Maths A2 Unit 2

Can sketch the graphs of the reciprocal trig functions cosecx, secx and cotx
Know the identities tanx = sinx/cosx and cotx = cosx/sinx
Know the identities sin²x + cos²x = 1, tan²x + 1 = sec²x and 1 + cot²x = cosec²x
Can use reciprocal trig functions and identities to solve equations

Ex 3A pg 52 Q5 - 7

Ex 8A pg 186 Q1acef, Q2acef

Can write down values for the inverse trig functions arcsin, arcos and arctan
Know the graphs and properties of the inverse trig functions

Can use the addition formulae to find exact values of sin, cos and tan
Can solve equations using the addition formulae
Can prove identities using the addition formulae

Ex 3C pg 64 Q1, 3a, 8, 12, 13, 19, 20

Can derive the double angle formulae from the addition formulae
Can derive the half angle formulae from the double angle formulae
Can find exact values using the double and half angle formulae
Can solve equations using the double and half angle formulae

Ex 3D pg 70Q1 a d g j m, 2 a d e, Q3 a, Q8, Q9

Can express acosq + bsinq in the form Rcos (q ± a) or Rsin (q ± a)
Solving equations using Rcos (q ± a) or Rsin (q ± a)
Can find maximum and minimum values using Rcos (q ± a) or Rsin (q ± a)
Can sketch graphs using Rcos (q ± a) or Rsin (q ± a) by applying transformations

Revision of trigonometry using review exercise if needed and/or help with binomial expansion below

Differentiate implictly

Use implicit differentiation to find gradients of curves, equations of tangents and normals

Understand the different types of mappings (1-1, many-1, 1-many, many-many)
Understand that a function is a 1-1 or many-1 mapping
Understand domain (values that go into the function) and range (values that come out of the function)
Use completing the square to find the range of a quadratic function

Ex 2A pg 18Q1a,c,e,g Q2a,c,e Q3 - 7

Solve problems involving exponential growth and decay
Differentiate a^x and and log_ax

Private study

Be able to sketch graphs with asymptotes - understand how to find the vertical asymptote (denominator cannot equal zero) and horizontal asymptote (algebraic division or find y as x tends to infinity) and find intersection with axes
Find the range and domain for functions involving asymptotes

Ex 10B pg 213 Q1 - 12

Ex 10C pg 220 Q 1 - 8

Ex 2A pg 18Q8, 9 + extra questions from JEE

Sketch curves given parametrically using a table of values
Find the cartesian equation of a curve given parametrically
Differentiate parametrically and use to find equations of tangents and normals and stationary points

Understand composite functions

Ex 11A pg 229 Q1a, 2acdhjklm

Ex 11B pg 235 Q1bcde, Q4a, Q6efg, Q9

Ex 2B pg 23Q1a,c Q2a,c,e,g Q3a,c,g Q4-7

Revision of vectors from GCSE

Use the scalar product to find the angle between 2 vectors and solve problems
Scalar Product JEE

Understand that only a 1-1 function can have an inverse function
Understand that a many-1 function will need to restrict its domain to have an inverse function Understand that the domain of the function is the same as the range of the inverse function and the range of the function is the same as the domain of the inverse function
Be able to find an inverse function algebraically (interchange x and y and rearrange)
Be able to sketch the graph of an inverse function from the graph of the function (by reflecting in the line y = x)

Ex 15A pg 365 Q2bd, Q3, Q6c, Q8-11, Q15aei, Q20'odds'
Ex 15B pg 370 Q1 - 7, 8a

Ex 15C pg 374 Q6ac, Q7aceg, Q8-10, Q15 - 18

Powerpoint- inverse functions from slide 24 and graphs of inverse functions

Ex 2C pg 29Q1a,d,g,j Q2a,d,g,j,m,p,s Q3, 4a, 8, 10, 13, 14

The vector equation of a line
Vector Equation of a Line

Ex 15D pg 379 Q1ace, Q2ace, Q3-5, Q6a, Q7-8

Know that even functions are symmetrical about the y axis and f(-x) = f(x)
Know that odd functions have rotational symmetry order 2 about the origin and f(-x) = -f(x)
Understand the difference between y = mod f(x) and y = f(mod x)
Sketch the graph of y = mod f(x) by sketching y = f(x) and reflecting any part of the graph that is below the x-axis in the x-axis
Sketch the graph of y = f(mod x) by sketching y = f(x) for x>0 and reflecting this in the y-axis
Can equations/inequalities with modulus signsü Can solve equations/inequalities by graphical methods and algebraic methods (squaring both sides)

Powerpoint 16 The Modulus Function Questions on slides

Ex 2E pg 37 Q1a,c,e,g,I

Week	Details & links	Assessed work / further work
Mon 14th Jan	Wednesday's lesson Powerpoint: Reciprocal Trig Functions JEE Can sketch the graphs of the reciprocal trig functions cosecx, secx and cotx Know the identities tanx = sinx/cosx and cotx = cosx/sinx Know the identities sin²x + cos²x = 1, tan²x + 1 = sec²x and 1 + cot²x = cosec²x Can use reciprocal trig functions and identities to solve equations Private study - partial fractions with distinct linear denominators	Ex 3A pg 52 Q5 - 7 Ex 8A pg 186 Q1acef, Q2acef
Mon 21st Jan	Wednesday's Lesson Powerpoint: Inverse Trig Functions Can write down values for the inverse trig functions arcsin, arcos and arctan Know the graphs and properties of the inverse trig functions Thursday's lesson Powerpoint: The addition formulae (proof) JEE Can use the addition formulae to find exact values of sin, cos and tan Can solve equations using the addition formulae Can prove identities using the addition formulae Private study - partial fractions with a repeated denominator and with improper fractions	Ex 3C pg 64 Q1, 3a, 8, 12, 13, 19, 20 Ex 8A pg 186 Q3abc, Q4ace
Mon 28th Jan	Wednesday's lesson Powerpoint:Double Angle Formulae JEE Can derive the double angle formulae from the addition formulae Can derive the half angle formulae from the double angle formulae Can find exact values using the double and half angle formulae Can solve equations using the double and half angle formulae Private study Binomial expansion of (1 + x)ⁿ and (a + x)ⁿ for negative and fractional values of n stating the conditions under which the expansion is valid	Ex 3D pg 70Q1 a d g j m, 2 a d e, Q3 a, Q8, Q9 Ex 9A pg 197 Q1adegjmnop
Mon 4th Feb	Wednesday's lesson Powerpoint: The function acosx + bsinx JEE Can express acosq + bsinq in the form Rcos (q ± a) or Rsin (q ± a) Solving equations using Rcos (q ± a) or Rsin (q ± a) Can find maximum and minimum values using Rcos (q ± a) or Rsin (q ± a) Can sketch graphs using Rcos (q ± a) or Rsin (q ± a) by applying transformations Thursday's lesson Revision of trigonometry using review exercise if needed and/or help with binomial expansion below Private study Use the binomial expansion to approximate Solve more challenging problems involving the binomial expansion Use partial fractions to find a binomial expansion	Ex 3F pg 79 Q1-3, 7, 8 Ex 9A pg 198 Q5, Q7b, Q12 - 20
	HALF TERM!!
Mon 18th Feb	Wednesday's lesson Powerpoint:Implicit Differentiation JEE Differentiate implictly Use implicit differentiation to find gradients of curves, equations of tangents and normals Private study Understand the different types of mappings (1-1, many-1, 1-many, many-many) Understand that a function is a 1-1 or many-1 mapping Understand domain (values that go into the function) and range (values that come out of the function) Use completing the square to find the range of a quadratic function	Ex 10A pg 208 Q1 'odds' Q2 'odds', Q4ceg, Q5, 7, 10, 12 Ex 2A pg 18Q1a,c,e,g Q2a,c,e Q3 - 7
Mon 25th Feb	Wednesday's lesson Powerpoint: Connected Rates of Change JEE Use the chain rule to find rates of change Thursday's lesson: Solve problems involving exponential growth and decay Differentiate a^x and and log_ax Private study Be able to sketch graphs with asymptotes - understand how to find the vertical asymptote (denominator cannot equal zero) and horizontal asymptote (algebraic division or find y as x tends to infinity) and find intersection with axes Find the range and domain for functions involving asymptotes	Ex 10B pg 213 Q1 - 12 Ex 10C pg 220 Q 1 - 8 Ex 2A pg 18Q8, 9 + extra questions from JEE
Mon 3rd March	Wednesday's lesson Sketch curves given parametrically using a table of values Find the cartesian equation of a curve given parametrically Differentiate parametrically and use to find equations of tangents and normals and stationary points Private study Understand composite functions	Ex 11A pg 229 Q1a, 2acdhjklm Ex 11B pg 235 Q1bcde, Q4a, Q6efg, Q9 Ex 2B pg 23Q1a,c Q2a,c,e,g Q3a,c,g Q4-7
Mon 10th March	Wednesday's lesson Revision of vectors from GCSE Thursday's Lesson Use the scalar product to find the angle between 2 vectors and solve problems Scalar Product JEE Private study Understand that only a 1-1 function can have an inverse function Understand that a many-1 function will need to restrict its domain to have an inverse function Understand that the domain of the function is the same as the range of the inverse function and the range of the function is the same as the domain of the inverse function Be able to find an inverse function algebraically (interchange x and y and rearrange) Be able to sketch the graph of an inverse function from the graph of the function (by reflecting in the line y = x)	Ex 15A pg 365 Q2bd, Q3, Q6c, Q8-11, Q15aei, Q20'odds' Ex 15B pg 370 Q1 - 7, 8a Ex 15C pg 374 Q6ac, Q7aceg, Q8-10, Q15 - 18 Powerpoint- inverse functions from slide 24 and graphs of inverse functions Ex 2C pg 29Q1a,d,g,j Q2a,d,g,j,m,p,s Q3, 4a, 8, 10, 13, 14
Mon 17th March	Wednesday's lesson The vector equation of a line Vector Equation of a Line Private study Revision of vectors	Ex 15D pg 379 Q1ace, Q2ace, Q3-5, Q6a, Q7-8 Ex 15E pg 381
	EASTER!!
Mon 7th April	Wednesday's Lesson Know that even functions are symmetrical about the y axis and f(-x) = f(x) Know that odd functions have rotational symmetry order 2 about the origin and f(-x) = -f(x) Understand the difference between y = mod f(x) and y = f(mod x) Sketch the graph of y = mod f(x) by sketching y = f(x) and reflecting any part of the graph that is below the x-axis in the x-axis Sketch the graph of y = f(mod x) by sketching y = f(x) for x>0 and reflecting this in the y-axis Can equations/inequalities with modulus signsü Can solve equations/inequalities by graphical methods and algebraic methods (squaring both sides)	Powerpoint 16 The Modulus Function Questions on slides Ex 2E pg 37 Q1a,c,e,g,I
Mon 14th April
Mon 21st April
Mon 28th April
Tues 6th May
Mon 12th May