UK MATH GRADE 12 – EDmama UK

A. Numbers and Counting

A.01. Understand roots of integers and rational numbers
A.02. Find roots using a calculator
A.03. Define and compute Nth roots
A.04. Evaluate rational indices
A.05. Simplify radical expressions with variables
A.06. Multiply and divide radical expressions
A.07. Evaluate expressions involving rational indices
A.08. Add and subtract radical expressions
A.09. Simplify radical expressions using the distributive property and conjugates
A.10. Use power rules to simply rational indices
A.11. Add, subtract, multiply and divide numbers with rational indices

B. Equations and Inequalities

B.01. Solve linear equations
B.02. Solve linear inequalities
B.03. Graph a linear inequality in one variable
B.04. Solve linear equations: word problems
B.05. Write a linear inequality: word problems
B.06. Graph solutions to linear inequalities
B.07. Write inequalities from graphs
B.08. Graph a linear inequality in the coordinate plane
B.09. Solve absolute value equations
B.10. Solve absolute value inequalities
B.11. Graph solutions to absolute value equations
B.12. Graph solutions to absolute value inequalities
B.13. Graph solutions to quadratic inequalities
B.14. Solve quadratic inequalities
B.15. Apply properties of equality to solve complex multi-step equations
B.16. Solve complex inequalities involving compound statements and absolute value

C. Factorising

C.01. Factorise out a monomial
C.02. Factorise quadratics using algebra tiles
C.03. Factorise quadratics
C.04. Factorise using a quadratic pattern
C.05. Factorise by grouping
C.06. Factorise sums and differences of cubes
C.07. Factorise polynomials
C.08. Factorise by recognizing special polynomial forms (e.g., difference of squares, perfect square trinomials)
C.09. Apply factorisation techniques to simplify rational expressions and solve equations

D. Functions and Relations

D.01. Identify functions
D.02. Domain and range
D.03. Evaluate functions
D.04. Find values using function graphs
D.05. Complete a table for a function graph
D.06. Find the gradient of a linear function
D.07. Graph a linear function
D.08. Write linear equations in standard form
D.09. Write linear equations in point-gradient form
D.10. Write an equation for a parallel or perpendicular line
D.11. Gradients of parallel and perpendicular lines
D.12. Complete a function table: absolute value functions
D.13. Graph an absolute value function
D.14. Linear functions over unit intervals
D.15. Analyse and interpret key features of function graphs, including intercepts, slope, and asymptotes
D.16. Sketch graphs of functions based on their algebraic representations and transformations

E. Simultaneous Equations

E.01. Is (x, y) a solution to the simultaneous equations?
E.02. Solve simultaneous equations by graphing
E.03. Find the number of solutions to simultaneous equations
E.04. Solve simultaneous equations using substitution
E.05. Solve simultaneous equations using elimination
E.06. Solve simultaneous equations using any method
E.07. Solve simultaneous equations by graphing: word problems
E.08. Solve simultaneous equations using substitution: word problems
E.09. Solve simultaneous equations using elimination: word problems
E.10. Solve simultaneous equations using any method: word problems
E.11. Solve nonlinear simultaneous equations
E.12. Apply simultaneous equations to model and solve real-world problems involving multiple variables
E.13. Interpret the solution sets of simultaneous equations in the context of the problem

F. Quadratic Functions

F.01. Characteristics of quadratic functions
F.02. Complete a function table: quadratic functions
F.03. Graph a quadratic function
F.04. Match quadratic functions and graphs
F.05. Find a quadratic function
F.06. Solve a quadratic equation using square roots
F.07. Solve a quadratic equation using the zero product property
F.08. Solve a quadratic equation by factorising
F.09. Complete the square
F.10. Solve a quadratic equation using the quadratic formula
F.11. Using the discriminant
F.12. New! Modelling projectile motion with quadratic equations
F.13. Analyze the effect of changing parameters on the graph of a quadratic function (e.g., vertex form)
F.14. Solve real-world problems involving optimization of quadratic functions (e.g., maximizing area, minimizing cost)

G. Radical functions and expressions

G.01. Domain and range of radical functions
G.02. Simplify radical expressions with variables I
G.03. Simplify radical expressions with variables II
G.04. Multiply radical expressions
G.05. Divide radical expressions
G.06. Add and subtract radical expressions
G.07. Simplify radical expressions using the distributive property
G.08. Simplify radical expressions using conjugates
G.09. Solve radical equations
G.10. Identify extraneous solutions when solving radical equations
G.11. Sketch graphs of radical functions and identify key features (e.g., intercepts, domain, range)

H. Rational functions and expressions

H.01. Rational functions: asymptotes and excluded values
H.02. Evaluate rational expressions I
H.03. Evaluate rational expressions II
H.04. Simplify rational expressions
H.05. Multiply and divide rational expressions
H.06. Add and subtract rational expressions
H.07. Solve rational equations
H.08. Analyze and classify discontinuities (holes and asymptotes) of rational functions
H.09. Use long division or synthetic division to rewrite improper rational expressions
H.10. Apply knowledge of rational functions to model real-world scenarios involving rates and ratios

I. Polynomials

I.01. Polynomial vocabulary
I.02. Add and subtract polynomials
I.03. Multiply polynomials
I.04. Divide polynomials using long division
I.05. Find the roots of factorised polynomials
I.06. Solve polynomial equations
I.07. Write a polynomial from its roots
I.08. Rational root theorem
I.09. Descartes’ Rule of Signs
I.10. Match polynomials and graphs
I.11. Pascal’s triangle
I.12. Pascal’s triangle and the Binomial Theorem
I.13. Binomial Theorem I
I.14. Binomial Theorem II
I.15. Fundamental Theorem of Algebra
I.16. Apply polynomial division to factor higher-degree polynomials
I.17. Prove polynomial identities and use them to simplify expressions
I.18. Determine end behavior of polynomial functions based on their degree and leading coefficient

J. Function operations

J.01. Add and subtract functions
J.02. Multiply functions
J.03. Divide functions
J.04. Composition of linear functions: find a value
J.05. Composition of linear functions: find an equation
J.06. Composition of linear and quadratic functions: find a value
J.07. Composition of linear and quadratic functions: find an equation
J.08. Identify inverse functions
J.09. Find values of inverse functions from tables
J.10. Find values of inverse functions from graphs
J.11. Find inverse functions and relations
J.12. Verify inverse relationships using function composition
J.13. Determine if a function is one-to-one and therefore has an inverse
J.14. Restrict the domain of a function to make it invertible

K. Families of functions

K.01. Translations of functions
K.02. Reflections of functions
K.03. Dilations of functions
K.04. Describe function transformations
K.05. Transformations of functions
K.06. Function transformation rules
K.07. Combine multiple transformations to graph complex functions
K.08. Write equations of transformed functions given their graphs or descriptions
K.09. Analyze the effect of transformations on key features of functions (e.g., intercepts, asymptotes)

L. Logarithms

L.01. Convert between exponential and logarithmic form: rational bases
L.02. Evaluate logarithms
L.03. Identify properties of logarithms
L.04. Product property of logarithms
L.05. Quotient property of logarithms
L.06. Power property of logarithms
L.07. Change of base formula
L.08. Properties of logarithms: mixed review
L.09. Evaluate logarithms: mixed review
L.10. Apply the change-of-base formula to evaluate logarithms with any base
L.11. Prove logarithmic identities using the properties of exponents and logarithms
L.12. Model and solve real-world problems involving logarithmic scales (e.g., Richter scale, decibel scale)

M. Exponential and logarithmic functions

M.01. Domain and range of exponential and logarithmic functions
M.02. Evaluate exponential functions
M.03. Match exponential functions and graphs
M.04. Solve exponential equations by rewriting the base
M.05. Solve exponential equations using common logarithms
M.06. Solve logarithmic equations I
M.07. Solve logarithmic equations II
M.08. Identify linear and exponential functions
M.09. Exponential functions over unit intervals
M.10. Describe linear and exponential growth and decay
M.11. Exponential growth and decay: word problems
M.12. Compound interest: word problems
M.13. Continuously compounded interest: word problems
M.14. Graph exponential and logarithmic functions and identify key features (e.g., intercepts, asymptotes)
M.15. Determine the exponential growth or decay rate from a given function or data set
M.16. Solve complex exponential and logarithmic equations using algebraic techniques and graphical methods

N. Parabolas

N.01. Identify the direction a parabola opens
N.02. Find the vertex of a parabola
N.03. Find the axis of symmetry of a parabola
N.04. Find the focus or directrix of a parabola
N.05. Write equations of parabolas in vertex form from graphs
N.06. Write equations of parabolas in vertex form using properties
N.07. Convert equations of parabolas from general to vertex form
N.08. Find properties of a parabola from equations in general form
N.09. Graph parabolas
N.10. Apply properties of parabolas to solve real-world problems involving reflection and optimization
N.11. Derive the equation of a parabola given its focus and directrix
N.12. Analyze the relationship between the equation of a parabola and its geometric properties

O. Angle measures

O.01. Quadrants
O.02. Graphs of angles
O.03. Convert between radians and degrees
O.04. Radians and arc length
O.05. Coterminal angles
O.06. Reference angles
O.07. Apply radians to solve real-world problems involving circular motion and angular speed
O.08. Use angle measures to determine trigonometric function values
O.09. Relate angle measures to points on the unit circle

P. Trigonometry

P.17. Solve a triangle
P.18. Area of a triangle: sine formula
P.19. Area of a triangle: Law of Sines
P.20. Solve trigonometric equations I
P.21. Solve trigonometric equations II
P.22. Apply trigonometric ratios to solve problems involving angle of elevation and depression
P.23. Derive the Law of Sines and Law of Cosines using geometric arguments
P.24. Determine the number of possible triangles given side-side-angle (SSA) information (ambiguous case)
P.01. Pythagoras’ Theorem and its converse
P.02. Special right triangles
P.03. Trigonometric ratios: sin, cos and tan
P.04. Trigonometric ratios: csc, sec and cot
P.05. Find trigonometric ratios using the unit circle
P.06. Sin, cos and tan of special angles
P.07. Csc, sec and cot of special angles
P.08. Trigonometric ratios in similar right triangles
P.09. Find trigonometric functions using a calculator
P.10. Inverses of sin, cos and tan
P.11. Inverses of csc, sec and cot
P.12. Trigonometric ratios: find a side length
P.13. Trigonometric ratios: find an angle measure
P.14. Solve a right triangle
P.15. Law of Sines
P.16. Law of Cosines

Q. Trigonometric functions

Q.01. Find properties of sine functions
Q.02. Write equations of sine functions from graphs
Q.03. Write equations of sine functions using properties
Q.04. Graph sine functions
Q.05. Find properties of cosine functions
Q.06. Write equations of cosine functions from graphs
Q.07. Write equations of cosine functions using properties
Q.08. Graph cosine functions
Q.09. Graph sine and cosine functions
Q.10. Analyze and describe the transformations of trigonometric functions (amplitude, period, phase shift, vertical shift)
Q.11. Model periodic phenomena using trigonometric functions (e.g., sound waves, tides)
Q.12. Graph trigonometric functions using technology and identify key features

R. Trigonometric identities

S. Circles

S.01. Central angles
S.02. Arcs and chords
S.03. Tangent lines
S.04. Inscribed angles
S.05. Angles in inscribed right triangles
S.06. Angles in inscribed quadrilaterals
S.07. Solve problems involving relationships between angles, arcs, and chords in circles
S.08. Construct tangent lines to circles using compass and straightedge
S.09. Apply circle theorems to solve real-world problems involving circular shapes

T. Circles in the coordinate plane

T.01. Find the centre of a circle
T.02. Find the radius or diameter of a circle
T.03. Write equations of circles in standard form from graphs
T.04. Write equations of circles in standard form using properties
T.05. Convert equations of circles from general to standard form
T.06. Find properties of circles from equations in general form
T.07. Graph circles
T.08. Derive the equation of a circle given its center and radius
T.09. Solve problems involving tangent lines to circles in the coordinate plane
T.10. Analyze the relationship between the equation of a circle and its geometric properties

U. Sequences and series

U.01. Classify formulas and sequences
U.02. Find terms of an arithmetic sequence
U.03. Find terms of a geometric sequence
U.04. Find terms of a recursive sequence
U.05. Evaluate formulas for sequences
U.06. Write a formula for an arithmetic sequence
U.07. Write a formula for a geometric sequence
U.08. Write a formula for a recursive sequence
U.09. Sequences: mixed review
U.10. Introduction to sigma notation
U.11. Identify arithmetic and geometric series
U.12. Find the sum of a finite arithmetic or geometric series
U.13. Introduction to partial sums
U.14. Partial sums of arithmetic series
U.15. Partial sums of geometric series
U.16. Partial sums: mixed review
U.17. Convergent and divergent geometric series
U.18. Find the value of an infinite geometric series
U.19. Write a repeating decimal as a fraction
U.20. Apply sequences and series to model real-world situations involving growth and decay
U.21. Prove formulas for the sums of arithmetic and geometric series using mathematical induction
U.22. Determine the convergence or divergence of infinite series using various tests

V. Probability

V.01. Introduction to probability
V.02. Theoretical and experimental probability
V.03. Compound events: find the number of outcomes
V.04. Factorials
V.05. Calculate probabilities of events
V.06. Counting principle
V.07. Permutations
V.08. Permutation and combination notation
V.09. Find probabilities using permutations and combinations
V.10. Find probabilities using two-way frequency tables
V.11. Identify independent events
V.12. Probability of independent and dependent events
V.13. Geometric probability
V.14. Find conditional probabilities
V.15. Independence and conditional probability
V.16. Find conditional probabilities using two-way frequency tables
V.17. Find probabilities using the addition rule
V.18. Apply probability concepts to analyze real-world scenarios involving risk and decision-making
V.19. Construct and interpret probability distributions
V.20. Use simulation to estimate probabilities and evaluate statistical claims

W. Statistics

X. Data and graphs

X.01. Interpret bar graphs for continuous data
X.02. Create bar graphs for continuous data
X.03. Interpret stem-and-leaf plots
X.04. Interpret box-and-whisker plots
X.05. Interpret a scatter plot
X.06. Scatter plots: line of best fit
X.07. Create and interpret histograms and frequency polygons
X.08. Analyze data sets to identify trends, patterns, and relationships
X.09. Use technology to create and analyze statistical graphs

Y. Introduction to limits

Z. Calculate limits

Z.01. Find limits using addition, subtraction and multiplication laws
Z.02. Find limits using the division law
Z.03. Find limits using power and root laws
Z.04. Find limits using limit laws
Z.05. Find limits of polynomials and rational functions
Z.06. Find limits involving factorisation and rationalisation
Z.07. Find limits involving absolute value functions
Z.08. Find limits involving trigonometric functions
Z.09. Evaluate limits using L’Hôpital’s Rule
Z.10. Determine limits at infinity and analyze the end behavior of functions
Z.11. Evaluate complex limits involving indeterminate forms

AA. Limits and rational functions

AA.01. Find limits at vertical asymptotes using graphs
AA.02. Determine end behaviour using graphs
AA.03. Determine end behaviour of polynomial and rational functions
AA.04. Find the limit at a vertical asymptote of a rational function I
AA.05. Find the limit at a vertical asymptote of a rational function II
AA.06. Analyze the relationship between limits and asymptotes of rational functions
AA.07. Use limits to identify slant asymptotes of rational functions
AA.08. Apply limit concepts to solve real-world problems involving rates of change and optimization

BB. Continuity

BB.01. Identify graphs of continuous functions
BB.02. Determine continuity using graphs
BB.03. Determine one-sided continuity using graphs
BB.04. Find and analyse points of discontinuity using graphs
BB.05. Determine continuity on an interval using graphs
BB.06. Determine the continuity of a piecewise function at a point
BB.07. Make a piecewise function continuous
BB.08. Intermediate Value Theorem
BB.09. Apply the Squeeze Theorem to determine the limit of a function
BB.10. Prove the continuity of a function using the formal definition
BB.11. Apply the Intermediate Value Theorem to prove the existence of roots of functions

CC. Introduction to derivatives

CC.01. Average rate of change I
CC.02. Average rate of change II
CC.03. Find instantaneous rates of change
CC.04. Velocity as a rate of change
CC.05. Find values of derivatives using limits
CC.06. Find the gradient of a tangent line using limits
CC.07. Find equations of tangent lines using limits
CC.08. Power rule I
CC.09. Power rule II
CC.10. Find derivatives of polynomials
CC.11. Find second derivatives of polynomials
CC.12. Analyze the relationship between differentiability and continuity
CC.13. Use derivatives to determine intervals of increasing and decreasing behavior of a function
CC.14. Apply derivatives to solve optimization problems involving maximizing or minimizing quantities

Course Content

A. Numbers and Counting

A.01. Understand roots of integers and rational numbers

A.02. Find roots using a calculator

A.03. Define and compute Nth roots

A.04. Evaluate rational indices

A.05. Simplify radical expressions with variables

A.06. Multiply and divide radical expressions

A.07. Evaluate expressions involving rational indices

A.08. Add and subtract radical expressions

A.09. Simplify radical expressions using the distributive property and conjugates

A.10. Use power rules to simply rational indices

A.11. Add, subtract, multiply and divide numbers with rational indices

B. Equations and Inequalities

B.01. Solve linear equations

B.02. Solve linear inequalities

B.03. Graph a linear inequality in one variable

B.04. Solve linear equations: word problems

B.05. Write a linear inequality: word problems

B.06. Graph solutions to linear inequalities

B.07. Write inequalities from graphs

B.08. Graph a linear inequality in the coordinate plane

B.09. Solve absolute value equations

B.10. Solve absolute value inequalities

B.11. Graph solutions to absolute value equations

B.12. Graph solutions to absolute value inequalities

B.13. Graph solutions to quadratic inequalities

B.14. Solve quadratic inequalities

B.15. Apply properties of equality to solve complex multi-step equations

B.16. Solve complex inequalities involving compound statements and absolute value

C. Factorising

C.01. Factorise out a monomial

C.02. Factorise quadratics using algebra tiles

C.03. Factorise quadratics

C.04. Factorise using a quadratic pattern

C.05. Factorise by grouping

C.06. Factorise sums and differences of cubes

C.07. Factorise polynomials

C.08. Factorise by recognizing special polynomial forms (e.g., difference of squares, perfect square trinomials)

C.09. Apply factorisation techniques to simplify rational expressions and solve equations

D. Functions and Relations

D.01. Identify functions

D.02. Domain and range

D.03. Evaluate functions

D.04. Find values using function graphs

D.05. Complete a table for a function graph

D.06. Find the gradient of a linear function

D.07. Graph a linear function

D.08. Write linear equations in standard form

D.09. Write linear equations in point-gradient form

D.10. Write an equation for a parallel or perpendicular line

D.11. Gradients of parallel and perpendicular lines

D.12. Complete a function table: absolute value functions

D.13. Graph an absolute value function

D.14. Linear functions over unit intervals

D.15. Analyse and interpret key features of function graphs, including intercepts, slope, and asymptotes

D.16. Sketch graphs of functions based on their algebraic representations and transformations

E. Simultaneous Equations

E.01. Is (x, y) a solution to the simultaneous equations?

E.02. Solve simultaneous equations by graphing

E.03. Find the number of solutions to simultaneous equations

E.04. Solve simultaneous equations using substitution

E.05. Solve simultaneous equations using elimination

E.06. Solve simultaneous equations using any method

E.07. Solve simultaneous equations by graphing: word problems

E.08. Solve simultaneous equations using substitution: word problems

E.09. Solve simultaneous equations using elimination: word problems

E.10. Solve simultaneous equations using any method: word problems

E.11. Solve nonlinear simultaneous equations

E.12. Apply simultaneous equations to model and solve real-world problems involving multiple variables

E.13. Interpret the solution sets of simultaneous equations in the context of the problem

F. Quadratic Functions

F.01. Characteristics of quadratic functions

F.02. Complete a function table: quadratic functions

F.03. Graph a quadratic function

F.04. Match quadratic functions and graphs

F.05. Find a quadratic function

F.06. Solve a quadratic equation using square roots

F.07. Solve a quadratic equation using the zero product property

F.08. Solve a quadratic equation by factorising