Mock Papers











Scheme of work


General Topic
No. of Hours*
Objectives

By the end of the module students should be able to …
Grade
Whole numbers
1 – 3
  • Understand and order integers
  • multiply and divide positive integers
  • multiply and divide negative integers
  • Round whole numbers to the nearest, 10, 100, 1000, …
  • Multiply and divide whole numbers by a given multiple of 10
  • Check their calculations by rounding, e.g. 29 ´ 31 » 30 ´ 30
G
F
E
G
D
Decimals
3 – 5
  • Put digits in the correct place in a decimal number
  • Write decimals in ascending order of size
  • Approximate decimals to a given number of decimal places or
  • significant figures
  • Multiply and divide decimal numbers by whole numbers and decimal numbers (up to 2 dp), e.g. 266.22 ¸ 0.34
  • Know that e.g. 13.5 ¸ 0.5 = 135 ¸ 5
  • Check their answer by rounding, know that e.g. 2.9 ´ 3.1 » 3.0 ´ 3.0
F
F
F
E
D
D
D
Fractions: Addition and subtraction
1 – 3
  • Write a fraction in its simplest form and recognise equivalent fractions
  • Compare the sizes of fractions using a common denominator
  • Add and subtract fractions by using a common denominator
  • Write an improper fraction as a mixed number, and visa versa
  • Add and subtract mixed numbers
F
D
D
C
Fractions: Multiplication and division
1 – 3
  • Convert a fraction to a decimal, or a decimal to a fraction
  • Find the reciprocal of whole numbers, fractions, and decimals
  • Multiply and divide a fraction by an integer, by a unit fraction and by a general fraction (expressing the answer in its simplest form)
  • Convert a fraction to a recurring decimal (and visa versa)
  • Use fractions in contextualised problems
D
C
C
B
Coordinates
1 – 3
  • Plot and reading coordinates on a coordinate grid (in all four quadrants)
  • Understand that one coordinate identifies a point on a line, two coordinates identify a point in a plane and three coordinates identify a point in space, and use the terms ‘1-D’, ‘2-D’ and ‘3-D’
  • Find the coordinates of the fourth vertex of a parallelogram
  • Identify the coordinates of the vertex of a cuboid on a 3-D grid
  • Writing down the coordinates of the midpoint of the line connecting two points
  • Calculate the length of the line segment joining to point in the plane (all four quadrants)
F
A
D
A
C
A
Introduction to algebra
1 – 3
  • Simplify algebraic expressions in one or more like terms by addition and subtraction
  • Multiply and divide with letters and numbers
  • Multiply and divide powers of the same letter
  • Understand and use the index rules to simplify algebraic expressions
  • Use brackets to expand and simplify simple algebraic expressions
E
D
C
C/B
C
Angles
5 – 7
  • Distinguish between acute, obtuse, reflex and right angles
  • Use angle properties on a line and at a point to calculate unknown angles
  • Use angle properties of triangles and quadrilaterals to calculate unknown angles
  • Use parallel lines to identify alternate and corresponding angles
  • Calculate interior and exterior angles in a polygon
  • Understand and use bearings
F
F
E
D
C
D
Collecting data
3 – 5
  • Design a suitable question for a questionnaire
  • Understand the difference between: primary and secondary data; discrete and continuous data
  • Design suitable data capture sheets for surveys and experiments
  • Understand about bias in sampling
  • Choose and justify an appropriate sampling scheme, including random and systematic sampling
  • Deal with practical problems in data collection, such as non-response, missing and anomalous data
C
B
D
A
D
Charts and graphs
1 – 3
  • Represent data as:
  • Pie charts (for categorical data)
  • Bar charts and histograms (equal class intervals)
  • Frequency polygons
  • Choose an appropriate way to display discrete, continuous and categorical data
  • Understand the difference between a bar chart and a histogram
  • Compare distributions shown in charts and graphs
E
B
D/C
B
A-E
2-D shapes
1 – 3
  • Construct:
  • An equilateral triangle with a given side
  • The mid-point and perpendicular bisector of a line segment
  • The perpendicular from a point on a line
  • The bisector of an angle
  • The angles 60, 30 and 45 degrees
  • A regular hexagon inside a circle, etc
  • A region bounded by a circle and an intersecting line
  • A path equidistant from 2 points or 2 line segments, etc
E
C
C
C
D
C
C
Properties of triangles and quadrilaterals
3 – 5
  • Mark parallel lines in a diagram
  • Find missing angles using properties of corresponding angles and alternate angles, giving reasons
  • Find the three missing angles in a parallelogram when one of them is missing
  • Identify and list the properties of quadrilaterals (including kites)
  • Name all quadrilaterals that have a pair of opposite sides that are equal
G
D
D
Factors and multiples
1 – 3
  • Find: squares; cubes; square roots; cube roots of numbers, with and without a calculator (including the use of trial and improvement)
  • Understand odd and even numbers, and prime numbers
  • Find the HCF and the LCM of numbers
  • Write a number as a product of its prime factors, e.g. 108 = 22 ´ 33
E
G
C
C
Percentages
5 – 7
  • Understand that a percentage is a fraction in hundredths
  • Write a percentage as a decimal; or as a fraction in its simplest terms
  • Write one number as a percentage of another number
  • Calculate the percentage of a given amount
  • Find a percentage increase/decrease of an amount
  • Find a reverse percentage, e.g. find the original cost of an item given the cost after a 10% deduction
  • Use a multiplier to increase by a given percent, e.g. 1.1 ´ 64 increases 64 by 10%
  • Calculate simple and compound interest for two, or more, periods of time
G
F
D
E
C
B
D
C
Perimeter and area
1 – 3
  • Use Pythagoras’ theorem to find unknown lengths, e.g. the height of an isosceles triangle given the lengths of all three sides
  • Find the perimeter and area of shapes made up from triangles and rectangles
  • Find when numbers are given to a specific degree of accuracy, the upper and lower bounds of perimeters and areas
  • Convert between units of area
C
D
B
D
3-D shapes
1 – 3
  • Count the vertices, faces and edges of 3-D shapes
  • Draw nets of solids and recognise solids from their nets
  • Draw and interpret plans and elevations
  • Draw planes of symmetry in 3-D shapes
  • Recognise and name examples of solids, including prisms, in the real world
D/G
D
D
E
Solving linear equations
5 – 7
  • Solve linear equations with one, or more, operations (including fractional coefficients)
  • Solve linear equations involving a single pair of brackets
C
D
Patterns and sequences
3 – 5
  • Find the missing numbers in a number pattern or sequence
  • Find the nth term of a number sequence as an algebraic expression
  • Explain why a number is, or is not, a member of a given sequence
  • Use a calculator to produce a sequence of numbers
E
C

Brackets
1 – 3
  • Expand or factorise algebraic expressions involving one pair of brackets
  • Expand and simplify expressions involving two pairs of brackets
  • Factorise quadratic expressions (including the difference of two squares)
D
B
B
Formulae
5 – 7
  • Use letters or words to state the relationship between different quantities
  • Substitute positive and negative numbers into simple algebraic formulae
  • Substitute positive and negative numbers into algebraic formulae involving powers
  • Find the solution to a problem by writing an equation and solving it
  • Change the subject of a formula, e.g. convert the formula for converting Centigrade into Fahrenheit into a formula that converts Fahrenheit into Centigrade
  • Generate a formula from given information, e.g. find the formula for the perimeter of a rectangle given its area A and the length of one side
D
C
D – A*
B
D – A*
Circle theorems
5 – 7
  • Understand, prove and use circle theorems (see below)
  • Use circle theorems to find unknown angles and explain their method- quoting the appropriate theorem(s)

  • Understanding that the tangent at any point on a circle is perpendicular to the radius at that point
  • Understanding and using the fact that tangents from an external point are equal in length
  • Explaining why the perpendicular from the centre to a chord bisect the chord
  • Proving and using the fact that the angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference
  • Proving and using the fact that the angle subtended at the circumference by a semicircle is a right angle
  • Proving and using the fact that angles in the same segments are equal
  • Proving and using the fact that opposite angles of a cyclic quadrilateral sum to 180 degrees
  • Proving and using the alternate segment theorem
B
B
B
B
B
A
A
A
A
Linear functions
y = mx + c
7 – 9
  • Substitute values of x into linear functions to find corresponding values of y
  • Plot points for linear functions on a coordinate grid and draw the corresponding straight lines
  • Interpret m and c as gradient and y-intercept in linear functions
  • Understand that the graphs of linear functions are parallel if they have the same value of m
  • Know that the line perpendicular to y = mx + c has gradient -1/m
  • Understand linear functions in practical problems, e.g. distance-time graphs
C
C
B
A

Similar shapes
5 – 7
  • Use integer and non-integer scale factors to find the length of a missing side in each of two similar shapes, given the lengths of a pair of corresponding sides
  • Know the relationship between linear, area and volume scale factors of similar shapes
  • Prove formally geometric properties of triangles, e.g. that the base angles of an isosceles triangle are equal
  • Prove formally that two triangles are congruent
B/C
E
A
Perimeter and area of circles
3 – 5
  • Find the perimeter and area of shapes made up from triangles, rectangles and parts of circles
  • Use and recall formulae to calculate perimeters and areas of circles, and parts of circles
C/D
D
Scatter graphs and correlation
3 – 5
  • Draw and produce a scatter graph
  • Appreciate that correlation is a measure of the strength of association between two variables
  • Distinguish between positive, negative and zero correlation using a line of best fit
  • Appreciate that zero correlation does not necessarily imply ‘no correlation’ but merely ‘no linear relationship’
  • Draw a line of best fit by eye and understand what it represents
  • Use a line of best fit to interpolate/ extrapolate
D
C
C
D

Ratio and scale
1 – 3
  • Appreciate that e.g. the ratio 1:2 represents 1/3 and 2/3 of a quantity
  • Divide quantities in a given ratio, e.g. divide £20 in the ratio 2:3
  • Solve word problems involving ratios, e.g. Find the cost of 8 pencils given that 6 cost 78p
  • Work out the real distance from a map, e.g. Find the real distance represented by 4 cm on a map with scale 1:25 000
  • Work out the distance on a map for a given real distance and scale
D/C
C
E
Direct and inverse proportion
5 – 7
  • Interpret direct and inverse proportions as algebraic functions, e.g. y µ x2 as y = kx2
  • Use given information to find the value of the constant of proportionality
  • Use algebraic functions for direct and inverse proportionality, with their value of k, to find unknown values
  • Recognise and sketch the graphs for direct and inverse proportions (y µ x, y µ x2, y µ x3, y µ 1/x, y µ 1/x2)
A
A
A
A
The mean (large data sets)
1 – 3
  • Find the mean of data given in an ungrouped frequency distribution
  • Use the mid interval value to find an estimate for the mean of data given in a grouped frequency distribution
  • Understand and use the sigma notation for the mean of ungrouped, and grouped, data
D
C
Simultaneous equations
5 – 7
  • Solve algebraically two simultaneous equations
  • Interpret the solution of two simultaneous equations as the point of intersection the corresponding lines
B
Probability
7 – 9
  • List all the outcomes from mutually exclusive events, e.g. from two coins, and sample space diagrams
  • Write down the probability associated with equally likely events, e.g. the probability of drawing an ace from a pack of cards
  • Know that if the probability of an event occurring is p than the probability of it not occurring is 1 – p
  • Find the missing probability from a list or table
  • Know that the probability of A or B is P(A) + P(B)
  • Know that the probability of A and B is P(A) ´ P(B)
  • Draw and use tree diagrams to solve probability problems (including examples of non-replacement)
  • Find estimates of probabilities by considering relative frequency in experimental results (including two-way tables)
  • Know that the more an experiment is repeated the better the estimate of probability
E
E
B
C
C

Standard form
1 – 3
  • Understand the standard form convention
  • Convert numbers to, and from, standard form
  • Calculate with numbers given in standard form with, and without, a calculator
  • Round numbers given in standard form to a given number of significant figures
B
B
B
B
Inequalities
3 – 5
  • Rearrange and solve linear inequalities in one variable and show the solution set on a number line, or to write down all the integer solutions.
  • Draw the graphs of linear inequalities in two variables and interpret the solution sets given by regions in the coordinate plane, or to identify all the integer coordinates with crosses
C
B
Quadratic functions
3 – 5
  • Plot the graphs of quadratic functions for positive and negative values of x
  • Find graphically the solutions of quadratic equations by considering the intercept on the x-axis
  • Solve quadratic equations by factorising (including values of a not equal to 1)
  • Use the quadratic formula to solve quadratic equations giving the answers to 1 dp
  • Use the quadratic formula to solve quadratic equations leaving the answer in surd form
  • Complete the square of a quadratic function (using this to write down the max/min of the function)
F
C
B
A
A
A*
Speed and density
3 – 5
  • Use the relationship between distance, speed and time to solve problems
  • Convert between metric units of speed e.g. km/h to m/s
  • Know that density is found by mass ÷ volume
  • Use the relationship between density, mass and volume to solve problems, e.g. find the mass of an object with a given volume and density
  • Convert between metric units of density e.g. kg/m to g/cm
G
Trial and improvement
1 – 3
  • Solve cubic functions by successive substitution of values of x
C
Angle properties of polygons
1 – 3
  • Calculate and use the sums of the interior angles of convex polygons of sides 3, 4, 5, 6, 8, 10
  • Know, or work out, the relationship between the number of sides of a polygon and the sum of its interior angles
  • Know that the sum of the exterior angles of any polygon is 360 degrees
  • Find the size of each exterior/interior angle of a regular polygon
D/C
C

Surface area and volume
1 – 3
  • Find volumes of shapes by counting cubes
  • Use formulae to calculate the surface areas and volumes of cuboids, right-prisms and cylinders
  • Solve a range of problems involving surface area and volume, e.g. given the volume and length of a cylinder find the radius
  • Convert between units of volume
G
C
A
Transformations
5 – 7
  • Understand translation as a combination of a horizontal and vertical shift including signs for directions
  • Understand rotation as a (clockwise) turn about a given origin
  • Reflect shapes in a given mirror line; parallel to the coordinate axes and then y = x or y = –x
  • Enlarge shapes by a given scale factor from a given point; using positive and negative scale factors greater than one
  • Enlarge shapes by a given fractional scale factor, e.g. 2/3
  • Understand that shapes produced by translation, rotation and reflection are congruent to its image
D
D/C
C
D
C
C
Further simultaneous equations
5 – 7
  • Find graphically the approximate solutions of linear and quadratic simultaneous equations
  • Find the exact solutions of linear and quadratic simultaneous equations
  • Draw a circle of radius r centred at the origin
  • Find graphically the approximate solutions of linear and circular simultaneous equations
  • Find the exact solutions of linear and circular simultaneous equations
B/A
A
A
A
A*
Surface area and volume
5 – 7
  • Find the surface area and the volume of more complex shapes, e.g. find the volume of an equilateral triangular prism
  • Solve more complex problems, e.g. given the surface area of a sphere find the volume
C – A*
A/A*

Median and interquartile range (large data sets)
5 – 7
  • Find the median and quartiles for large sets of ungrouped data
  • Draw a cumulative frequency table for grouped data (using the upper class boundary)
  • Draw a cumulative frequency curve for grouped data
  • Use a cumulative frequency diagram to find estimates for the median and quartiles of a distribution
  • Use a cumulative frequency diagram to solve problems, e.g. how many greater than a particular value
  • Draw a box plot to summarise information given in cumulative frequency diagrams
  • Compare cumulative frequency diagrams and box lots to make inferences about distributions
C
B
B
B
B
B
B
Histograms
3 – 5
  • Complete a histogram from a frequency table
  • Complete a frequency table from a histogram
  • Use a histogram to work out the frequency in part of a class interval
A
A
A
Sine, cosine and tangent
5 – 7
  • Use trigonometric ratios (sin, cos and tan) to calculate angles in right-angled triangles
  • Use the trigonometric ratios to calculate unknown lengths in right-angled triangles
B
B
Trigonometry for non right-angled triangles
3 – 5
  • Find the unknown lengths, or angles, in non right-angle triangles using the sine and cosine rules
  • Find the area of triangles given two lengths and an included angle
A
Applications of trigonometry in 3-D
3 – 5
  • Calculate the length of a diagonal of a rectangle given the lengths of the sides of the rectangle
  • Calculate the diagonal through a cuboid, or across the face of a cuboid
  • Find the angle between the diagonal through a cuboid and the base of the cuboid
  • Find the angle between a sloping edge of a pyramid and the base of the pyramid
  • Identify when to use the sine or cosine rule and adapt the relevant formula to the given triangle
C
B
A*
A*
A
Further functions
5 – 7
  • Plot and recognise cubic, reciprocal, exponential and circular functions
  • Use the graphs of these functions to find approximate solutions to equations, e.g. given x find y (and visa versa)
  • Find the values of p and q in the function y = pqx given the graph of y = pqx
  • Match equations with there graphs
  • Sketch graphs of given functions

Vectors
5 – 7
  • Understand that 2a is parallel to a and twice its length
  • Understand that a is parallel to -a and in the opposite direction
  • Use and interpret vectors as displacements in the plane (with an associated direction)
  • Use standard vector notation to combine vectors by addition, e.g. AB + BC

    AC and a + b

    c
  • Represent vectors, and combinations of vectors, in the plane
  • Solve geometrical problems in 2-D, e.g. show that joining the mid-points of the sides of any quadrilateral forms a parallelogram
A
A
A
A
A
A*
Transformations of graphs
5 – 7
  • § Represent translations in the x and y direction, reflections in the x-axis and the y‑axis, and stretches parallel to the x-axis and the y-axis
  • § Sketch the graph of y = 3 sin 2x, given the graph of y=sin x
  • § Sketch the graph of y = f(x + 2), y = f(x) + 2, y=2f(x), y = f(2x) given the shape of the graph y = f(x)
  • § Find the coordinates of the minimum of y = f(x + 3), y = f(x) + 3 given the coordinates of the minimum of y=x2 – 2x
A*
A*
A*