UK MATH GRADE 13 – EDmama UK

A. Roots and Rational Indices

A.01. Find roots of integers using calculators.
A.02. Find roots of rational numbers using calculators.
A.03. Evaluate rational indices.
A.04. Simplify radical expressions with variables.
A.05. Perform operations with rational indices.
A.06. Simplify expressions involving rational indices.
A.07. Understand and apply the concept of nth roots.
A.08. Extend knowledge of nth roots to include complex numbers.

B. Trigonometry

B.01. Convert between radians and degrees.
B.02. Identify quadrants in the unit circle.
B.03. Determine coterminal and reference angles.
B.04. Define trigonometric ratios using right triangles.
B.05. Find trigonometric ratios using the unit circle.
B.06. Find sin, cos, and tan using reference angles.
B.07. Find csc, sec, and cot using reference angles.
B.08. Determine trigonometric ratios for special angles (30°, 45°, 60°).
B.09. Apply trigonometric ratios to solve right triangle problems.
B.10. Explore the relationships between trigonometric ratios and their reciprocals.

C. Probability

C.01. Understand basic probability concepts.
C.02. Calculate probabilities of simple events.
C.03. Find probabilities using two-way frequency tables.
C.04. Apply the addition rule to find probabilities.
C.05. Differentiate between combinations and permutations.
C.06. Calculate probabilities using combinations and permutations.
C.07. Define and identify independent events.
C.08. Calculate conditional probabilities.
C.09. Apply conditional probability in independence scenarios.
C.10. Apply Bayes’ Theorem to solve complex conditional probability problems.

D. Statistics

D.01. Calculate variance and standard deviation.
D.02. Identify biased samples in statistical data.
D.03. Identify outliers in a dataset.
D.04. Describe the effect of removing an outlier from a dataset.
D.05. Recognize outliers in scatter plots.
D.06. Match correlation coefficients to scatter plots.
D.07. Calculate correlation coefficients for given data sets.
D.08. Find the equation of a regression line.
D.09. Interpret regression lines in the context of the data.
D.10. Analyze a regression line of a data set.
D.11. Analyze a regression line using statistics of a data set.
D.12. Construct confidence intervals for population means.
D.13. Construct confidence intervals for population proportions.
D.14. Conduct hypothesis tests to draw inferences about population parameters.

E. Sequences and Series

E.01. Find terms of a sequence given a formula.
E.02. Find terms of a sequence defined recursively.
E.03. Identify a sequence as explicit or recursive.
E.04. Find a recursive formula for a given sequence.
E.05. Find both recursive and explicit formulas for a sequence.
E.06. Convert a recursive formula to an explicit formula.
E.07. Convert an explicit formula to a recursive formula.
E.08. Convert between explicit and recursive formulas effectively.
E.09. Understand and apply sigma notation.
E.10. Identify arithmetic and geometric series.
E.11. Find the sum of a finite arithmetic series.
E.12. Find the sum of a finite geometric series.
E.13. Understand partial sums of series.
E.14. Calculate partial sums of arithmetic series.
E.15. Calculate partial sums of geometric series.
E.16. Apply partial sums in mixed review problems.
E.17. Determine if a geometric series is convergent or divergent.
E.18. Find the value of an infinite geometric series.
E.19. Write a repeating decimal as a fraction using geometric series.
E.20. Explore and apply the binomial theorem to expand binomial expressions.

F. Introduction to Derivatives

F.01. Calculate average rate of change over an interval.
F.02. Calculate average rate of change using different methods.
F.03. Determine instantaneous rates of change.
F.04. Relate velocity as a rate of change.
F.05. Find values of derivatives using limits.
F.06. Find the gradient of a tangent line using limits.
F.07. Find equations of tangent lines using limits.
F.08. Explore the relationship between differentiability and continuity.
F.09. Interpret derivatives in real-world contexts.

G. Derivative Rules

G.01. Apply the sum rule to find derivatives.
G.02. Apply the difference rule to find derivatives.
G.03. Apply the product rule to find derivatives.
G.04. Apply the quotient rule to find derivatives.
G.05. Apply the power rule I for derivatives.
G.06. Apply the power rule II for derivatives.
G.07. Apply the chain rule to find derivatives.
G.08. Apply the inverse function rule to find derivatives.
G.09. Combine multiple derivative rules to find derivatives.

H. Calculate Derivatives

H.01. Find derivatives of polynomial functions.
H.02. Find derivatives of rational functions.
H.03. Find derivatives of trigonometric functions I.
H.04. Find derivatives of trigonometric functions II.
H.05. Find derivatives of exponential functions.
H.06. Find derivatives of logarithmic functions.
H.07. Find derivatives of inverse trigonometric functions.
H.08. Find derivatives of radical functions.
H.09. Find derivatives using the product rule I.
H.10. Find derivatives using the product rule II.
H.11. Find derivatives using the quotient rule I.
H.12. Find derivatives using the quotient rule II.
H.13. Find derivatives using the chain rule I.
H.14. Find derivatives using the chain rule II.
H.15. Apply logarithmic differentiation to find derivatives.

I. Trigonometric Functions

I.01. Identify properties of sine functions (amplitude, period, phase shift).
I.02. Identify properties of cosine functions (amplitude, period, phase shift).
I.03. Write equations of sine functions from graphs.
I.04. Write equations of cosine functions from graphs.
I.05. Write equations of sine functions using properties.
I.06. Write equations of cosine functions using properties.
I.07. Graph sine functions.
I.08. Graph cosine functions.
I.09. Graph sine and cosine functions together.
I.10. Analyze and compare transformations of sine and cosine functions.
I.11. Model real-world periodic phenomena using trigonometric functions.

J. Exponential and Logarithmic Functions

J.01. Convert between exponential and logarithmic form.
J.02. Identify the domain and range of exponential functions.
J.03. Identify the domain and range of logarithmic functions.
J.04. Evaluate logarithms.
J.05. Apply the change of base formula.
J.06. Apply the product property of logarithms.
J.07. Apply the quotient property of logarithms.
J.08. Apply the power property of logarithms.
J.09. Evaluate logarithms using properties.
J.10. Solve exponential equations by rewriting the base.
J.11. Solve exponential equations using logarithms.
J.12. Solve logarithmic equations with one logarithm.
J.13. Solve logarithmic equations with multiple logarithms.
J.14. Identify linear and exponential functions.
J.15. Model exponential functions over unit intervals.
J.16. Describe linear and exponential growth and decay.
J.17. Solve exponential growth and decay word problems.
J.18. Solve compound interest word problems.
J.19. Explore and apply logistic growth models.

K. Radical Functions

L. Functions

L.01. Identify functions from relations.
L.02. Determine the domain and range of a function.
L.03. Evaluate functions for given inputs.
L.04. Find values using function graphs.
L.05. Complete a table for a function graph.
L.06. Find the gradient of a linear function.
L.07. Graph a linear function.
L.08. Write the equation of a linear function.
L.09. Model linear functions over unit intervals.
L.10. Add, subtract, multiply and divide functions.
L.11. Compose functions.
L.12. Identify inverse functions.
L.13. Find values of inverse functions from tables.
L.14. Find values of inverse functions from graphs.
L.15. Find inverse functions and relations algebraically.
L.16. Determine the conditions for the existence of an inverse function.
L.17. Analyze and apply piecewise functions in real-world scenarios.

M. Families of Functions

M.01. Describe translations of functions graphically and algebraically.
M.02. Describe reflections of functions graphically and algebraically.
M.03. Describe dilations of functions graphically and algebraically.
M.04. Combine transformations of functions.
M.05. Apply function transformation rules.
M.06. Describe function transformations verbally.
M.07. Predict the effect of transformations on specific points of a function.
M.08. Decompose complex transformations into simpler steps.
M.09. Use transformations to graph complex functions efficiently.

N. Quadratic Functions

N.01. Identify characteristics of quadratic functions (vertex, axis of symmetry).
N.02. Find the maximum or minimum value of a quadratic function.
N.03. Graph a quadratic function.
N.04. Match quadratic functions and graphs.
N.05. Solve a quadratic equation using square roots.
N.06. Solve a quadratic equation by factorising.
N.07. Solve a quadratic equation by completing the square.
N.08. Solve a quadratic equation using the quadratic formula.
N.09. Apply the discriminant to determine the nature of the roots.
N.10. Model real-world scenarios using quadratic functions.
N.11. Analyze and interpret quadratic models in context.

O. Polynomials

O.01. Divide polynomials using long division.
O.02. Write a polynomial from its roots.
O.03. Find the roots of factorised polynomials.
O.04. Apply the Rational Root Theorem to find possible rational roots.
O.05. Apply the Complex Conjugate Theorem.
O.06. Understand and apply Conjugate Root Theorems.
O.07. Apply Descartes’ Rule of Signs to predict the number of real roots.
O.08. Understand the Fundamental Theorem of Algebra.
O.09. Match polynomials and graphs.
O.10. Factorise sums and differences of cubes.
O.11. Solve equations with sums and differences of cubes.
O.12. Factorise using a quadratic pattern.
O.13. Solve equations using a quadratic pattern.
O.14. Construct Pascal’s triangle.
O.15. Relate Pascal’s triangle to the Binomial Theorem.
O.16. Apply the Binomial Theorem I.
O.17. Apply the Binomial Theorem II.
O.18. Factor polynomials using synthetic division.
O.19. Determine the end behavior of polynomial functions.

P. Rational Functions

Q. Simultaneous Equations

Q.01. Solve simultaneous equations by graphing.
Q.02. Solve simultaneous equations by graphing: word problems.
Q.03. Classify simultaneous equations (independent, dependent, inconsistent).
Q.04. Solve simultaneous equations using substitution.
Q.05. Solve simultaneous equations using substitution: word problems.
Q.06. Solve simultaneous equations using elimination.
Q.07. Solve simultaneous equations using elimination: word problems.
Q.08. Solve simultaneous equations in three variables using substitution.
Q.09. Solve simultaneous equations in three variables using elimination.
Q.10. Determine the number of solutions to simultaneous equations in three variables.
Q.11. Apply matrix methods to solve systems of linear equations.

R. Two-Dimensional Vectors

R.01. Find the magnitude of a vector.
R.02. Find the direction angle of a vector.
R.03. Find the component form of a vector.
R.04. Find the component form of a vector from its magnitude and direction angle.
R.05. Find a unit vector.
R.06. Add and subtract vectors graphically and algebraically.
R.07. Multiply a vector by a scalar.
R.08. Find the magnitude or direction of a vector scalar multiple.
R.09. Find the magnitude and direction of a vector sum.
R.10. Express vectors as linear combinations of other vectors.
R.11. Graph a resultant vector using the triangle method.
R.12. Graph a resultant vector using the parallelogram method.
R.13. Apply vector operations to solve problems involving displacement and force.

Course Content

A. Roots and Rational Indices

A.01. Find roots of integers using calculators.

A.02. Find roots of rational numbers using calculators.

A.03. Evaluate rational indices.

A.04. Simplify radical expressions with variables.

A.05. Perform operations with rational indices.

A.06. Simplify expressions involving rational indices.

A.07. Understand and apply the concept of nth roots.

A.08. Extend knowledge of nth roots to include complex numbers.

B. Trigonometry

B.01. Convert between radians and degrees.

B.02. Identify quadrants in the unit circle.

B.03. Determine coterminal and reference angles.

B.04. Define trigonometric ratios using right triangles.

B.05. Find trigonometric ratios using the unit circle.

B.06. Find sin, cos, and tan using reference angles.

B.07. Find csc, sec, and cot using reference angles.

B.08. Determine trigonometric ratios for special angles (30°, 45°, 60°).

B.09. Apply trigonometric ratios to solve right triangle problems.

B.10. Explore the relationships between trigonometric ratios and their reciprocals.

C. Probability

C.01. Understand basic probability concepts.

C.02. Calculate probabilities of simple events.

C.03. Find probabilities using two-way frequency tables.

C.04. Apply the addition rule to find probabilities.

C.05. Differentiate between combinations and permutations.

C.06. Calculate probabilities using combinations and permutations.

C.07. Define and identify independent events.

C.08. Calculate conditional probabilities.

C.09. Apply conditional probability in independence scenarios.

C.10. Apply Bayes’ Theorem to solve complex conditional probability problems.

D. Statistics

D.01. Calculate variance and standard deviation.

D.02. Identify biased samples in statistical data.

D.03. Identify outliers in a dataset.

D.04. Describe the effect of removing an outlier from a dataset.

D.05. Recognize outliers in scatter plots.

D.06. Match correlation coefficients to scatter plots.

D.07. Calculate correlation coefficients for given data sets.

D.08. Find the equation of a regression line.

D.09. Interpret regression lines in the context of the data.

D.10. Analyze a regression line of a data set.

D.11. Analyze a regression line using statistics of a data set.

D.12. Construct confidence intervals for population means.

D.13. Construct confidence intervals for population proportions.

D.14. Conduct hypothesis tests to draw inferences about population parameters.

E. Sequences and Series

E.01. Find terms of a sequence given a formula.

E.02. Find terms of a sequence defined recursively.

E.03. Identify a sequence as explicit or recursive.

E.04. Find a recursive formula for a given sequence.

E.05. Find both recursive and explicit formulas for a sequence.

E.06. Convert a recursive formula to an explicit formula.

E.07. Convert an explicit formula to a recursive formula.

E.08. Convert between explicit and recursive formulas effectively.

E.09. Understand and apply sigma notation.

E.10. Identify arithmetic and geometric series.

E.11. Find the sum of a finite arithmetic series.

E.12. Find the sum of a finite geometric series.

E.13. Understand partial sums of series.

E.14. Calculate partial sums of arithmetic series.

E.15. Calculate partial sums of geometric series.

E.16. Apply partial sums in mixed review problems.

E.17. Determine if a geometric series is convergent or divergent.

E.18. Find the value of an infinite geometric series.

E.19. Write a repeating decimal as a fraction using geometric series.

E.20. Explore and apply the binomial theorem to expand binomial expressions.

F. Introduction to Derivatives

F.01. Calculate average rate of change over an interval.

F.02. Calculate average rate of change using different methods.

F.03. Determine instantaneous rates of change.

F.04. Relate velocity as a rate of change.

F.05. Find values of derivatives using limits.

F.06. Find the gradient of a tangent line using limits.

F.07. Find equations of tangent lines using limits.

F.08. Explore the relationship between differentiability and continuity.

F.09. Interpret derivatives in real-world contexts.

G. Derivative Rules

G.01. Apply the sum rule to find derivatives.