BC Math 10

bc math 10
Here you will find a concise collection of math practice problems aligned with the BC Math 10 curriculum. Visit this page directly at hunkim.com/10

BC Math 10 Resources

Topic 1: Prime Factorization

Grasping the concept of prime factorization trees enhances your comprehension of the mathematical topic “entire vs. mixed radicals.” Determining the least common multiple (LCM) of two or more numbers simplifies the process of adding and subtracting fractions. Recognizing the greatest common factor (GCF) serves as the initial step in mastering factoring techniques.

Topic 2: Review of Algebra, Equations, and BEDMAS

While algebra is not a formal requirement of the BC Math 10 curriculum, it is included because it provides fundamental skills essential for solving mathematical problems. Visit hunkim.com /10 for more BC Math resources.

Topic 3: Operations on Powers

Last year, you explored the fundamentals of exponent laws using whole-number exponents. This year, in BC Math 10, you’ll expand your understanding to include negative exponents. Looking ahead to next year, you’ll dive into the world of fractional exponents, building on the skills you’ve already developed.  

Topic 4: Multiplying Polynomials

Expanding polynomials, a key topic in BC Math 10, involves the reverse process of factoring. Mastering the ability to multiply polynomials and combine like terms accurately is a fundamental and valuable mathematical skill.

BC Math 10 Topic 5: Polynomial Factoring

Mastering the skill of factoring is a crucial first step in understanding quadratic functions. In this BC Math 10 course, strive to perfect your factoring abilities, as they will remain a vital tool in your mathematical journey through future grades.

BC Math 10 Topic F:
Primary Trigonometric Ratios

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  • Sine, cosine, and tangent ratios
  • Right-triangle problems: determining missing sides and/or angles using trigonometric ratios and the Pythagorean theorem
  • Contexts involving direct and indirect measurement
  1. Explain the acronym SOH CAH TOA

Linear Functions

Linear functions are a cornerstone of the BC Math 10 curriculum. While you may already be familiar with foundational concepts like points, slopes, and intercepts from earlier math courses, this year you’ll gain a comprehensive understanding of lines as a mathematical concept. Later in the course, you’ll also explore the importance of two lines intersecting, deepening your grasp of this essential topic.

BC Math 10 Topic H: Arithmetic Sequences (and Series)

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  • Applying formal language (common difference, first term, general term) to increasing and decreasing linear patterns
  • Connecting to linear relations
  • Extension: exploring arithmetic series
  1. 2, 5, 8, 11, ...
    Video
    1. Find the 100th number using your knowledge of lines
      Solution
      299

    2. Find the common difference d
      Solution
      3

    3. Find t_1
      Solution
      2

    4. Find the 100th number using the arithmetic sequence formula: t_n=t_1+(n-1)d
      Solution
      299

  2. Explain why the arithmetic sequence formula used above works
    Solution
    The value of an unknown term is based on the initial term t_1.  We repeatedly add or subtract the common difference d, (n-1) times.

  3. \frac{1}{2} and \frac{3}{5} are the first two terms of an arithmetic sequence. Find the 4th term.

BC Math 10 Topic 9: Functions and Relations

  • Communicating domain and range in both situational and non-situational contexts
  • Connecting graphs and context
  • Understanding the meaning of a function
  • Identifying whether a relation is a function
  • Using function notation
  • Connecting data, graphs, and situations
  1. Domain and range?
    1. f(x)=3x+2
      Solution
      Domain: x\in\mathbb{R}
      Range: y\in\mathbb{R}
    2. f(x)=5
      Solution
      Domain: x\in\mathbb{R}
      Range: y=5
    3. x=3
      Solution
      Domain: x=3
      Range: y\in\mathbb{R}
  2. f(x)=2x+3, x\geq 1
    1. Domain?
      Solution
      x\geq 1 or [1,\infty)
    2. Range?
      Solution
      y\geq 5 or [5,\infty)
    3. Graph this ray on Desmos using curly brace notation: y=2x+3\{x\geq 1\}
      Solution
    4. Evaluate f(2)
      Solution
      7
  3. Write in interval notation and as a number line:
    1. y<3
    2. 2\leq x<4
  4. Is the following graph a function?
    1. See below:

    2. See below:

    3. See below:

    4. See below:

    5. See below:

    6. See below:

    7. See below:

    8. See below:

  5. Evaluate f(-3) given:
    1. f(x)=x^2
    2. f(x)=x^2-2x
    3. Challenge: f(x)=3x^3-\frac{2^x}{5x}
  6. Money is a function of time (hours): M(t)=50t+100
    1. How much does this plumber charge for just “showing up”?
    2. How much does this plumber charge for working 8 hours? 
    3. How long does this plumber need to work to earn $400?
    4. In the context of this question, what is the domain?
    5. A different plumber’s earning is modelled by E(t)=70t. This plumber does not charge a fee for showing up. When does E(t) surpass M(t)?
  7. V(t)=100-20t models the volume of gas (L) as a function of time.
    1. Sketch this function and label the axes.
    2. What is the meaning of the intercepts?
    3. What is the meaning of the slope of this function?
  8. Challenge: See f(x) below:
    1. Domain?
    2. Range?
  9. Challenge: Given f(x)=x^2, simplify \frac{f(x+h)-f(x)}{(x+h)-x}

BC Math 10 Topic J:
Systems of Linear Equations

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  • Solving graphically
  • Solving algebraically by inspection, substitution, elimination
  • Connecting ordered pair with meaning of an algebraic solution
  • Solving problems in situational contexts
  1. x+2y=13 and 3x-y=-11
    Is (-1,7) a point of intersection?
    Solution
    No

  2. 2x-4=4y and x+y=11
    Is (8,3) a point of intersection?
    Solution
    Yes

  3. x+y=2 and y=3
    1. Solve by graphing

BC Math 10 Topic K: Types of Income

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  • Types of income
  • Income tax and other deductions
  1. What’s the difference between being paid a salary vs. by hourly wage?
    Solution
    Salary: paid a fixed amount in a year (regardless of “overtime” work). Hourly wage: paid per hour of work

  2. You work 8 hours a day, 5 days a week, and make $20 per hour.
    1. How much will your gross pay be this month (assume 4 weeks)?
      Solution
      $3200

    2. Now assume your work 10 hours a day.  In BC you are paid 1.5 times your pay if your work beyond 8 hours.  How much will your gross pay be this month? Assume that there are 4 weeks in a month.
      Solution
      $4400

  3. Your net income is less than your gross income because of which of the following?
    • Income Tax (paid to the government at both the Federal and Provincial levels)
    • Canada Pension Plan (CPP)
    • Employment Insurance (EI)
    • All of the above
      Solution
      All of the above

  4. In BC, what percentage of your net income is being deducted if your annual income is:
    1. $40,000
      Solution
      25%

    2. $80,000
      Solution
      27.5%

    3. $160,000
      Solution
      32.6%

  5. If you rent out your basement suite, can you deduct a portion of your utility bills to reduce your taxes?
    Solution
    Yes

  6. As a car salesperson how much would you have to sell to match (and possibly surpass) a $60,000 annual salary if you earn $20,000 plus 5% on the sale of each car you sell?
    Solution
    $800 000

  7. As a realtor, suppose you earn 3% of the value of each home you sell.
    1. Approximately how many homes do you need to sell each year to gross $100,000 each year?
      Solution
      3.\bar{3} million in sales. About 3 one million dollar homes

    2. When can a realtor expect more customers?  At the beginning or end of their career?
      Solution
      At the end

  8. Suppose you are a police officer or nurse working a 12-hour shift.  You are needed to do a double shift and work for 24 hours.  In BC you are paid double time (twice the regular hourly wage) if you work beyond 12 hours.  Suppose you are paid $40 per hour.  How much do you gross for working 24 hours straight?
    Solution
    $1440

  9. True or False:
    1. If you show up for work as scheduled but are sent home because you are no longer needed you must be paid a for a minimum number of hours of work.
      Solution
      True

    2. In BC you must have a minimum of 8 hours of rest between shifts.
      Solution
      True

    3. Whether you’re 9 or 90, age has no effect on your requirement to file a tax return.
      Solution
      True

    4. Keeping your receipts is important because tax payers can receive a number of tax refunds after filing their annual taxes.
      Solution
      True

  10. There are 3 types of income.  Define:
    1. Active income
      Solution
      You actively work to earn money

    2. Passive income
      Solution
      You earn money with little to no effort for it to keep coming

    3. Portfolio income
      Solution
      Money that comes from interest on your investments

  11. Explain the following types of Youtube income revenue streams:
    Video link: https://www.youtube.com/watch?v=0DnKKn2IG2k
    1. Adsense
      Solution
      Advertisements on your Youtube videos or website

    2. Product sales / merchandise



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