and
volume in problem solving;
6. Find the circumference/perimeters and the area of triangles, parallelograms, trapezoids, and
circles;
7. Find the surface area and volume of selected prisms, pyramids, spheres and cylinders;

Functions:
1. Determine whether a relation represents a function; and evaluate the value of a function
2. Make connections between the graphical, tabular, verbal, and symbolic representations of the
function.
3. Find the sum, difference, product, quotient and composition of two functions and determine
their domain.
4. Determine the interval where a function is increasing, decreasing, or constant
5. Sketch the graph of a polynomial function using properties of end behavior, zeros, and
multiplicity of zeros
6. Write the equation for a polynomial function given its graph or a set of data
7. Graph rational functions, including those containing vertical asymptote, horizontal asymptotes,
an oblique asymptote and “holes”.
8. Graph piecewise-defined functions.
9. Identify a function as odd, even, or neither;
10. Know the meaning of inverse functions and find inverse of a function algebraically and
graphically;
11. Recognize the graph of most common functions of type f (constant function) f(x) = x, (identity
function), quadratic function), f(x) = x3 (cubic function), (square root function), reciprocal
function), and (absolute value function).
12. Graph functions using transformations such as vertical and horizontal shift; reflection; rotation,
compression and stretches.
13. Know the definition (logarithmic function as the inverse of an exponential function) and
properties of exponential and logarithmic functions and simplify the expressions involving
logarithms and exponent using their properties/ laws
14. Solve logarithmic and exponential equations using their properties
15. Use exponential growth and decay formulas to solve application problems
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16. Solve real world problems involving compound interest

Trigonometry
1. Convert between radian measure and degree measure
2. Find arc length ( and area of a sector
3. Know the unit circle definition as well as right triangle definition of six trigonometric functions
4. Find the sine, cosine and tangent values of special angles (multiples of π/6, π/4, or , )
5. Solve right triangles using six trig functions
6. Simplify trig expressions using the standard formulas and identities: Pythagorean formulas,
quotient and reciprocal formulas, complementary angle formulas, sums and differences
formulas, and double- and half-angle formulas.
7. Given the value of one of the six trigonometric functions at an angle and the quadrant in which
this angle lies, find trigonometric values of the six trigonometric functions
8. Solve application problems involving navigation and surveying, including angles of elevation and
depression
9. Solve triangle using Law of Sine and Law of Cosine
10. Given the graph, identify the equation of trig function; and given the trig function, sketch the
graph of trig functions identifying their period, amplitude, domain, range and zeros
11. Graph transformation of trig functions
12. Solve trigonometric equations (linear and quadratic).
13. Evaluate expressions involving inverse trigonometric functions.
14. Find exact values of inverse trig functions for the corresponding angles (at multiples of π/6, π/4,
or , )
15. Sketch the graphs of the inverse trig functions and state the domain and range.
Study Resources:
Please check the following ministry web site for the most current list of recommended learning
resources in the Mathematics 10- 12 Grade Collections:
www.bced.gov.bc.ca/irp_resources/lr/resource/gradcoll.htm



Blitzer, Robert F. Precalculus, 4th Prentice Hall, Inc., 2009. Print. ISBN-13:978-0321559845
Foundations of Mathematics 11: Student Resource and eBook CD–ROM. Nelson
Education.[ISBN: 9780176352684]

Pre-calculus 11: Student Resource, McGraw-Hill Ryerson. [ISBN: 9780070738737]
Foundations of Mathematics 12 Student Resource andeBook online. Nelson Education. [ISBN:

9780176504229]
Pre-calculus 12: Student Resource. McGraw-Hill Ryerson. [ISBN: 0070738726]
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