E Maths  45 days revision plan  2 hours a day
 
Content
Exercises
Day 1
Numbers
 
natural numbers
integers (positive, negative and zero)
prime numbers
common factors and common multiples
 
Day 2 rational and irrational numbers
real numbers
number sequences
 
Day 3
Squares, square roots, cubes and cube roots
 
squares
square roots
cubes
cube roots
 
Vulgar , decimal fractions and percentages
 
vulgar fractions
decimal fractions
percentages

 
Day 4
Ordering
 
order quantities by magnitude
symbols =, ?, >, <
 
Standard form
 
standard form  
The four operations
 
mathematical operations with whole numbers, decimal fractions and vulgar (and mixed) fractions
ordering of operations
brackets
 
Estimation
 
estimates of numbers, quantities and lengths
significant figures
decimal places
rounding off
accuracy

 
Day 5
Ratio, proportion, rate
 
ratios
direct and inverse proportion
measures of rate
dividing a quantity in a given ratio
scales in practical situations
express direct and inverse variation in algebraic terms and and solving for unknown quantities
 
Percentages
 
calculate a given percentage of a quantity
express one quantity as a percentage of another
calculate percentage increase or decrease
carry out calculations involving reverse percentages
 
Use of a scientific calculator
 
use a scientific calculator efficiently
checks of accuracy

 
Day 6
Everyday mathematics
 
use directed numbers in practical situations
use current units of mass, length, area, volume, capacity and time in practical situations
calculate times in terms of the 12-hour and 24-hour clock
solve problems involving money and convert from one currency to another
solve problems on personal and household finance involving earnings, simple interest, compound interest discount, profit and loss
extract data from tables and charts
 
Day 7
Graphs in practical situations
 
graphs in practical situations
travel graphs
conversion graphs
draw graphs from given data
distance-time
speed-time graphs
acceleration
retardation
area under speed-time graph
 
Day 8
Graphs of functions
 
construct tables of values and draw graphs for functions of the form y = axn where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these and for functions of the form y = kax where a is a positive integer
interpret graphs of linear, quadratic, reciprocal and exponential functions
find the gradient of a straight line graph
solve equations approximately by graphical methods
estimate gradients of curves by drawing tangents
 
Day 9
Coordinate geometry
 
demonstrate familiarity with Cartesian coordinates in two dimensions
calculate the gradient of a straight line from the coordinates of two points on it
interpret and obtain the equation of a straight line graph in the form y = mx + c
calculate the length and the coordinates of the midpoint of a line segment from the coordinates of its end points
 
Algebraic representation and formulae
 
use letters to express generalised numbers and express basic arithmetic processes algebraically
substitute numbers for words and letters in formulae
transform simple and more complicated formulae
construct equations from given situations
 
Day 10
Algebraic manipulation
 
manipulate directed numbers
use brackets and extract common factors
expand products of algebraic expressions
factorise expressions of the form ax + ay; ax + bx + kay + kby; a2x2 – b2y2; a2 + 2ab + b2; ax2 + bx + c
manipulate simple algebraic fractions
 
Day 11
Indices
 
positive, negative, zero and fractional indices  
Solutions of equations and inequalities
 
solve simple linear equations in one unknown
solve fractional equations with numerical and linear algebraic denominators
solve simultaneous linear equations in two unknowns
solve quadratic equations by factorisation and either by use of the formula or by completing the square
solve simple linear inequalities
 
Day 12
Geometrical terms and relationships
 
use and interpret the geometrical terms: point, line, plane, parallel, perpendicular, right angle, acute, obtuse and reflex angles, interior and exterior angles, regular and irregular polygons, pentagons, hexagons, octagons, decagons
use and interpret vocabulary of triangles, circles, special quadrilaterals
solve problems (including problems leading to some notion of proof) involving similarity and congruence
use and interpret vocabulary of simple solid figures: cube, cuboid, prism, cylinder, pyramid, cone, sphere
use the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes of similar solids
 
Day 13
Geometrical constructions
 
measure lines and angles
construct simple geometrical figures from given data using protractors or set squares as necessary

construct angle bisectors and perpendicular bisectors using straight edges and compasses only
read and make scale drawings
construct a triangle given the three sides using only ruler and compasses
 
Bearings
 
interpret and use three-figure bearings measured clockwise from the north
 
Day 14
Symmetry
 
recognise line and rotational symmetry (including order of rotational symmetry) in two dimensions, and properties of triangles, quadrilaterals and circles directly related to their symmetries
recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone)
use the following symmetry properties of circles:
(a) equal chords are equidistant from the centre
(b) the perpendicular bisector of a chord passes
through the centre

(c) tangents from an external point are equal in
length

 
Day 15
Angle
 
calculate unknown angles and solve problems (including problems leading to some notion of proof) using the following geometrical properties:
(a) angles on a straight line
(b) angles at a point
(c) vertically opposite angles
(d) angles formed by parallel lines
(e) angle properties of triangles and quadrilaterals
calculate unknown angles and solve problems (including problems leading to some notion of proof) using the following geometrical properties:

(f) angle properties of polygons including angle sum
(g) angle in a semi-circle
(h) angle between tangent and radius of a circle
(i) angle at the centre of a circle is twice the angle at
the circumference
(j) angles in the same segment are equal
(k) angles in opposite segments are supplementary

 
Day 16
Locus
 
use the following loci and the method of intersecting loci:
(a) set of points in two dimensions
(i) which are at a given distance from a given
point;
(ii) which are at a given distance from a given
straight line

(iii) which are equidistant from two given points
(b) sets of points in two dimensions which are
equidistant from two given intersecting straight
lines
 
Day 17
Mensuration
 
solve problems involving:
(i) the perimeter and area of a rectangle and a triangle
(ii) the circumference and area of a circle
(iii) the area of a parallelogram and a trapezium
(iv) the surface area and volume of a cuboid, cylinder, prism, sphere, pyramid and cone. (Formulae will be given for the sphere, pyramid and cone.)
(v) arc length and sector area as fractions of the circumference and area of a circle
 
Day 18
Trigonometry
 
apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right-angled triangle (angles will be quoted in, and answers required in, degrees and decimals of a degree to one decimal place)
solve trigonometrical problems in two dimensions including those involving angles of elevation and depression and bearings;
extend sine and cosine functions to angles between 90o and 180o
solve problems using the sine and cosine rules for any triangle and the formula 21ab sinC for the area of a triangle
solve simple trigonometrical problems in three dimensions
 
Day 19
Statistics
 
• collect, classify and tabulate statistical data;
• read, interpret and draw simple inferences from tables and statistical diagrams;
• construct and use bar charts, pie charts, pictograms, dot diagrams, stem-and-leaf diagrams, simple frequency distributions and frequency polygons;
• use frequency density to construct and read histograms with equal and unequal intervals;
 
Day 20 calculate the mean, median and mode for individual data and distinguish between the purposes for which they are used;
• construct and use cumulative frequency diagrams;
• estimate the median, percentiles, quartiles and interquartile range from the cumulative frequency diagrams;
• calculate the mean for grouped data;
• identify the modal class from a grouped frequency distribution.
 
Day 21
Probability
 
calculate the probability of a single event as either a fraction or a decimal (not a ratio)  
Day 22 calculate the probability of simple combined events, using possibility diagrams and tree diagrams where appropriate (in possibility diagrams outcomes will be represented by points on a grid and in tree diagrams outcomes will be written at the end of branches and probabilities by the side of the branches)  
Day 23
Transformations
 

Performing the following transformations of the plane:
reflection (M),
rotation (R),
translation (T),
enlargement (E),
shear (H),
stretch (S)
and their combinations

 
Day 24

Identifying and giving precise descriptions of transformations connecting given figures

 
Day 25
Vectors in 2 dimensions
 

Describing a translation by using a vector represented by :


 

Adding vectors
Multiplying a vector by a scalar

 

Calculating the magnitude of a vector :


 
Day 26

Representing vectors by directed line segments
Using the sum and difference of two vectors to express given vectors in terms of two coplanar vectors
Using position vectors

 
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)  
Day 31    
Day 32    
Day 33    
Day 34    
Day 35    
Day 36    
Day 37    
Day 38    
Day 39    
Day 40    
Day 41    
Day 42    
Day 43    
Day 44    
Day 45