Work through the following math practice problems aligned with the BC Pre-Calculus 11 curriculum. Visit this page directly at hunkim.com/11
BC Pre-Calculus 11 Youtube Playlist
Click here for a concise playlist on BC Pre-Calculus 11 practice problems. Each math video is about 5 minutes long and can be used as lesson examples or for reviewing the course. Subscribe to the channel if you find these videos useful!
Pre-Calculus 11 Topics
- Types of Numbers – hunkim.com/11a
- Powers – hunkim.com/11b
- Radicals – hunkim.com/11c
- Trigonometry – hunkim.com/11trig
- Polynomial Factoring – hunkim.com/11e
- Quadratic Functions and Equations – hunkim.com/11f
- Linear and Quadratic Inequalities – hunkim.com/11g
- Rational Expressions – hunkim.com/11h
- Financial Literacy – hunkim.com/11i
Pre-Calculus 11 Topic A:
Types of Numbers
Types of Numbers is the first topic of the BC Pre-Calculus 11 curriculum. The symbol for integers \mathbb{Z} is based on the German word “Zahlen.” BC students do not have to worry about complex numbers but BC math students who are interested in studying in the US should learn that i=\sqrt{-1}.
- Real number classification
Pre-Calculus 11 Topic B: Powers
Powers is another topic in the BC Pre-Calculus 11 curriculum. Although you may have learned about exponent laws since Grade 9, this is the first year that BC math students fully learn the topic of powers which include negative exponents and fractional exponents.
- Positive and negative rational exponents
- Exponent laws
- Evaluation using order of operations
- Numerical and variable bases
Pre-Calculus 11 Topic C: Radicals
Radicals is a math topic that has a connection with exponents. A fractional exponent can be rewritten as a radical. This year in Pre-Calculus 11 we will focus on simplifying radicals and working with radical equations. Next year you will learn more about graphing and transforming radical functions.
- Simplifying radicals
- Ordering a set of irrational numbers
- Performing operations with radicals
- Solving simple (one radical only) equations algebraically and graphically
- Identifying domain restrictions and extraneous roots of radical equations
Pre-Calculus 11 Topic D: Trigonometry
Last year you learned about right-angle trigonometry: SOH CAH TOA. This year in Pre-Calculus 11 you will learn how to solve non right-angle triangles using the Sine Law and the Cosine Law. Do your best to understand this year’s trigonometry concepts because you will learn more about trigonometry next year. Visit hunkim.com/10 to review SOH CAH TOA Trigonometry.
- Use of sine and cosine laws to solve non-right triangles, including ambiguous cases
- Contextual and non-contextual problems
- Angles in standard position
- Degrees
- Special angles, as connected with the 30-60-90 and 45-45-90 triangles
- Unit circle
- Reference and co-terminal angles
- Terminal arm
- Trigonometric ratios
- Simple trigonometric equations
- Label the location of the four quadrants
Pre-Calculus 11 Topic E:
Polynomial Factoring
We continue factoring this year in Pre-Calculus 11 because factoring is an important part of quadratic functions and equations. This year we factor quadratics and next year we factor higher degree polynomials. By factoring, we reveal the roots of a polynomial which are also known as x-intercepts or solutions.
- Greatest common factor of a polynomial
- Trinomials of the form ax^2+bx+c
- Difference of squares of the form a^2x^2-b^2y^2
- May extend to a(f(x))^2+b(f(x))+c and a^2(f(x))^2-b^2(f(x))^2
- Factor 2x^2-4x
Pre-Calculus 11 Topic F:
Quadratic Functions and Equations
Quadratics is the largest math topic in Pre-Calculus 11. We can use our understanding of quadratics to determine the exact height of a basketball or find the optimal dimensions to maximize or minimize area.
- Identifying characteristics of graphs (including domain and range, intercepts, vertex, symmetry), multiple forms, function notation, extrema
- Exploring transformations
- Solving equations (ex. factoring, quadratic formula, completing the square, graphing, square root method)
- Connecting equation-solving strategies
- Connecting equations with functions
- Solving problems in context
- y=x^2
- Sketch and label three points
- Sketch and label three points
Pre-Calculus 11 Topic G:
Linear and Quadratic Inequalities
In Pre-Calculus 11, we extend our understanding of quadratics and lines by studying the meaning of the inequality symbol. You may be familiar with solving the equation x^2=9. But did you know that x^2<9 is equivalent to -3<x<3?
- single variable (ex. 3x-7\leq-4, x^2-5x+6>0)
- domain and range restrictions from problems in situational contexts
- sign analysis: identifying intervals where a function is positive, negative, or zero
- symbolic notation for inequality statements, including interval notation
- Sketch y=3x+2
Pre-Calculus 11 Topic H:
Rational Expressions
This year, in Pre-Calculus 11, we focus on simplifying rational expressions and introduce a few word problems. Next year you will better understand how to graph rational functions.
- Simplifying and applying operations to rational expressions
- Identifying non-permissible values
- Solving equations and identifying and extraneous roots
- What is a rational expression?
Pre-Calculus 11 Topic I:
Financial Literacy
As a young person, you have the power to be wealthy even with a minimum wage job. By living within (or below) your means, you will have money left over to invest. If you invest $6 a day (less than the cost of some Starbucks drinks) for 50 years (at an annual interest rate of 10%) your investment will grow to be more than $3 million!
- compound interest
- introduction to investments / loans with regular payments, using technology
- buying / leasing
- The simple interest formula is A=P(1+rt). If the annual interest rate is 10%, explain how a $1000 investment would grow over three years.
