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PURE MATHEMATICS 9709 A LEVEL

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Ариунгэрэл Бямбаа

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AS&A

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1.1.b Exercise	Урьдчилсан харагдац	00:15
1.1.с Quiz-The modulus function		00:15
1.2. Graphs of y=\|f(x)\| where f(x) is linear	Урьдчилсан харагдац	00:15
1.2 How to solve \|2x+3\|-\|x+4\|=6	Урьдчилсан харагдац	00:00
1.2 How to solve \|3x+9\|=\|2x+1\|	Урьдчилсан харагдац	00:00
1.2 Exercise- Modulus equation	Урьдчилсан харагдац	00:20
1.2 lesson-modulus equation	Урьдчилсан харагдац	00:30
1.3 lesson - graphs of the modulus function	Урьдчилсан харагдац	00:30
1.3 quiz - graphs of the modulus function		00:20
1.4 lesson- y=f(\|x\|) graphs	Урьдчилсан харагдац	00:30
1.4 Quiz- y=f(\|x\|) function graphs		00:20
1.5. lesson- solving modulus inequalities	Урьдчилсан харагдац	00:15
1.5 Quiz - solving modulus inequalities		00:15
1.6 Lesson Division of polynomials	Урьдчилсан харагдац	00:30
1.6 Quiz - Division of polynomials		00:10
1.7. The factor theorem	Урьдчилсан харагдац	00:30
1.7 lesson - The factor theorem	Урьдчилсан харагдац	00:00
1.7 Quiz - The factor theorem		00:20
1.8 lesson - Factor and Remainder theorem	Урьдчилсан харагдац	00:30
1.8 quiz- Factor and Remainder Theorem		00:20

2.1. Logarithms to base 10		00:20
2.2. Logarithms to base a		00:08
2.3. The laws of logarithms: Adding logarithms		00:10
2.4. Solving logarithmic equations		00:15
2.5. Solving exponential equations		00:21
2.6. Solving exponential inequalities		00:15
2.7. Natural logarithms		00:17
2.8. Transforming a relationship to linear form		00:15

3.1. The cosecant, secant and cotangent ratios		00:25
3.2. Compound anlge formulae and Double angle formulae		00:10
3.3. Double angle formulae		00:10
Worked Example 1: Double angle formulae		00:09
Worked Example 2: Double angle formulae		00:12
3.4 How to solve trigonometric equations using the Quadrant Rule		00:23
3.4. Further trigonometric identities		00:08
Worked Example: Further trigonometric identities		00:07
3.5. Expressing asinx+bcosx in the form Rsin(x+y) or Rcos(x+y)		00:13
Worked Example 2: Expressing asinx+bcosx in the form Rsin(x+y) or Rcos(x+y)		00:12

4.1. The product rule		00:12
Worked Example: The product rule		00:15
4.2. The quotient rule		00:13
Worked Example: The quotient rule		00:11
4.3. Derivatives of exponential functions		00:03
Worked Example 1: Derivatives of exponential functions		00:05
Worked Example 2: Derivatives of exponential functions		00:10
4.4. Derivatives of natural logarithmic functions		00:12
Worked Example: Derivatives of natural logarithmic functions		00:08
4.5. Derivatives of trigonometric functions	Урьдчилсан харагдац	00:08
Worked Example: Derivatives of trigonometric functions		00:13
4.6. Implicit differentiation		00:10
Worked Example 1: Implicit differentiation		00:05
Worked Example 2: Implicit differentiation		00:06
4.7. Parametric differentiation		00:10
Worked Example: Parametric differentiation		00:07

5.1. Integration of exponential functions		00:25
Worked Example: Integration of exponential functions		00:18
5.2. Integration of 1/(ax+b)		00:18
5.3. Integration of sin(ax+b), cos(ax+b) and sec2(ax+b)		00:00
5.4. Further integration of trigonometric functions		00:00
5.5. The trapezium rule		00:00

6.1. Finding a starting point		00:00
6.2. Improving your solution		00:00
6.3. Using iterative processes to solve problems involving other areas of mathematics		00:00

7.1. Improper algebraic fractions		00:00
7.2. Partial fractions		00:00
7.3. Binomial expansion of (1+x)n for values of n that are not positive integers		00:00
7.4. Binomial expansion of (a+x)n for values of n that are not positive integers		00:00
7.5. Partial fractions and binomial expansions		00:00

8.1. Derivative of tan-1x		00:00
8.2. Integration of 1/(a2+x2)		00:00
8.3. Integration of kf’(x)/f(x)		00:00
8.4. Integration by substitution		00:00
8.5. The use of partial fractions in integration		00:00
8.6. Integration by parts		00:00
8.7. Further integration		00:00

9.1. Displacement or translation vectors	Урьдчилсан харагдац	00:20
Worked Example 1: Vector addition and subtraction, Parallel vectors		00:10
Worked example 2: Magnitude of the vector		00:10
Worked example 3 & 4: Unit vector		00:10
9.2. Position vectors		00:00
9.3. The scalar product		00:00
9.4. The vector equation of a line		00:00
9.5. Intersection of two lines		00:00

10.1. The technique of separating the variables		00:00
10.2. Forming a differential equation from a problem		00:00

11.1. Imaginary numbers and Complex numbers		00:15
11.2. The complex plane		00:15
11.3. Solving equations		00:00
11.4. Loci (1)		00:14
11.5. Loci		00:20
Complex number Example 1: 9709_w18_qp_32		00:07
Complex number Example 2: 9709_w18_qp_31		00:10
Complex number Example 3: 9709_s18_qp_33		00:12
Complex number Example 4: 9709_s18_qp_32		00:12
Complex number Example 5: 9709_s18_qp_31		00:08