E Maths 90 days revision plan 2 hours a day 

Content 
Exercises 
Day 1 


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 12hour and 24hour 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
distancetime
speedtime graphs
acceleration
retardation
area under speedtime 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 threefigure 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 semicircle
(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 rightangled 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, stemandleaf 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) 

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Day 46 


Day 47 


Day 48 


Day 49 


Day 50 


Day 51 


Day 52 


Day 53 


Day 54 


Day 55 


Day 56 


Day 57 


Day 58 


Day 59 


Day 60 


Day 61 


Day 62 


Day 63 


Day 64 


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Day 66 


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Day 90 

