A Maths 30 days revision plan 2 hours a day 

Content 
Exercises 
Day 1 
Set language and notation 

use set language and notation , and Venn diagrams to describe sets and represent relationships between sets as follows :
A = { x : x is a natural number }
B = { ( x , y ) : y = m x + c }
C = { x : a < x < b }
D = { a , b , c , ... }
understand and use the following notation :
Union of A and B 
A ∪ B 
Intersection of A and B 
A ∩ B 
Number of elements in set A 
n(A) 
"... is an element of ..." 
∈ 
"... is not an element of ..." 
∉ 
Complement of set A 
A' 
The empty set 
∅ 
Universal set 
U 
A is a subset of B 
A ⊂ B 
A is a proper subset of B 
A ⊂ B 
A is not a subset of B 
A ⊄ B 
A is not a proper subset of B 
A ⊄ B 


Day 2 
Functions 

understand the terms :
function
domain
range (image set)
oneone function
inverse function
composition of functions
use the notation f ( x ) = sin x , f : x > l g x , ( x > 0 ) ,
f ^{– 1} ( x ) and f ^{2} ( x ) [ = f ( f ( x ) ) ]
understand the relationship between y = f ( x ) and
y =  f ( x )  , where f ( x ) may be linear , quadratic or trigonometric

Q1
Q2
Q3
Q6 
Day 3 
explain in words why a given function is a function or why it does not have an inverse
find the inverse of a oneone function and form composite functions
use sketch graphs to show the relationship between a function and its inverse

Q7
Q8
Q9 
Day 4 
Quadratic functions 

find the maximum or minimum value of the quadratic function f : x > a x ^{2} + b x + c by any method
use the maximum or minimum value of f ( x ) to sketch the graph or determine the range for a given domain

quadratic formula
Q1
quadratic functions
Q1
Q2
Q3

Day 5 
know the conditions for f ( x ) = 0 to have
(i) two real roots
(ii) two equal roots
(iii) no real roots
and the related conditions for a given line to
(i) intersect a given curve
(ii) be a tangent to a given curve
(iii) not intersect a given curve
solve quadratic equations for real roots and find the solution set for quadratic inequalities

quadratic functions
Q4
Q5
Q6 
Day 6 
Indices and surds 

perform simple operations with indices and with surds, including rationalising the denominator

indices
Q1
Q2
surds
Q1
Q2
Q3

Day 7 
Factors of polynomials 

know and use the remainder and factor theorems


Day 8 
find factors of polynomials
solve cubic equations


Day 9 
Simultaneous equations 

solve simultaneous equations in two unknowns with at least one linear equation


Day 10 
Logarithmic and exponential functions 

know simple properties and graphs of the logarithmic and exponential functions including l n x and e ^{ x}


Day 11 
know and use the laws of logarithms (including change of base of logarithms)
solve equations of the form ax= b 

Day 12 
Straight line graphs 

interpret the equation of a straight line graph in the form
y = mx +c
transform given relationships, including y = axn and y = Abx, to straight line form and hence determine unknown constants by calculating the gradient or intercept of the transformed graph 

Day 13 
solve questions involving midpoint and length of a line
know and use the condition for two lines to be parallel or perpendicular 

Day 14 
Circular measure 

solve problems involving the arc length and sector area of a circle 

Day 15 
knowledge and use of radian measure 

Day 16 
Trigonometry 

know the six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent)
understand amplitude and periodicity and the relationship between graphs of e.g. sin x and sin 2x 

Day 17 
draw and use the graphs of y = a sin(bx) + c,
y = a cos(bx) + c, y = a tan(bx) + c, where a, b are positive integers and c is an integer 

Day 18 
use the relationships AAcossin= tan A, AAsincos= cot A,
sin2 A + cos2 A = 1, sec2 A = 1 + tan2 A,
cosec2 A = 1 + cot2 A, and solve simple trigonometric equations involving the six trigonometric functions and the above relationships (not including general solution of trigonometric equations)
prove simple trigonometric identities 

Day 19 
Permutations and combinations 

recognise and distinguish between a permutation case and a combination case
know and use the notation n!, (with 0! = 1), and the expressions for permutations and combinations of n items taken r at a time
answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle or involving both permutations and combinations, are excluded) 

Day 20 
Binomial expansions 

use the Binomial Theorem for expansion of (a + b)n for positive integral n
use the general term
a
rnn –
r
br, 0
r
n


Day 21 
Vectors in 2 dimensions 

use vectors in any form, e.g. , AB , p, ai + bj
know and use position vectors and unit vectors
find the magnitude of a vector. Add and subtract vectors and multiply vectors by scalars
compose and resolve velocities
use relative velocity including solving problems on interception (but not closest approach) 

Day 22 
Matrices 

display information in the form of a matrix of any order and interpret the data in a given matrix;
• solve problems involving the calculation of the sum and product (where appropriate) of two matrices and interpret the results;
• calculate the product of a scalar quantity and a matrix;
• use the algebra of 2 x 2 matrices (including the zero and identity matrix);
• calculate the determinant and inverse of a nonsingular 2 x 2 matrix and solve simultaneous linear equations 
Day 23 
Differentiation and integration 

understand the idea of a derived function;
• use the notations f ˈ (x), f "(x),;dddddd,dd22=xyxxyxy
• use the derivatives of the standard functions xn (for any rational n), sinx, cosx, tanx, ex, lnx, together with constant multiples, sums and composite functions of these 

Day 24 
differentiate products and quotients of functions;
• apply differentiation to gradients, tangents and normals, stationary points, connected rates of change, small increments and approximations and practical maxima and minima problems;
• discriminate between maxima and minima by any method;
• understand integration as the reverse process of differentiation;
• integrate sums of terms in powers of x excluding x1 

Day 25 
integrate functions of the form
(ax + b)n (excluding n = –1), eax+b, sin(ax + b),
cos(ax + b);
• evaluate definite integrals and apply integration to the evaluation of plane areas; 

Day 26 
• apply differentiation and integration to kinematics problems that involve displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration, and the use of xt and vt graphs 

Day 27 
Test 1 (must pass) 

Day 28 
Test 2 (must pass) 

Day 29 
Test 3 (should pass) 

Day 30 
Test 4 (good to pass) 
