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 Youtube Playlist

Click here for a concise playlist on BC Math 10 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.

BC Math 10 Course Topics

• Topic 1: Prime Factorization
• Topic 2: Algebra Review
• Topic 3: Operations on Powers
• Topic 4: Multiplying Polynomials
• Topic 5: Polynomial Factoring
• Topic 6: Primary Trigonometric Ratios
• Topic 7: Linear Functions
• Topic 8: Arithmetic Sequences (and series)
• Topic 9: Functions and Relations
• Topic 10: Systems of Linear Equations
• Topic 11: Types of Income
• Final Exam Review
  • Core final review video playlist
  • Course review video playlist

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BC Math 10 Topic 1: Prime Factorization

Understanding prime factorization trees will help you understand the math topic “entire vs. mixed radicals.” Finding the LCM of two or more numbers will help you add and subtract fractions. Identifying the GCF is the first step in factoring.

• Expressing prime factorization of a number using powers
• Identifying the factors of a number
• Includes greatest common factor (GCF) and least common multiple (LCM)
• Strategies include using factor trees and factor pairs

1. Enrichment: List the first four prime numbers
   Solution
   2, 3, 5, 7
2. Find the prime factorization of 27000
   Solution
   2^3\times 3^3\times 5^3
3. What are the factors of 12?
   Solution
   1, 2, 3, 4, 6, 12
4. What are the prime factors of 24?
   Solution
   2, 3
5. Find the GCF and LCM of:
   1. 10 and 15
      Solution
      GCF 5, LCM 20
   2. 8, 12, and 20
      Solution
      GCF 4, LCM 120
   3. 6, 20, and 30
      Solution
      GCF 2, LCM 60
6. Your turn: Find the GCF and LCM of:
   15ab^2, 10a^3b^5, 25a^2b^7
   Solution
   GCF 5ab^2, LCM 150a^3b^7
7. Challenge:  Why do perfect squares have an odd number of factors?
   Solution
   The factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Here, there is an odd number of factors because the square root of the perfect square (in this case 6) does not have a pair.
   
   
   

BC Math 10 Topic 2: Algebra Review

Although algebra is not an explicit requirement of the BC Math 10 curriculum, this topic is included because it is an essential part of solving math problems.

1. Simplify 2x-5x
   Solution
   -3x
2. \frac{1}{2}x+\frac{x}{3}-x
   Solution
   -\frac{x}{6}
3. Solve 2x-1=x+3
   Solution
   4
4. \frac{x}{2}+3=3x-\frac{1}{3}
   Solution
   x=4/3
5. \frac{x}{5}=\frac{2}{3}
   Solution
   x=10/3
6. 5=\frac{x}{3}
   Solution
   x=15
7. -2=\frac{5}{k}
   Solution
   k=-5/2
8. \frac{4}{5}=\frac{3}{2x-1}
   Solution
   x=19/8
9. 2(x-5)=3(x+2)
   Solution
   x=-16
10. \frac{2}{3}(1-2x)=-\frac{3x+5}{2}
    Solution
    x=-19
11. \frac{1-\frac{2}{3}}{\frac{1}{2}+\frac{3}{4}}=1\div\frac{1}{x}
    Solution
    4/15

BC Math 10 Topic 3: Operations on Powers

Last year you learned about exponent laws with whole-number exponents. This year, in BC Math 10, you will learn about negative exponents. Next year, you will learn about fractional exponents.

• Positive and negative exponents
• Exponent laws
• Evaluation using order of operations
• Numerical and variable bases

1. Evaluate:
   1. 2^3
      Solution
      8
   2. (-5)^3
      Solution
      -125
   3. -3^2
      Solution
      -9
2. Evaluate:
   1. (-1)^{100}
      Solution
      1
   2. (-1)^{123}
      Solution
      -1
   3. -1^{666}
      Solution
      -1
3. Evaluate:
   1. -2(-2)^2
      Solution
      -8
   2. -2^2-(-2)^2
      Solution
      -8
4. Evaluate:
   1. 0^1
      Solution
      0
   2. 1^0
      Solution
      1
   3. \pi^0
      Solution
      1
   4. 0^0
      Solution
      Undefined
5. Evaluate:
   1. \left(\frac{2}{3}\right)^2
      Solution
      4/9
   2. 2^{-3}
      Solution
      1/8
   3. \left(\frac{3}{2}\right)^{-2}
      Solution
      4/9
6. Evaluate:
   1. -2(-2)^{-2}
      Solution
      -1/2
   2. 4(-2)^{-3}\div\frac{1}{2^{-2}}
      Solution
      -1/8
7. Simplify:
   1. a(2a^3\times 3a^2)
      Solution
      6a^6
   2. \frac{x(x^2)(x^5)}{x^4}
      Solution
      x^4
   3. (2x^3y^2)^3
      Solution
      8x^9y^6
8. Simplify:
   1. \left(\frac{4x^5}{2x^3}\right)^3
      Solution
      8x^6
   2. \left(\frac{3a}{9a^{-2}}\right)^2
      Solution
      \frac{a^6}{9}
   3. \left(\frac{5x^2yz^3}{25x^{-1}yz^3}\right)^{-3}
      Solution
      \frac{125y^6}{x^9z^9}

BC Math 10 Topic D: Multiplying Polynomials

Expanding polynomials is a BC Math 10 topic that is the opposite process of factoring. Multiplying polynomials and gathering like terms reliably is an important math skill. Visit this section directly at hunkim.com/10d

1. -3x(x-1)
   Solution
   -3x^2+3x
2. Your turn: -5x(x-5)
   Solution
   -5x^2+25x
3. 2x^2(2-3x+4x^2)
   Solution
   8x^4-6x^3+4x^2
4. Your turn: 3x^2(1-2x+7x^2)
   Solution
   21x^4-6x^3+3x^2
5. (x-3)(x-5)
   Solution
   x^2-8x+15
6. Your turn: (x+2)(x-7)
   Solution
   x^2-5x-14
7. (3x-2)(x-3)
   Solution
   3x^2-11x+6
8. Your turn: (2x-1)(x+4)
   Solution
   2x^2+7x-4
9. (2x-7)^2
   Solution
   4x^2-28x+49
10. Your turn: (11x-5)^2
    Solution
    121x^2-110x+25
11. -3(5-2x)^2
    Solution
    -12x^2+60x-75
12. Your turn: -2(3x-1)^2
    Solution
    -18x^2+12x-2
13. 2(3x-1)(x-2)
    Solution
    6x^2-14x+4
14. Your turn: -3(x+1)(2x-5)
    Solution
    -6x^2+9x+15
15. (x+2)(-2)(x-4)
    Solution
    -2x^2+4x+16
16. Your turn: (2x-1)(-3)(x+1)
    Solution
    -6x^2-3x+3
17. (x-1)(x^2+x+1)
    Solution
    x^3-1
18. Your turn: (a+b)(a^2-ab+b^2)
    Solution
    a^3+b^3
19. (x^2+x+1)(1-x-x^2)
    Solution
    -x^4-2x^3-x^2+1
20. Your turn: (a^2+a-1)(a^2-a+1)
    Solution
    a^4-a^2+2a-1
21. Expand (x-2)^2(x+1)^2
    Solution
    x^4-2x^3-3x^2+4x+4
22. Your turn: Expand (2x-1)^2(3x+1)^2
    Solution
    36x^4-12x^3-11x^2+2x+1
23. (3x-3y)^3
    Solution
    27x^3-81x^2y+81xy^2-27y^3
24. Your turn: (2y+3z)^3
    Solution
    8y^3+36y^2z+54yz^2+27z^3
25. (2x-1)^4
    Solution
    16x^4-32x^3+24x^2-8x+1
26. Your turn: (3a+1)^4
    Solution
    81a^4+108a^3+54a^2+12a+1
27. Represent the product of the following factors using algebra tiles: (2x-1)(x+2)
28. Your turn: Represent the product of the following factors using algebra tiles: (3x+2)(x-1)
29. The length of an edge of a cube is x-1. Find the area of the cube.
    Solution
    6x^2-12x+6 units squared
30. Your turn: Find the surface area of the top of the box only in the form ax^2+bx+c
    
    Solution
    x^2+3x+2 units squared
31. Find the area of the shaded region below:
    
    Solution
    2x^2+14x+30 units squared
32. Your turn: Find the area of the shaded region below:
    
    Solution
    10x^2+9x-10 units squared
33. Find the area of the shaded region below:
    
    Solution
    36x^2-9\pi x units squared
34. Your turn: Find the area of the shaded region below:
    
    Solution
    28x^2-32\pi x^2 units squared
35. The diameter of a circle is 2x+4
    1. Area in expanded form?
       Solution
       \pi x^2+4\pi x+4\pi units squared
    2. Circumference?
       Solution
       2\pi x+4\pi
36. Your turn: The diameter of a circle is 6x+12
    1. Area in expanded form?
       Solution
       9\pi x^2+36\pi x+36\pi units squared
    2. Circumference?
       Solution
       6 \pi x+12\pi
37. See cylinder below:
    
    1. Volume in expanded form?
       Solution
       \pi x^3+\pi x^2 units cubed
    2. Total surface area including the bottom (in expanded form)?
       Solution
       4\pi x^2+2\pi x units squared
38. Your turn:
    
    1. Volume?
       Solution
       400 \pi x^2 units cubed
    2. Area?
       Solution
       8\pi x^2+400\pi x units squared
39. Challenge: Find the area of the shaded region
    
    Solution
    3-\frac{9\pi}{16} units squared

BC Math 10 Topic E: Polynomial Factoring

Learning how to factor is the first step in learning about quadratic functions.  Try to master factoring in this BC Math 10 course because you will continue to factor in future grades.  Visit this section directly at hunkim.com/10e

• Greatest common factor of a polynomial
• Simpler cases involving trinomials y=x^2+bx+c and difference of squares

Factor fully:

1. 15x^5-10x^7
   Solution
   5x^5(3-2x^2)
2. Your turn: 30x^3-20x^2
   Solution
   10x^2(3x-2)
3. x^2-25
   Solution
   (x+5)(x-5)
4. Your turn: t^2-9
   Solution
   (t+3)(t-3)
5. 9a^2-25
   Solution
   (3a+5)(3a-5)
6. Your turn: 100p^2-49
   Solution
   (10p+7)(10p-7)
7. 25a^6-y^2 z^{10}
   Solution
   (5a^3+yz^5)(5a^3-yz^5)
8. Your turn: 49a^4b^6-9z^8
   Solution
   (7a^2b^3+3z^4)(7a^2b^3-3z^4)
9. a^2+9
   Solution
   Cannot factor or (a+3i)(a-3i)
10. Your turn: x^2+4
    Solution
    Cannot factor
11. 5x^2-45
    Solution
    5(x+3)(x-3)
12. Your turn: 3a^2-12
    Solution
    3(a+2)(a-2)
13. x^2-8x+15
    Solution
    (x-3)(x-5)
14. Your turn: x^2+2x-24
    Solution
    (x+6)(x-4)
15. x^2-6x-72
    Solution
    (x+6)(x-12)
16. Your turn: x^2+4x-96
    Solution
    (x-8)(x+12)
17. 3x^2-12x+12
    Solution
    3(x-2)^2
18. Your turn: 2x^2+12x+18
    Solution
    2(x+3)^2
19. 2x^2+7x-4
    Solution
    (2x-1)(x+4)
20. Your turn: 5x^2-32x+12
    Solution
    (5x-2)(x-6)
21. 4x^2-35x+24
    Solution
    (4x-3)(x-8)
22. Your turn: 6x^2+31x-30
    Solution
    (6x-5)(x+6)
23. 30x^2+52x-48
    Solution
    2(3x-2)(5x+12)
24. Your turn: 36x^2+194x-22
    Solution
    2(9x-1)(2x+11)
25. -9(x+1)+x^2(x+1)
    Solution
    (x+1)(x+3)(x-3)
26. Your turn: a^2(x-2)-4(x-2)
    Solution
    (x-2)(a+2)(a-2)
27. a^2(3x-1)+9(1-3x)
    Solution
    (3x-1)(a+3)(a-3)
28. Your turn: w^2(2w-7)+25(7-2w)
    Solution
    (2w-7)(w+5)(w-5)
29. 5x^3-10x^2+3x-6
    Solution
    (x-2)(5x^2+3)
30. Your turn: 3x^3+3x^2+4x+4
    Solution
    (x+1)(3x^2+4)
31. 112ab-16a+128a^2-14b
    Solution
    2(8a-1)(7b+8a)
32. Your turn: 60x^2+36xy-45x-27y
    Solution
    3(4x-3)(5x+3y)
33. -4x^4y+12x^3+x^2y-3x
    Solution
    x(2x+1)(2x-1)(3-xy)
34. Your turn: -9a^4b+9a^3+4a^2b-4a
    Solution
    a(3a-2)(3a+2)(1-ab)
35. Challenge:
    1. What is the area of the shaded region below in fully factored form?
       
       Solution
       4\pi (x+1) units squared
    2. Factor 2(\sin\theta)^2-5\sin\theta-3
       Solution
       (2\sin\theta+1)(\sin\theta-3)
    3. Factor e^{2x}-25 (e\approx 2.718 is a special constant)
       Solution
       (e^x+5)(e^x-5)
    4. x^2+kx+8. Find the possible values of k such that this trinomial can be factored.
       Solution
       \pm 9, \pm 6
    5. Factor x^3+1
       Solution
       (x+1)(x^2-x+1)
    6. Factor 8a^6-b^3
       Solution
       (2a^2-b)(4a^4+2a^2b+b^2)
    7. Factor x^3-3x^2+4
       Solution
       (x-2)^2(x+1)
    8. Factor x^n-y^n
       Solution
       When n is odd, notice that x-y is a factor and the counting down and up pattern with the exponents. Ex. x^7-y^7=(x-y)(x^6+x^5y+x^4y^2+x^3y^3+x^2y^4+xy^5+y^6)
       
       
       
       

BC Math 10 Topic F:
Primary Trigonometric Ratios

Visit this page directly at hunkim.com/10f

• 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
   

BC Math 10 Topic G: Linear Functions

Visit the page directly at hunkim.com/10g

• Slope: positive, negative, zero, and undefined
• Types of equations and lines (point-slope, slope-intercept, and general)
• Equations of parallel and perpendicular lines
• Equations of horizontal and vertical lines
• Connections between representations: graphs, tables, equations

1. Slope = \frac{\text{rise}}{\text{?}}=\frac{y_2-y_1}{?}
   

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

Visit this page directly at hunkim.com/10h

• 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

Visit this page directly at hunkim.com/10j

• 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

Visit this page directly at hunkim.com/10k

• 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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