UK MATH GRADE 11 – EDmama UK

A. Numbers and Counting

A.01. Identify prime and composite numbers.
A.02. Understand the definition of a square root and cube root.
A.03. Add, subtract, multiply, and divide rational numbers proficiently.
A.04. Estimate the values of square roots and cube roots without a calculator.
A.05. Identify and differentiate between rational and irrational numbers.
A.06. Compare and order rational numbers on a number line.
A.07. Evaluate numerical expressions involving rational numbers using the order of operations.
A.08. Express recurring decimals as fractions using algebraic methods.
A.09. Explore the properties of rational and irrational numbers within the real number system.
A.10. Apply the concept of significant figures when dealing with approximations of irrational numbers

B. Percents and Proportions

B.01. Understand and calculate basic percentages of given quantities.
B.02. Calculate the percent of change (increase or decrease).
B.03. Solve multi-step problems involving successive percentage changes.
B.04. Calculate sale prices and VAT (Value Added Tax) to find the original price of an item.
B.05. Solve word problems involving percent of change, including finding the original amount.
B.06. Apply percentages in real-world scenarios, such as discounts, taxes, and interest rates.
B.07. Analyze and solve complex percentage problems involving multiple steps and variables.
B.08. Solve reverse percentage problems, finding the original value after a percentage increase or decrease.

C. Expressions and Properties

C.01. Understand and apply the commutative, associative, and distributive properties.
C.02. Identify and combine like terms in algebraic expressions.
C.03. Apply the distributive property to expand and simplify algebraic expressions.
C.04. Write equivalent expressions using the properties of addition and multiplication.
C.05. Simplify variable expressions involving like terms and the distributive property.
C.06. Recognize and identify equivalent linear expressions through simplification.
C.07. Use properties of operations to justify steps in simplifying expressions.
C.08. Model algebraic expressions using manipulatives (e.g., algebra tiles) to enhance understanding.

D. Solving Linear Equations

D.01. Solve one- and two-step linear equations using inverse operations.
D.02. Rearrange multi-variable equations to solve for a specific variable.
D.03. Solve advanced linear equations involving multiple steps and operations.
D.04. Solve equations with variables on both sides of the equal sign.
D.05. Determine the number of solutions (none, one, or infinite) for a linear equation.
D.06. Solve linear equations presented in real-world word problems.
D.07. Complete the steps to solve a given linear equation.
D.08. Create equations with no solutions or infinitely many solutions, and explain why.
D.09. Solve linear equations and check the validity of the solutions.
D.10. Solve linear equations with fractional coefficients and constants.
D.11. Analyze and solve complex word problems that require setting up and solving linear equations.

E. Problem Solving with Equations

F. Single-Variable Linear Inequalities

F.01. Solve one- and two-step linear inequalities using inverse operations.
F.02. Represent solutions to linear inequalities on a number line.
F.03. Solve advanced linear inequalities, including those with variables on both sides.
F.04. Solve compound inequalities involving “and” and “or” conditions.
F.05. Graph the solutions to compound inequalities on a number line.
F.06. Write compound inequalities from given graphs on a number line.
F.07. Interpret the solution of an inequality in the context of a problem.
F.08. Solve absolute value inequalities by splitting them into two separate inequalities.
F.09. Solve linear inequalities and represent the solutions sets using interval notation.

G. Relations and Functions

G.01. Define the terms “relation,” “domain,” and “range” in the context of functions.
G.02. Identify the domain and range of a relation from various representations.
G.03. Evaluate a function for a given input value using function notation.
G.04. Find values using function graphs.
G.05. Convert between tables, graphs, mappings, and lists of points for relations.
G.06. Complete a function table from a graph or from an equation.
G.07. Identify independent and dependent variables in a functional relationship.
G.08. Determine if a given relation is a function using the vertical line test.
G.09. Find solutions to equations using a table.
G.10. Approximate solutions using a table.
G.11. Interpret functions using everyday language and real-world contexts.
G.12. Calculate and interpret the rate of change from tables and graphs.
G.13. Analyze and model real-world situations using functional relationships.

H. Direct and Inverse Variation

H.01. Recognize proportional relationships from equations, tables, and graphs.
H.02. Calculate the constant of variation in a direct or inverse variation.
H.03. Write direct variation equations to model proportional relationships.
H.04. Graph direct variation relationships on the coordinate plane.
H.05. Write and solve direct variation equations to find unknown values.
H.06. Write inverse variation equations to represent inversely proportional relationships.
H.07. Write and solve inverse variation equations to solve problems.
H.08. Differentiate between direct and inverse variation relationships.
H.09. Apply direct and inverse variation concepts to real-world problems involving scaling and rates.

I. Linear Functions: Slope-Intercept Form

I.01. Identify linear functions from equations, graphs, and tables.
I.02. Understand and interpret points on the graph of a linear function in context.
I.03. Calculate the gradient (slope) of a line from a graph or two points.
I.04. Find a missing coordinate on a line given its gradient and another point.
I.05. Determine the gradient and y-intercept of a linear equation in slope-intercept form (y = mx + c).
I.06. Graph a linear equation in slope-intercept form.
I.07. Find the equation of a line given its slope and y-intercept.
I.08. Determine the equation of a line from its graph in slope-intercept form.
I.09. Convert linear equations to slope-intercept form.
I.10. Write the equation of a line in slope-intercept form from a table of values.
I.11. Write the equation of a line in slope-intercept form from a word problem.
I.12. Find x- and y-intercepts for equations in ax + by = c form.
I.13. Graph an equation in ax + by = c form.
I.14. Understand and apply the equations of horizontal and vertical lines.
I.15. Write linear functions to solve word problems.
I.16. Complete a table and graph a linear function
I.17. Compare linear functions: graphs, tables and equations.
I.18. Write an equation for a parallel line
I.19. Write an equation for a perpendicular line
I.20. Write an equation for a parallel or perpendicular line
I.21. Transformations of linear functions
I.22. Apply the point-gradient form to graph an equation
I.23. Apply the point-gradient form to write an equation
I.24. Apply the point-gradient form to write an equation from a graph
I.25. Investigate the properties of the gradients of parallel and perpendicular lines
I.26. Develop an understanding of how slope impacts real world situations

J. Systems of Linear Equations

J.01. Determine if an ordered pair (x, y) is a solution to a system of linear equations.
J.02. Solve systems of linear equations graphically by finding the point of intersection.
J.03. Apply graphing methods to solve simultaneous equations word problems
J.04. Determine the number of solutions (none, one, or infinite) of a system of linear equations graphically.
J.05. Determine the number of solutions to simultaneous equations by algebraic methods
J.06. Solve systems of linear equations using the substitution method.
J.07. Apply the substitution method to solve simultaneous equations word problems
J.08. Solve systems of linear equations using the elimination method (addition/subtraction).
J.09. Apply the elimination method to solve simultaneous equations word problems
J.10. Choose the most efficient method (graphing, substitution, or elimination) to solve a system of equations.
J.11. Solve a system of equations using any method
J.12. Solve a system of equations using any method: word problems
J.13. Create and solve systems of linear equations to model and solve real-world problems.

K. Linear Inequalities in Two Variables

L. Indices and Exponents

L.01. Review basic index laws (product, quotient, power of a power).
L.02. Simplify expressions involving negative indices.
L.03. Apply index laws to simplify expressions with multiplication.
L.04. Apply index laws to simplify expressions with division.
L.05. Apply both multiplication and division index laws to simplify expressions.
L.06. Apply the power rule (power of a power) to simplify expressions.
L.07. Evaluate expressions using properties of indices (exponents).
L.08. Identify equivalent expressions involving indices through simplification.
L.09. Extend the understanding of indices to include rational exponents.
L.10. Use scientific notation to perform calculations with very large or very small numbers.

M. Number Sequences

M.01. Recognize and classify arithmetic and geometric sequences.
M.02. Determine the common difference in an arithmetic sequence.
M.03. Determine the common ratio in a geometric sequence.
M.04. Evaluate variable expressions for number sequences
M.05. Evaluate variable expressions for number sequences.
M.06. Determine the nth term in an arithmetic sequence.
M.07. Determine the nth term in a geometric sequence.
M.08. Write variable expressions for arithmetic sequences.
M.09. Write variable expressions for geometric sequences.
M.10. Recognize and continue sequences of square and cube numbers.
M.11. Identify and generate terms in Fibonacci-type sequences.
M.12. Apply knowledge of sequences to solve mixed review problems.
M.13. Model patterns with recursive formulas and understand their relationship to explicit formulas

N. Standard Form (Scientific Notation)

O. Exponential Functions

O.01. Evaluate exponential functions for given input values.
O.02. Write exponential functions to model real-world scenarios, such as population growth or decay.
O.03. Match exponential functions to their corresponding graphs.
O.04. Graph exponential functions.
O.05. Identify the domain and range of exponential functions.
O.06. Solve exponential growth and decay word problems.
O.07. Apply exponential functions to calculate compound interest.
O.08. Analyze and interpret the parameters of exponential functions in context.
O.09. Model and analyse compound interest and depreciation problems

P. Monomials

Q. Polynomials

Q.01. Define polynomial vocabulary, including terms like degree, coefficient, and constant.
Q.02. Add and subtract polynomials using algebra tiles.
Q.03. Add and subtract polynomials algebraically.
Q.04. Multiply a polynomial by a monomial.
Q.05. Multiply two polynomials using algebra tiles.
Q.06. Multiply two binomials using the distributive property (FOIL method).
Q.07. Identify and multiply two binomials that represent special cases (difference of squares, perfect square trinomials).
Q.08. Multiply polynomials of various degrees.
Q.09. Apply polynomial operations to solve geometric problems, such as finding the perimeter of a shape.
Q.10. Express geometric shapes using polynomial expressions

R. Factorising Polynomials

R.09. Apply the null factor law to solve polynomial equations.
R.01. Find the highest common factor (HCF) of monomials.
R.02. Factorise out a monomial from a polynomial expression.
R.03. Factorise quadratic expressions using algebra tiles.
R.04. Factorise quadratic expressions with a leading coefficient of 1.
R.05. Factorise quadratic expressions with leading coefficients other than 1.
R.06. Factorise quadratic expressions that are special cases (difference of squares, perfect square trinomials).
R.07. Factorise polynomials by grouping.
R.08. Factorise polynomials of various degrees using a combination of techniques.

S. Quadratic Equations and Inequalities

S.01. Identify the key characteristics of quadratic functions from their graphs (vertex, axis of symmetry, intercepts).
S.02. Identify the key characteristics of quadratic functions from their equations.
S.03. Complete a function table for a quadratic function.
S.04. Match quadratic functions to their corresponding graphs.
S.05. Graph a quadratic function by finding its vertex, intercepts, and axis of symmetry.
S.06. Solve a quadratic equation using square roots.
S.07. Solve a quadratic equation using the zero product property (factorising).
S.08. Solve a quadratic equation with leading coefficient 1 by factorising.
S.09. Solve a quadratic equation with other leading coefficients by factorising.
S.10. Complete the square to rewrite a quadratic expression in vertex form.
S.11. Solve a quadratic equation by completing the square.
S.12. Solve a quadratic equation using the quadratic formula.
S.13. Solve simultaneous quadratic and linear equations graphically.
S.14. Solve simultaneous quadratic and linear equations algebraically.
S.15. Graph solutions to quadratic inequalities on a number line.
S.16. Solve quadratic inequalities algebraically.
S.17. Apply the discriminant to determine the nature and number of roots in a quadratic equation.
S.18. Solve quadratic equations arising from real-world applications, such as projectile motion or area optimization.

T. Function Types: Linear, Quadratic, and Exponential

T.01. Identify linear, quadratic, and cubic functions from their graphs.
T.02. Identify linear, quadratic, cubic, and exponential functions from their graphs.
T.03. Identify linear, quadratic, and exponential functions from tables of values.
T.04. Write linear, quadratic, and exponential functions to model given data.
T.05. Calculate linear functions over unit intervals and interpret the rate of change.
T.06. Calculate exponential functions over unit intervals and interpret the growth or decay factor.
T.07. Describe linear and exponential growth and decay in context.
T.08. Analyze the long-term behavior of linear, quadratic, and exponential functions.
T.09. Compare and contrast the characteristics of linear, quadratic, and exponential functions.

U. Function Operations: Composition and Inverses

U.01. Evaluate the composition of linear functions for a given value.
U.02. Find the equation of the composition of two linear functions.
U.03. Evaluate the composition of linear and quadratic functions for a given value.
U.04. Find the equation of the composition of linear and quadratic functions.
U.05. Identify inverse functions from their equations, graphs, or tables.
U.06. Find values of inverse functions from tables.
U.07. Find values of inverse functions from graphs.
U.08. Find inverse functions and relations algebraically.
U.09. Determine the domain and range of inverse functions.
U.10. Verify inverse functions using composition.

V. Function Transformations

W. Radical Expressions

W.01. Simplify radical expressions by factoring out perfect squares or cubes.
W.02. Simplify radical expressions involving fractions by rationalizing the denominator.
W.03. Multiply radical expressions using the distributive property.
W.04. Add and subtract radical expressions by combining like terms.
W.05. Simplify radical expressions using the distributive property.
W.06. Simplify radical expressions using conjugates.
W.07. Simplify radical expressions: mixed review
W.08. Convert between radicals and rational exponents.
W.09. Solve equations involving radical expressions.

X. Fractional Indices (Rational Exponents)

X.01. Evaluate expressions with fractional indices (rational exponents).
X.02. Apply the product rule to simplify expressions with fractional indices.
X.03. Apply the quotient rule to simplify expressions with fractional indices.
X.04. Apply the power rule to simplify expressions with fractional indices.
X.05. Simplify expressions involving fractional indices I
X.06. Simplify expressions involving fractional indices II
X.07. Express fractional indices as radical expressions and vice versa.
X.08. Apply fractional indices to solve equations and problems involving roots.
X.09. Use fractional indices to simplify surds

Y. Rational Functions and Expressions

Y.01. Identify asymptotes and excluded values of rational functions.
Y.02. Simplify complex fractions by multiplying by the reciprocal of the denominator.
Y.03. Simplify rational expressions by factorising and cancelling common factors.
Y.04. Multiply and divide rational expressions.
Y.05. Divide polynomials using long division or synthetic division.
Y.06. Add and subtract rational expressions with like and unlike denominators.
Y.07. Solve rational equations by clearing fractions and solving the resulting equation.
Y.08. Identify and address extraneous solutions in rational equations.
Y.09. Formulate rational functions to model real-world relationships and solve related problems.

Z. Midpoints and Distance in Coordinate Geometry

AA. Transformations in Geometry

AA.01. Recognize and identify translations, reflections, and rotations.
AA.02. Perform translations on geometric figures and graph the image.
AA.03. Determine the coordinates of the image after a translation.
AA.04. Write the rule for a given translation.
AA.05. Reflect geometric figures across the x-axis, y-axis, and other lines, and graph the image.
AA.06. Determine the coordinates of the image after a reflection.
AA.07. Rotate polygons about a point by specified angles.
AA.08. Perform rotations on geometric figures and graph the image.
AA.09. Determine the coordinates of the image after a rotation.
AA.10. Describe transformations that map one figure onto another.
AA.11. Reflections and rotations: write the rule
AA.12. Sequences of translations, reflections and rotations: graph the image
AA.13. Sequences of congruence transformations: choose the sequence
AA.14. Transformations that carry a polygon onto itself
AA.15. Translations, reflections and rotations: mixed review
AA.16. Perform dilations on geometric figures and graph the image.
AA.17. Determine the coordinates of the image after a dilation.
AA.18. Determine length, perimeter and area following dilations
AA.19. Dilations: scale factor and classification
AA.20. Dilations: find the scale factor and center of the dilation
AA.21. Dilations and parallel lines
AA.22. Classify transformations as isometric or non-isometric.
AA.23. Explore tessellations and their relationship to transformations.

BB. Congruence in Geometry

BB.01. Identify congruent figures based on visual inspection.
BB.02. Write congruence statements and identify corresponding parts of congruent figures.
BB.03. Solve problems involving corresponding parts of congruent figures.
BB.04. Determine if two figures are congruent and justify the answer using congruence postulates and theorems.
BB.05. Apply the Side-Side-Side (SSS) congruence theorem.
BB.06. Apply the Side-Angle-Side (SAS) congruence theorem.
BB.07. Apply the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) congruence theorems.
BB.08. Apply SSS, SAS, ASA and AAS Theorems to solve geometric problems
BB.09. Apply the SSS Theorem in the coordinate plane.
BB.10. Prove congruency in isosceles and equilateral triangles.
BB.11. Apply the Hypotenuse-Leg (HL) congruence theorem for right triangles.
BB.12. Use congruence criteria to prove geometric constructions are valid.
BB.13. Determine what minimum criteria can be used to show that triangles are congruent.

CC. Similarity in Geometry

CC.01. Identify similar figures based on visual inspection and proportional reasoning.
CC.02. Determine the ratios of corresponding sides in similar figures.
CC.03. Write similarity statements for similar figures.
CC.04. Determine side lengths and angle measures in similar figures using proportionality.
CC.05. Apply similar triangles to solve problems using indirect measurement.
CC.06. Determine the relationship between perimeters of similar figures.
CC.07. Apply similarity rules for triangles (AA, SSS, SAS).
CC.08. Relate similar triangles to transformations (dilations).
CC.09. Determine the relationship between areas of similar figures.
CC.10. Use similarity theorems to prove geometric relationships.

DD. Right Triangles: Pythagoras’ Theorem and Special Triangles

EE. Trigonometry

EE.01. Define the primary trigonometric ratios (sin, cos, tan) in terms of right triangles.
EE.02. Define the reciprocal trigonometric ratios (csc, sec, cot).
EE.03. Find trigonometric functions of special angles: sin, cos and tan.
EE.04. Find trigonometric functions of special angles: csc, sec and cot.
EE.05. Use a calculator to find trigonometric functions of angles in degrees or radians.
EE.06. Understand and apply the inverses of trigonometric functions (arcsin, arccos, arctan).
EE.07. Use trigonometric ratios to find a side length in a right triangle.
EE.08. Use trigonometric ratios to find an angle measure in a right triangle.
EE.09. Solve a right triangle by finding all missing side lengths and angle measures.
EE.10. Apply the Law of Sines to solve non-right triangles.
EE.11. Apply the Law of Cosines to solve non-right triangles.
EE.12. Solve a triangle by using Law of Sines and Law of Cosines
EE.13. Calculate the area of a triangle using the sine formula.
EE.14. Graph sine functions
EE.15. Graph cosine functions
EE.16. Graph sine and cosine functions
EE.17. Apply trigonometric functions to solve real-world problems involving angles, heights, and distances.
EE.18. Relate trigonometric functions to the unit circle.
EE.19. Model periodic phenomena using sine and cosine functions.

FF. Perimeter, Area, and Volume

FF.01. Calculate the perimeter of various geometric shapes.
FF.02. Calculate the area of triangles and quadrilaterals.
FF.03. Calculate area and perimeter in the coordinate plane I
FF.04. Calculate area and perimeter in the coordinate plane II
FF.05. Calculate the area and circumference of circles.
FF.06. Calculate the area of compound figures by dividing them into simpler shapes.
FF.07. Determine the area between two shapes by subtraction.
FF.08. Determine area and perimeter of similar figures
FF.09. Apply area formulas to solve real-world problems involving surface coverage and design.
FF.10. Extend area and perimeter concepts to irregular and composite shapes.

GG. Three-Dimensional Figures

GG.01. Identify parts of three-dimensional figures (faces, edges, vertices).
GG.02. Learn and apply three-dimensional figure vocabulary.
GG.03. Draw and interpret front, side, and top views of three-dimensional figures.
GG.04. Interpret and create base plans of three-dimensional structures.
GG.05. Draw and construct nets of three-dimensional figures.
GG.06. Describe and sketch cross-sections of three-dimensional figures.
GG.07. Visualise and describe solids of revolution formed by rotating two-dimensional shapes.
GG.08. Use orthogonal views to construct 3-D objects and determine their volume and surface area.

HH. Surface Area and Volume of Solids

HH.01. Calculate the surface area and volume of cuboids (rectangular prisms).
HH.02. Calculate the surface area of prisms and cylinders.
HH.03. Calculate the surface area of pyramids and cones.
HH.04. Calculate the surface area of spheres.
HH.05. Apply surface area formulas to solve mixed review problems.
HH.06. Calculate the volume of prisms and cylinders.
HH.07. Calculate the volume of pyramids and cones.
HH.08. Calculate the volume of spheres.
HH.09. Calculate the volume of compound figures by addition or subtraction.
HH.10. Apply volume formulas to solve mixed review problems.
HH.11. Analyse similar solids
HH.12. Analyse surface area of similar solids
HH.13. Analyse volume of similar solids
HH.14. Analyse surface area and volume of similar solids
HH.15. Apply surface area and volume formulas to solve real-world problems involving packaging, construction, and design.
HH.16. Model and design optimal shapes for minimal surface area or maximal volume.

II. Circles: Geometry and Equations

II.01. Identify and define the parts of a circle (center, radius, diameter, chord, secant, tangent).
II.02. Define and measure central angles in a circle.
II.03. Understand arc length and sector area of a circle
II.04. Calculate arc measure and arc length.
II.05. Calculate the area of sectors.
II.06. Apply circle measurement formulas to solve mixed review problems.
II.07. Analyse arcs and chords
II.08. Analyse tangent lines
II.09. Apply angles formed by chords, secants, and tangents
II.10. Apply segments formed by chords, secants, and tangents
II.11. Analyse perimeter of polygons with an inscribed circle
II.12. Analyse inscribed angles
II.13. Analyse angles in inscribed right triangles
II.14. Analyse angles in inscribed quadrilaterals I
II.15. Analyse angles in inscribed quadrilaterals II
II.16. Write equations of circles centered at the origin from graphs
II.17. Write equations of circles centered at the origin from properties
II.18. Analyse properties of circles from equations
II.19. Graph circles centered at the origin
II.20. Apply circle theorems to solve geometric problems.
II.21. Construct tangent lines to a circle from a point outside the circle.

JJ. Vectors in Two Dimensions

JJ.01. Use compass directions and vectors
JJ.02. Calculate the magnitude of a vector.
JJ.03. Find the component form of a vector.
JJ.04. Find the component form of a vector given its magnitude and direction angle.
JJ.05. Graph a resultant vector using the triangle method.
JJ.06. Graph a resultant vector using the parallelogram method.
JJ.07. Add vectors by adding their components.
JJ.08. Subtract vectors by subtracting their components.
JJ.09. Multiply a vector by a scalar.
JJ.10. Find the magnitude of a vector scalar multiple
JJ.11. Determine the direction of a vector scalar multiple
JJ.12. Find linear combinations of vectors
JJ.13. Resolve vectors into horizontal and vertical components.
JJ.14. Use vectors to solve problems involving forces, velocities, and displacements.

KK. Measurement and Units

KK.01. Convert rates and measurements: metric units
KK.02. Metric mixed units
KK.03. Convert rates and measurements: imperial units
KK.04. Imperial mixed units
KK.05. Convert between metric and imperial units
KK.06. Understand and apply the concept of precision in measurement.
KK.07. Calculate the greatest possible error in a measurement.
KK.08. Determine the minimum and maximum possible area and volume based on measurement precision.
KK.09. Calculate percent error in a measurement.
KK.10. Calculate percent error: area and volume
KK.11. Perform unit analysis to check the validity of calculations.

LL. Data Representation and Interpretation

LL.08. Choose the best type of graph to represent a given data set.
LL.09. Interpret and create box plots to display data distributions.
LL.10. Critically evaluate the effectiveness and potential biases of different graphical representations.
LL.01. Interpret information presented in tables.
LL.02. Interpret information presented in line graphs.
LL.03. Create line graphs from data sets.
LL.04. Interpret bar graphs for grouped data.
LL.05. Create bar graphs for grouped data.
LL.06. Interpret information presented in pie charts.
LL.07. Interpret information presented in stem-and-leaf plots.

MM. Descriptive Statistics

MM.01. Calculate the mean, median, mode, and range of a data set.
MM.02. Determine quartiles and interquartile range (IQR) of a data set.
MM.03. Calculate variance and standard deviation of a data set.
MM.04. Describe distributions in line plots
MM.05. Populations and samples
MM.06. Identify biased samples
MM.07. Create scatter plots to display the relationship between two variables.
MM.08. Identify trends (positive, negative, or no correlation) using scatter plots.
MM.09. Make predictions based on trends observed in scatter plots.
MM.10. Identify outliers in scatter plots and discuss their potential impact on analysis.
MM.11. Write an equation for a line of best fit to model the relationship between variables in a scatter plot.
MM.12. Understand the difference between correlation and causation.
MM.13. Use statistical software and tools to analyze and visualize data sets.

NN. Probability

NN.01. Calculate theoretical probability of simple events.
NN.02. Determine experimental probability based on observed outcomes.
NN.03. Make predictions based on probabilities.
NN.04. Determine the number of outcomes in compound events.
NN.05. Calculate the probability of compound events.
NN.06. Solve probability problems involving compound events.
NN.07. Find probabilities using two-way frequency tables.
NN.08. Identify independent and dependent events.
NN.09. Calculate the probability of independent and dependent events.
NN.10. Find conditional probabilities.
NN.11. Identify independence and conditional probability
NN.12. Find conditional probabilities using two-way frequency tables
NN.13. Determine geometric probability
NN.14. Design and conduct probability experiments to test theoretical predictions.
NN.15. Analyse and compare simulations of events with theoretical outcomes.

Course Content

A. Numbers and Counting

A.01. Identify prime and composite numbers.

A.02. Understand the definition of a square root and cube root.

A.03. Add, subtract, multiply, and divide rational numbers proficiently.

A.04. Estimate the values of square roots and cube roots without a calculator.

A.05. Identify and differentiate between rational and irrational numbers.

A.06. Compare and order rational numbers on a number line.

A.07. Evaluate numerical expressions involving rational numbers using the order of operations.

A.08. Express recurring decimals as fractions using algebraic methods.

A.09. Explore the properties of rational and irrational numbers within the real number system.

A.10. Apply the concept of significant figures when dealing with approximations of irrational numbers

B. Percents and Proportions

B.01. Understand and calculate basic percentages of given quantities.

B.02. Calculate the percent of change (increase or decrease).

B.03. Solve multi-step problems involving successive percentage changes.

B.04. Calculate sale prices and VAT (Value Added Tax) to find the original price of an item.

B.05. Solve word problems involving percent of change, including finding the original amount.

B.06. Apply percentages in real-world scenarios, such as discounts, taxes, and interest rates.

B.07. Analyze and solve complex percentage problems involving multiple steps and variables.

B.08. Solve reverse percentage problems, finding the original value after a percentage increase or decrease.

C. Expressions and Properties

C.01. Understand and apply the commutative, associative, and distributive properties.

C.02. Identify and combine like terms in algebraic expressions.

C.03. Apply the distributive property to expand and simplify algebraic expressions.

C.04. Write equivalent expressions using the properties of addition and multiplication.

C.05. Simplify variable expressions involving like terms and the distributive property.

C.06. Recognize and identify equivalent linear expressions through simplification.

C.07. Use properties of operations to justify steps in simplifying expressions.

C.08. Model algebraic expressions using manipulatives (e.g., algebra tiles) to enhance understanding.

D. Solving Linear Equations

D.01. Solve one- and two-step linear equations using inverse operations.

D.02. Rearrange multi-variable equations to solve for a specific variable.

D.03. Solve advanced linear equations involving multiple steps and operations.

D.04. Solve equations with variables on both sides of the equal sign.

D.05. Determine the number of solutions (none, one, or infinite) for a linear equation.

D.06. Solve linear equations presented in real-world word problems.

D.07. Complete the steps to solve a given linear equation.

D.08. Create equations with no solutions or infinitely many solutions, and explain why.

D.09. Solve linear equations and check the validity of the solutions.

D.10. Solve linear equations with fractional coefficients and constants.

D.11. Analyze and solve complex word problems that require setting up and solving linear equations.

E. Problem Solving with Equations

E.01. Apply linear equations to solve consecutive integer problems.

E.02. Solve word problems involving rates of travel using distance, speed, and time relationships.

E.03. Solve word problems involving weighted averages, such as mixtures or grades.

E.04. Formulate and solve algebraic equations based on real-world scenarios.

E.05. Use problem-solving strategies, such as making a table or drawing a diagram, to solve mathematical problems

F. Single-Variable Linear Inequalities

F.01. Solve one- and two-step linear inequalities using inverse operations.

F.02. Represent solutions to linear inequalities on a number line.

F.03. Solve advanced linear inequalities, including those with variables on both sides.

F.04. Solve compound inequalities involving “and” and “or” conditions.

F.05. Graph the solutions to compound inequalities on a number line.

F.06. Write compound inequalities from given graphs on a number line.

F.07. Interpret the solution of an inequality in the context of a problem.

F.08. Solve absolute value inequalities by splitting them into two separate inequalities.

F.09. Solve linear inequalities and represent the solutions sets using interval notation.

G. Relations and Functions

G.01. Define the terms “relation,” “domain,” and “range” in the context of functions.

G.02. Identify the domain and range of a relation from various representations.

G.03. Evaluate a function for a given input value using function notation.

G.04. Find values using function graphs.

G.05. Convert between tables, graphs, mappings, and lists of points for relations.

G.06. Complete a function table from a graph or from an equation.

G.07. Identify independent and dependent variables in a functional relationship.

G.08. Determine if a given relation is a function using the vertical line test.

G.09. Find solutions to equations using a table.

G.10. Approximate solutions using a table.

G.11. Interpret functions using everyday language and real-world contexts.

G.12. Calculate and interpret the rate of change from tables and graphs.

G.13. Analyze and model real-world situations using functional relationships.

H. Direct and Inverse Variation

H.01. Recognize proportional relationships from equations, tables, and graphs.

H.02. Calculate the constant of variation in a direct or inverse variation.

H.03. Write direct variation equations to model proportional relationships.

H.04. Graph direct variation relationships on the coordinate plane.

H.05. Write and solve direct variation equations to find unknown values.

H.06. Write inverse variation equations to represent inversely proportional relationships.

H.07. Write and solve inverse variation equations to solve problems.