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Infection and response
Organisation
Cell biology
Biological molecules
Homeostasis and response
Responding to change (a2 only)
Energy transfers (a2 only)
The control of gene expression (a-level only)
Substance exchange
Bioenergetics
Genetic information & variation
Inheritance, variation and evolution
Genetics & ecosystems (a2 only)
Ecology
Cells
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1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
Britain & the wider world: 1745 -1901
Inter-war germany
World war one
2n revolution and dictatorship: russia, 1917-1953
World war two & the holocaust
1l the quest for political stability: germany, 1871-1991
The cold war
2j america: a nation divided, c1845-1877
Medieval period: 1066 -1509
The fight for female suffrage
2m wars and welfare: britain in transition, 1906-1957
2d religious conflict and the church in england, c1529-c1570
Britain: 1509 -1745
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05/09/2022
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16.8.21 dy dx Equation of a langent./ M -= dy de ہے tangent Therefore we need to know two things about the tangent. given. point, of which at least one coordinate will be • the gradient, which is calculated by differentiating and substitulay x at the required point. in the value of Examples; 1. Find the equation of the langent to the curve with equation y= x²-3 at the point (2.1). ( dy = 2x de To work out the equation of a tangent y-b= m(x-a). m = 2x we use M = 2x2 m = 4 y-b= a (x-2) y-1 = 4(x-2) y-1 = 4x=8 y = 4x-7 2. Find the equation of the langent to the y = x² - 2x at the point where x=-1. Find y X1-2x y = y = (¹1) ³ - 2 (-¹1) y = -1 +2 y=1 (-11) 19.8.21 m= dy de Y- 8 = 11 (x - 1) 4- 8 = 11 x - 11 y=11x - 3 Gradient. dy dx dy = ME Equation of a targent.... cont. dy dx M = 3(-1) ²-1 m = 3-2 M = 1 6x + 5 3x²-2 Find the equation of the langeet to the curve gradient of the Langent is 11. 6x + 5 = 11 6x = 6 x=1 curve wife wild Equation: y=1=1 (x + 1) y-1 = x+1 y=x+2 y = 3x² + 5x ²/1 y = 3 (1) ² + 5 (1) y = 8 (1.8) Note: Find gradi I tangent x² = More Langents x² = For y U 23 M Find the equation of the tangents to the curve y=x²-4x when the gradient of the langents dy dx For x = -2 y = -2² -4 (-2) y = 0 (-2,0) dy dx =...
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3x² - 4 3x²-4=8 3x² = 12 X² = 4 x = √√4= .8 رنا OR: 3x²-12=0 3 (x² - 4) = 0 3 (x-2)(x+2) = 0 x = 2 x = -2 y-0 = 8(x - 2) y=8x-16 For x=2 Y = 2³ - 4 (2) y=0 (2,0) y-0. = 8(x+2) y = 8x + 16