Youtube Videos on Drawing Graphs/Solving Systems of Equations:
Solving Simultaneous Equations Algebraically
Solving Simultaneous Equations Graphically
1. Draw the graph: y = x + 2
2. Draw the graph: y = 3x + 1
3. Draw the graph: 2y = 3x + 2
4. Draw the graph: 6y = 12 - 2x
5. Draw the graph: 4x = 12 - 3y
6. Draw the graph: 2y = -x + 4
7. Draw the graph: 3y = -2x - 6
8. Draw the graph: 3x - 2y = 4
9. Draw the graph: 2x - 1 - y = 0
10. Draw the graph: 3x + 2y - 7 = 0
11. Solve by substitution: x + y = 5 and x + 4y = 11
12. Solve by substitution: 3x + 4y = 23 and x = y - 4
13. Solve by substitution: 6x - 7y = 3 and 2x = 2(y + 1)
14. Solve by substitution: 11x + 4y = 88 and 3 + 2y = 6x + 1
15. Solve by elimination: 3x + 5y = 53 and 2x + 3y = 32
16. Solve by elimination: 28x + 5y = 89 and 7x + 3y = 24
17. Solve graphically: 2x + y = 4 and 3x - 2y = 6
18. Solve graphically: 3a + 4b = 12 and 5a - 2b = 7
19. Solve graphically: 300x + 500y = 1100 and 50x - 75y = 25 (clue: can these be simplified?)
20. Solve graphically: 3 sweets + 7 chocolates = AED 52 and 5 sweets + 2 chocolates = AED 48
1. Interactive Student Guide, page 4 - example 1.
2. Interactive Student Guide, page 5 - example 2.
3. Interactive Student Guide, page 7 - question 3.
4. Interactive Student Guide, page 7 - question 5.
5. Fatima's age and Ghala's age combined is 35. The sum of three times Ghala's age and four times Fatima's age is 120. How old are Fatima and Ghala?
Youtube Videos on Solving Inequalities Graphically:
Graphing Systems of linear inequalities
Graphing 3 or more linear inequalities
1. Shade on a graph: 2x + y < 4 and 3x - 2y < 6
2. Shade on a graph: 3a + 4b > 12 and 5a - 2b > 7
3. Shade on a graph: 2x - y < 4 and 3x + 2y > -6
4. Shade on a graph: 3x + 2y < 6 and y < 4x
1. Interactive Student Guide, page 8 - example 1.
2. Interactive Student Guide, page 9 - example 3.
3. Interactive Student Guide, page 11 - question 6.
4. Shade the feasible region on a graph for: 15x + 20y < 60, 10x + 5y < 30, x > 0, y > 0 and y < 2
Youtube Videos on Linear Programming:
Linear Programming word problems
1. Solve the system of equations: 3x - y + 2z = 11, x + 2y - z = 4 and -2 + y + 3z = 11
2. Solve the system of equations: 7x - 4y - 2z = 7, 8x - 2y - 8z = 1 and x + 2y - 6z = -6
3. Solve the system of equations: 2x + y = - 2 - 3z, x - y = z - 3 and 3(x + z) = 2(y - 6)
4. Solve the system of equations: x = 6 - y - z, 2x + 3z = 9 + y and 2(y + z) = x + 9
1. Interactive Student Guide, page 16 - example 1a.
2. Interactive Student Guide, page 18 - example 3b.
3. Interactive Student Guide, page 19 - question 1.
4. 12 apples, 6 bananas and 4 coconuts cost AED23, 12 bananas and 7 coconuts cost AED20. Finally, 23 apples, 7 bananas and 6 coconuts cost AED38.5 exactly. Determine the cost of 2 apples, 3 bananas and 1 coconut.
Youtube Videos on Matrix Operations:
Mathematics Grade 10A Book: p51, questions 2 to 11 and questions 22 to 27
Mathematics Grade 10A Book: p59, questions 4 to 11 and p60 questions 29 and 34
Youtube Videos on Finding Determinants:
Mathematics Grade 10A Book: p65, questions 1A to 2B
1. Find the area of the triangle with ordered pairs: (3, 7), (2, 4) and (-4, 7)
2. Find the area of the triangle given by co-ordinates: (-5, -4), (2, 9) and (13, -9)
Youtube Videos on Solving Systems of Equations using Cramer's Rule:
1. Solve using Cramer's Rule: 6x - 7y = 3 and 2x = 2(y + 1)
2. Solve using Cramer's Rule: 11x + 4y = 88 and 3 + 2y = 6x + 1
3. Solve using Cramer's Rule: 3x + 5y = 53 and 2x + 3y = 32
4. Solve using Cramer's Rule: 28x + 5y = 89 and 7x + 3y = 24
5. Solve the system of equations using Cramer's Rule: 3x - y + 2z = 11, x + 2y - z = 4 and -2 + y + 3z = 11
6. Solve the system of equations using Cramer's Rule: 7x - 4y - 2z = 7, 8x - 2y - 8z = 1 and x + 2y - 6z = -6
7. Solve the system of equations using Cramer's Rule: 2x + y = - 2 - 3z, x - y = z - 3 and 3(x + z) = 2(y - 6)
8. Solve the system of equations using Cramer's Rule: x = 6 - y - z, 2x + 3z = 9 + y and 2(y + z) = x + 9
Youtube Videos on Inverses of Matrices:
Solving Simultaneous Equations using the Inverse of a matrix
1. Solve by finding the inverse matrix: 6x - 7y = 3 and 2x - 2y = 2
2. Solve by finding the inverse matrix: 11x + 4y = 88 and 3 + 2y = 6x + 1
Youtube Videos on Graphing Quadratic Equations:
How to graph a quadratic equation
1. Draw a graph of each of the following functions and find their a) y-intercept, b) vertex co-ordinates, c) equations of the axis of symmetries, d) whether it has a minimum or maximum value:
a) f(x) = x² + 6x - 2
b) f(x) = 2x² - 8x + 4
c) f(x) = 4x² - 24x + 11. Also give the domain and range for this function.
Questions 11, 32, 56 and 57 on page 100-101
Youtube Videos on Solving Quadratic Equations:
Questions 5, 7, 9, 11 and 14-19 on page 109
Questions 30 and 38 on page 110
Youtube Videos on Solving Quadratic Equations by Factoring:
Solving a quadratic equation by factoring
Questions 4, 8, 10, 14, 19, 33, 34, 36 and 41 on page 118
Questions 55, 66 and 69 on page 119
Youtube Videos on Complex Numbers:
Questions 2, 7, 9, 13, 16 and 37 on page 126
Questions 55, 58 and 67 on page 127
Youtube Videos on Complex Numbers:
Basics of Completing the Square
Slightly harder completing the square (when a is larger than 1)
Completing the Square with complex roots
Questions 14, 21, 31, 37, 41 and 50 on page 136
Youtube Videos on The quadratic formula:
Solving Equations using the quadratic formula
Questions 3, 8, 10, 12 on page 145
Questions 41 and 42 on page 147
Youtube Videos on Transformations of Quadratic Graphs:
Converting a quadratic equation to vertex form
Transformations of Quadratic Functions
Questions 8, 15, 19, 22, 27, 37, and 40 on pages 154-155
Youtube Videos on Quadratic Inequalities:
Solving Quadratic Inequalities
Questions 1, 5, 9 and 11 on page 161
Questions 27, 33 and 55 on pages 162-163
Youtube Videos on Polynomial Operations:
Adding and Subtracting Polynomials
Questions 2, 4, 6, 11, 12 and 14 on page 183
Questions 52, 57 and 62 on page 184
Youtube Videos on Dividing Polynomials:
Dividing Polynomials by Long Division
Dividing Polynomials by Synthetic Division
Questions 12, 14, 17, 19, 22, 25, 29 on page 191
Youtube Videos on Polynomial Functions:
Introduction to polynomial functions
Questions 15, 17, 20, 24, 33, 34, 36 and 39 on pages 200-201
Youtube Videos on Polynomial Functions:
Questions 16, 19, 24, 29 and 36 on page 209
Youtube Videos on Factoring Polynomial Equations:
Factoring polynomial equations
Questions 21, 24, 28, 32, 34, 38, 43 and 57 on page 220-221
Youtube Videos on Solving Polynomial Equations:
Solving polynomial functions by synthetic division
Questions 11, 13, 16, 18, 25, 27, 29 and 33 on page 229-230
Questions 17, 24, 26, 29, 31, 35, 40, 43 and 53 on page 237-238
Youtube Videos on Finding Roots and Zeros:
Youtube Videos on Operations of Functions:
Questions 11, 13, 15, 18, 31, 42 and 48 on page 261-262
Youtube Videos on Inverse Functions and Relations:
Inverse Functions and Relations
Questions 10, 18, 23, 32, 35 and 40 on page 268-269
Youtube Videos on Square Root Functions:
Questions 14, 18, 22, 24, 26, 29, 36 and 45 on page 275-277
Youtube Videos on Nth roots:
Questions 12, 17, 21, 25, 27, 33, 42, 43, 44, 46 and 55 on page 282
Youtube Videos on Radical Expressions Operations:
Questions 18, 20, 23, 27, 32, 34, 35, 36, 40, 41, 43 and 54 on page 291-292
Youtube Videos on Rational Exponents:
Questions 16, 19, 23, 25, 27, 28, 31, 34, 40, 42 and 52 on page 298-299
Youtube Videos on Solving Radical Equations:
Questions 23, 25, 28, 32, 35, 38, 41, 45, 56, 48, 57 and 62 on page 305