# Maths Syllabus Chapter 1

## Chapter 1-1

Youtube Videos on Drawing Graphs/Solving Systems of Equations:

Drawing Simple Graphs

Solving Simultaneous Equations Algebraically

Graphing Linear Equations

Solving Simultaneous Equations Graphically

### Questions:

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

### Harder Questions: Use a dictionary or translator for any words you don't know.

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?

## Chapter 1-2

Youtube Videos on Solving Inequalities Graphically:

Graphing Systems of linear inequalities

Graphing 3 or more linear inequalities

### Chapter 1-2 Questions:

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

### Harder Questions: Use a dictionary or translator for any words you don't know.

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

## Chapter 1-3

How to do linear programming

Linear Programming word problems

## Chapter 1-4

### Chapter 1-4 Questions:

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

### Harder Questions: Use a dictionary or translator for any words you don't know.

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.

## Chapter 1-5 and 1-6

Multiplying Matrices

Multiplying Other Matrices

### Chapter 1-5 and 1-6 Questions:

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

## Chapter 1-7

2x2 Matrices

3x3 Matrices

Area of a triangle

### Chapter 1-7 Questions:

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)

## Chapter 1-8

Youtube Videos on Solving Systems of Equations using Cramer's Rule:

2x2 Matrices

3x3 Matrices

### Chapter 1-8 Questions:

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

## Chapter 1-9

Youtube Videos on Inverses of Matrices:

Inverse of a 2x2 Matrix

Solving Simultaneous Equations using the Inverse of a matrix

### Chapter 1-9 Questions:

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

# Maths Syllabus Chapter 2

## Chapter 2-1

How to graph a quadratic equation

### Chapter 2-1 Questions:

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

## Chapter 2-2

### Chapter 2-2 Questions:

Questions 5, 7, 9, 11 and 14-19 on page 109

Questions 30 and 38 on page 110

## Chapter 2-3

Solving a quadratic equation by factoring

### Chapter 2-3 Questions:

Questions 4, 8, 10, 14, 19, 33, 34, 36 and 41 on page 118

Questions 55, 66 and 69 on page 119

## Chapter 2-4

Basics of Complex Numbers

Dividing Complex Numbers

### Chapter 2-4 Questions:

Questions 2, 7, 9, 13, 16 and 37 on page 126

### Harder Questions:

Questions 55, 58 and 67 on page 127

## Chapter 2-5

Basics of Completing the Square

Slightly harder completing the square (when a is larger than 1)

Completing the Square with complex roots

### Chapter 2-5 Questions:

Questions 14, 21, 31, 37, 41 and 50 on page 136

## Chapter 2-6

Solving Equations using the quadratic formula

### Chapter 2-6 Questions:

Questions 3, 8, 10, 12 on page 145

Questions 41 and 42 on page 147

## Chapter 2-7

Converting a quadratic equation to vertex form

### Chapter 2-7 Questions:

Questions 8, 15, 19, 22, 27, 37, and 40 on pages 154-155

## Chapter 2-8

### Chapter 2-8 Questions:

Questions 1, 5, 9 and 11 on page 161

Questions 27, 33 and 55 on pages 162-163

# Maths Syllabus Chapter 3

## Chapter 3-1

### Chapter 3-1 Questions:

Questions 2, 4, 6, 11, 12 and 14 on page 183

Questions 52, 57 and 62 on page 184

## Chapter 3-2

Dividing Polynomials by Long Division

Dividing Polynomials by Synthetic Division

### Chapter 3-2 Questions:

Questions 12, 14, 17, 19, 22, 25, 29 on page 191

## Chapter 3-3

Introduction to polynomial functions

### Chapter 3-3 Questions:

Questions 15, 17, 20, 24, 33, 34, 36 and 39 on pages 200-201

## Chapter 3-4

Graphing polynomial functions

### Chapter 3-4 Questions:

Questions 16, 19, 24, 29 and 36 on page 209

## Chapter 3-5

Youtube Videos on Factoring Polynomial Equations:

Factoring polynomial equations

### Chapter 3-5 Questions:

Questions 21, 24, 28, 32, 34, 38, 43 and 57 on page 220-221

## Chapter 3-6

Youtube Videos on Solving Polynomial Equations:

Solving polynomial functions by synthetic division

### Chapter 3-6 Questions:

Questions 11, 13, 16, 18, 25, 27, 29 and 33 on page 229-230

## Chapter 3-7

### Chapter 3-7 Questions:

Questions 17, 24, 26, 29, 31, 35, 40, 43 and 53 on page 237-238

## Chapter 3-8

Youtube Videos on Finding Roots and Zeros:

Rational Zero Theorem

# Maths Syllabus Chapter 4

## Chapter 4-1

Youtube Videos on Operations of Functions:

Operations of Functions

### Chapter 4-1 Questions:

Questions 11, 13, 15, 18, 31, 42 and 48 on page 261-262

## Chapter 4-2

Youtube Videos on Inverse Functions and Relations:

Inverse Functions and Relations

### Chapter 4-2 Questions:

Questions 10, 18, 23, 32, 35 and 40 on page 268-269

## Chapter 4-3

Youtube Videos on Square Root Functions:

Square root Functions

### Chapter 4-3 Questions:

Questions 14, 18, 22, 24, 26, 29, 36 and 45 on page 275-277

## Chapter 4-4

### Chapter 4-4 Questions:

Questions 12, 17, 21, 25, 27, 33, 42, 43, 44, 46 and 55 on page 282

## Chapter 4-5

### Chapter 4-5 Questions:

Questions 18, 20, 23, 27, 32, 34, 35, 36, 40, 41, 43 and 54 on page 291-292

## Chapter 4-6

Rational Exponents

### Chapter 4-6 Questions:

Questions 16, 19, 23, 25, 27, 28, 31, 34, 40, 42 and 52 on page 298-299