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Stage G
Topic 1: Inequalities
1. TBAT solve inequalities and express the solution in the required form
S1 TBAT use inequalities to specify error intervals due to rounding e.g. writing
limits of accuracy (not bounds)
S2 TBAT express inequalities on a number line
S3 TBAT solve inequalities in one variable and show the solution on a number line
S4 TBAT solve inequalities in closed intervals 4 < 3 𝑛 + 1 ≤ 10
Topic 2: Calculations
1. TBAT use BIDMAS to calculate solutions
S1 TBAT solve problems involving 3 operations with mixed fractions
S2 TBAT solve problems involving 3 operations with mixed fractions and negatives
Topic 3: Surface Area
1. TBAT know and apply the formulae to calculate the surface area of any shape
S1 TBAT calculate the surface area of cones and spheres including frustums
S2 TBAT calculate the surface area of composite shapes
S3 TBAT calculate the surface area of shapes in context
Topic 4: Volume
1. TBAT know and apply the formulae to calculate the volume of a shape
S1 TBAT calculate the volume of pyramids and prism’s including frustums
S2 TBAT calculate the volume of composite shapes
S3 TBAT calculate the volume of the above shapes in context
Topic 5: Indices
1. TBAT state and use the laws of indices, with integer indices and multiple operations
S1 TBAT simplify expressions involving three laws; 𝑎
𝑛
× 𝑎
𝑚
𝑚+𝑛
𝑛
÷ 𝑎
𝑚
𝑚−𝑛
𝑛
𝑚
𝑚𝑛
S2 TBAT simplify expressions using the negative indices law
S3 TBAT simplify expressions using properties from S1 and S
Topic 6: Probability
1. TBAT calculate the probability of successive dependent events (not replacing)
S1 TBAT construct a fully labelled tree diagram to list outcomes
S2 TBAT use a tree diagram to calculate the probabilities of dependent events
S3 TBAT understand when to use the and/or rule to calculate dependent
probability
Topic 7 : Pythagoras’ Theorem
1. TBAT use Pythagoras’ theorem in right - angled triangles (2D problems)
S1 TBAT identify when to use Pythagoras’ theorem – a right-angled triangle and
its hypotenuse
S2 TBAT show whether a triangle is right-angled or not
S3 TBAT calculate the length of the hypotenuse
S4 TBAT calculate the length of the shorter side
TBAT apply Pythagoras’ theorem in context
S1 TBAT solve worded problems involving Pythagoras’ theorem (ladders against
walls, bearings)
S2 TBAT find the distance between two points from their coordinates
Topic 8: Standard Form
1. TBAT express very big and very small numbers in a more efficient way
S1 TBAT convert ordinary numbers into standard form, with positive and negative
indices
S2 TBAT convert numbers in standard form with positive and negative indices, to
ordinary numbers
TBAT solve problems calculating with numbers expressed in standard form
S1 TBAT ordinary numbers in standard form (e.g. ordering the mass of different
planets)
S2 TBAT solve problems involving adding and subtracting numbers in standard
form
S3 TBAT solve problems involving multiplying and dividing numbers in standard
form
S4 TBAT enter values in standard form into the calculator
Topic 9 : Venn Diagrams
1. TBAT use set notation to define sets
S1 TBAT know the meaning of the universal set, ξ
S2 TBAT list members of a set from given notation including ∈
S3 TBAT write a set from a description using set notation including ∈
TBAT draw Venn diagrams
S1 TBAT draw sets given a universal set and two subsets with overlaps
S2 TBAT draw sets given a universal set and three subsets with overlaps
S3 TBAT interpret from a Venn diagram
S4 TBAT solve problems using Venn diagrams
To be able to use and define intersection, union, complements and subsets
S1 TBAT list set members from set notation including ∪, ∩, A’, A ⊆ B, A ⊂ B
S2 TBAT write sets using notation including ∪, ∩, A’, A ⊆ B, A ⊂ B
S3 TBAT draw Venn diagrams from sets using notation including ∪, ∩, A’, A ⊆ B,
A ⊂ B
S4 TBAT solve problems using intersection, union, complements and subsets
Topic 10: Rearranging Formula
1. TBAT change the subject of a simple formula
S1 TBAT rearrange the subject of a formula where subject appears once e.g make
x the subject in y=mx+c
S2 TBAT rearrange the subject of a simple formula involving brackets e.g make x
the subject y=3(2x-2)
S3 TBAT rearrange the subject of a simple formula involving brackets and
fractions e.g y=2(3x+2)/
Stage H
Topic 1: Graphing (Core)
2. TBAT plot, interpret and sketch graphs of quadratics
S1 TBAT identify where a quadratic crosses the y-axis.
S2 TBAT identify where a quadratic will cross the x-axis
S3 TBAT identify the turning point of a quadratic
S4 TBAT understand the property of symmetry of a quadratic
3. TBAT plot and interpret graphs of cubics
S1 TBAT plot the graph of 𝑦 = 𝑥
3
S2 TBAT plot graphs of the form 𝑦 = 𝑥
3
3
4. TBAT plot and interpret graphs of the reciprocal function
S1 TBAT plot and interpret graphs of positive reciprocal functions
S2 TBAT plot and interpret graphs of negative reciprocal functions
5. TBAT interpret and sketch graphs of real life graphs
S1 TBAT interpret graphs involving straight lines, quadratics, cubics and
reciprocals
S2 TBAT sketch graphs of real life situations.
S3 TBAT identify graphs of proportion
Topic 2: Trigonometry
1. TBAT know and use the trigonometric ratios SOH/CAH/TOA in right angled triangles
S1 TBAT understand the link between the trig ratios and similarity
S2 TBAT identify the parts of a right-angled triangle (hypotenuse, opposite and
adjacent sides)
S3 TBAT find missing sides in right-angled triangles, using all three ratios
S4 TBAT find missing angles in right-angled triangles, using all three ratios
2. TBAT apply the trigonometric ratios in context
S1 TBAT solve problems involving a diagram
S2 TBAT solve problems expressed in words by sketching and labelling diagrams
S3 TBAT solve problems involving bearings
Topic 3: Shape (Core)
1. TBAT use similarity
S1 TBAT identify the properties of similarity by comparing lengths and angles
S2 TBAT calculate the scale factor for similar shapes to find missing lengths
Topic 4: Simultaneous Equations
1. TBAT solve simultaneous equations with unknowns on both sides, including brackets
S1 TBAT solve simultaneous equations using elimination where one variable is
equal.
S2 TBAT solve simultaneous equations using elimination.
S3 TBAT solve simultaneous equations using substitution.
S4 TBAT solve simultaneous equations graphically.
Topic 5: Percentages (Core)
2. TBAT calculate proportional change
S1 TBAT calculate repeated percentage change
S2 TBAT calculate compound interest
S3 TBAT calculate depreciation
S4 TBAT set up and solve growth and decay problems
Topic 6: Vectors
2. Solve simple geometrical problems in 2D using vectors, including use of the commutative and
associative properties of vector addition.
S2 TBAT Rationalising the denominator where the denominator isn’t a pure surd
3
3
1
4
Topic 3: Algebra
2. TBAT expand brackets
S1 TBAT expand double brackets with more than two terms (𝑥 − 1 )(𝑥 + 𝑦 − 𝑧)
S2 TBAT expand products of two or more binomials (𝑥 + 1 )(𝑥 − 3 )(𝑥 + 5 )
3. TBAT factorise quadratics where the coefficient of the 𝒙
𝟐
term is not 𝟏 or −𝟏.
S1 TBAT factorise simple quadratics where |𝑎| > 1 , 6 𝑥
2
S2 TBAT factorise more complex quadratics where
2
2
4. TBAT solve quadratic equations using an appropriate strategy
S1 TBAT solve a quadratic equation using factorising where
S2 TBAT solve a quadratic equation using the formula.
S3 TBAT solve quadratic equations requiring rearranging.
S4 TBAT form and solve quadratic equations given in different contexts.
Topic 4: Representing Data
3. TBAT construct and interpret histograms with unequal class widths
S1 TBAT construct a histogram from a grouped frequency table
S2 TBAT complete a frequency table given the histogram
S3 TBAT complete an incomplete histogram and frequency table
S4 TBAT make estimates from different ranges in the histogram
- TBAT find the interquartile range and use it to compare data sets
S1 TBAT find the interquartile range from a data set
S2 TBAT compare data sets using the median and the interquartile range
- TBAT interpret and construct cumulative frequency diagram
S1 TBAT construct a cumulative frequency diagram from a grouped frequency table
S2 TBAT identify the median, the quartiles and the IQR from a cumulative frequency
diagram
- TBAT Find Mean, Median and Mode from a frequency table
S1 TBAT find Mean, Median and Mode from a frequency table
S2 TBAT find the class which contain the mode, median and find estimate of mean from
a group frequency table.
S1 TBAT derive the sine rule and know its limitations
S2 TBAT use the sine rule to find missing sides in any triangle
S3 TBAT use the sine rule to find missing angles in any triangle
S4 TBAT solve problems involving exact values
3. TBAT know and apply the cosine rule to find unknown lengths and angles
S1 TBAT derive the cosine rule and know its limitations
S2 TBAT use the cosine rule to find missing sides in any triangle
S3 TBAT use the cosine rule to find missing angles in any triangle
S4 TBAT solve problems involving exact values
- TBAT know and apply area =
𝟏
𝟐
ab𝐬𝐢𝐧 𝒄
S1 TBAT derive the sine area formula
S2 TBAT use the formula for the area of a non-right angled triangles
S3 TBAT find a missing side given the area and an angle
S4 TBAT solve problems involving exact values
Topic 6: Formulae
2. TBAT change the subject of a formula where the variable appears twice
S1 TBAT rearrange equation such as 5 𝑥 + 𝑎 = 3 𝑥 + 𝑏
S2 TBAT rearrange equation such as 𝑝 =
𝑎𝑏+𝑐
𝑏−𝑑
S3 TBAT rearrange equation such as 𝑎 = 𝑏 +
𝑏𝑐
3
S4 TBAT rearrange equation such as 𝑇 = 2 𝜋√
𝑙
𝑔
S5 TBAT rearrange equation such as 𝑉 =
4
3
3
Topic 7: Circles
5. TBAT solve problems involving the angle properties of circles
S1 TBAT use that the angle in a semi-circle is 90°
S2 TBAT use that the opposite angles in a cyclic quad add to 180°
S3 TBAT use that the angle subtended by an arc is always the same
S4 TBAT use that the angle subtended by an arc at the centre of a circle is twice the angle
subtended at any point on the circumference
S5 TBAT understand that if two Chords PQ and RS cross at point T, then PTxQT=RTxST, it
is true whether T is inside or outside of a circle.
6. TBAT solve problems involving tangents and chords
S1 TBAT understand that tangent at any point on a circle is perpendicular to the radius
S2 TBAT know that the perpendicular bisector of any chord will pass through the centre
S3 TBAT use the alternative segment theorem
Topic 8: Proportion
3. TBAT form and evaluate a formula which models a direct proportion relationship.
S1 TBAT understand the meaning and notation of direct proportion
S2 TBAT form formulas to express a direct proportion relationship with no powers
S3 TBAT form formulas to express a direct proportion relationship with powers
S4 TBAT form formulas to express a direct proportion relationship with more than two
variables and powers
S5 TBAT form formulas to express a direct proportion relationship with more than two
variables and powers
4. TBAT form and evaluate a formula which models an indirect proportion relationship.
S1 TBAT understand the meaning and notation of indirect proportion
S2 TBAT form formulas to express an indirect proportion relationship with no powers
S3 TBAT form formulas to express an indirect proportion relationship with powers
S4 TBAT form formulas to show an indirect proportion relationship with more than two
variables and powers
5. TBAT solve mixed proportion problems.
S1 TBAT form formulae for problems involving both direct & indirect proportion (no
powers) and use to solve problems.
S2 TBAT form formulae for problems involving both direct & indirect proportion (with
powers) and use to solve problems.
6. TBAT identify, sketch and construct the graphs of direct and indirect relationships.
S1 TBAT identify and interpret graphs of direct proportion relationship
S2 TBAT identify and interpret graphs of indirect proportion relationship
Topic 9: Probability
1. TBAT calculate non-conditional probability using a variety of methods to sort data
S1 TBAT solve simple problems involving cards, dice or coins.
S2 TBAT interpret non-conditional probabilities from a tree diagram
S3 TBAT interpret non-conditional probabilities from a Venn diagram
S4 TBAT construct a diagram to interpret a context and then calculate probabilities from
it
2. TBAT interpret conditional probability
S1 TBAT solve problems where an item is removed and not replaced using tree diagrams
S2 TBAT solve problems where items are removed with more than two events
Topic 10: Functions
1. TBAT use function notation to find a numerical solution
S1 TBAT find solutions to simple functions using the correct notation 𝑓(𝑥) = 3 𝑥 − 1 , find
S2 TBAT find solution give more complex functions 𝑓
𝑥
2
− 6
3 − 2 𝑥
, find 𝑓( 3 )
Topic 11: Graphing
3. TBAT solve problems involving perpendicular and parallel lines
S1 TBAT solve problems involving perpendicular lines
S2 TBAT solve problems involving perpendicular and parallel lines
S2 TBAT find the equation of a line parallel or perpendicular to a given line
- TBAT sketch graphs of quadratics after completing the square
S1 TBAT identify the turning point and y-intercept of a quadratic after completing the
square
S2 TBAT sketch the graphs of quadratics after completing the square
5. TBAT to find the gradient and intersection of graphs
S1 TBAT find the gradient of non-liner graphs by drawing the tangent
S2 TBAT find the point of intersection of a linear (y=2x +1) and non-linear (y=x
2
+3x-2)
graph and recognise that the solutions correspond to x
2
+x-3=
Topic 12: Constructions
1. TBAT draw 2D shapes accurately and can draw perpendicular bisector of a line
and angle.
S1 TBAT construct triangles and other two-dimensional shapes using a
combination of a ruler, a protractor and pair of compass
S2 TBAT solve problems using scale drawings
S3 TBAT use straight edge and compasses to:
(i) construct the perpendicular bisector
of a line segment
(ii) construct the bisector of an angle
S2 TBAT find the area of a sector of a circle
Topic 4: Quadratics
5. TBAT solve a quadratic by completing the square
S1 TBAT express a quadratic in completed square form
S2 TBAT solve a quadratic by completing the square
S3 TBAT identify the turning point and y-intercept of a quadratic after completing the
square
S4 TBAT sketch the graphs of quadratics after completing the square
TBAT solve simultaneous equations where one is quadratic and the other is linear
S1 TBAT solve problems already in the correct form which can be factorised. 𝑦 = 𝑥 +
2
S2 TBAT solve problems which have to be rearranged and can be factorised. 𝑦 − 𝑥 =
2
S3 TBAT solve problems which require the use of the quadratic formula. 𝑦 = 𝑥 + 3 , 𝑦 =
2
Topic 5: Graphing
5. TBAT recognise, sketch and interpret the graphs of the trigonometric functions
S1 TBAT recognise, sketch and interpret the graph of sinx,cosx and tanx
S2 TBAT recognise, sketch and interpret the graph of quadratic, cubic, reciprocal and
exponential functions, e.g be able to identify and sketch graphs of y = x
3
− 3 x, y = 2
x
, y
4
x
, y = 8 x − 2 x
2
etc
Topic 6: Functions
3. TBAT find the inverse of a function using the correct notation
Simple functions only using the 4 main operations. 𝑓
= 3 𝑥 − 1 , find 𝑓(− 1 )
Functions involving squares and cubes. 𝑓(𝑥) = 3 𝑥
2
− 1
𝑥
3
TBAT find composite functions
Find composite functions with no indices or surds. 𝑓(𝑥) = 3 𝑥 + 1 , 𝑔(𝑥) = 2 − 4 𝑥
Where there are powers and surds. 𝑓
4
2
TBAT transform graphs of functions
S1 TBAT solve problems involving transformations of the form 𝑦 = 𝑓
𝑏), y = f(−x), y = −f(x), 𝑦 = 𝑎𝑓(𝑥)
S 2 TBAT solve problems involving the sketching/interpreting of combined
transformations applied to linear, quadratic, sine, cosine graphs 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑟𝑚 𝑦 =
, y= f(ax+b),y=f(x/a + b) ,y=af(bx+c)
Topic 7: Bounds
7. TBAT state maximum and minimum values as a result of rounding and interpret limits of accuracy
S1 TBAT state the upper and lower bound of a value rounded to a whole number
S2 TBAT state the upper and lower bound of a value rounded to any number of decimal
places
S3 TBAT state the upper and lower bound of a value rounded to any number of significant
figures
8. TBAT use upper and lower bounds in calculations
S1 TBAT upper/Lower bound in addition or multiplication calculations
S2 TBAT upper/lower bound in subtraction or division calculations
S3 TBAT calculate the upper and lower bound of formulae
Topic 8: Similar Shapes
7. TBAT use scale factors and ratios of lengths in calculations involving area
S1 TBAT know that if the ratio of sides is a:b then the ratio of areas is 𝑎
2
2
S2 TBAT use scale factors and ratios of lengths to calculate area
S3 TBAT calculate the scale factor enlargement, given the area of two similar shapes
S4 TBAT solve problems involving area of similar shapes
8. TBAT use scale factors and ratios of lengths in calculations involving area
S1 TBAT know that if the ratio of sides is a:b then the ratio of volume is 𝑎
3
3
S2 TBAT use scale factors and ratios of lengths to calculate volume
S3 TBAT calculate the scale factor enlargement, given the volume of two similar shapes
S4 TBAT solve problems involving volume of similar shapes
Topic 9: Vectors
5. TBAT solve problems using vector geometry
S1 TBAT express lines in terms of vectors
S2 TBAT express line segments in terms of vectors
S3 TBAT lines are parallel or collinear using vector geometry
Topic 10: Sequences
2. TBAT find terms and sums of arithmetic sequences
S1 TBAT understand the common difference (d) and the first term (a) in an arithmetic
sequence
S2 TBAT use the nth term = a +(n-1)d
S3 TBAT find the sum of the first n terms of an arithmetic series (Sn)
Topic 11: Compound Measure
1. TBAT use compound measure
S1 TBAT use compound measure such as speed,
density and pressure (Formula for pressure
will be given )
Topic 12: Proof
1. TBAT proof statements algebraically
S1 TBAT use algebra to support and construct
proofs
Topic 1 3 : Calculus
1. TBAT find and apply rates of change
S1 TBAT understand the concept of a variable rate of change
S2 TBAT differentiate integer powers of x
S3 TBAT determine gradients, rates of change, stationary points, turning points (max,
min) by differentiation and relate these to graphs
S4 TBAT distinguish between maxima and minima by considering the general shape of
the graph only
S5 TBAT find an expression for the velocity and acceleration of a particle, given the
displacement
