Class ix
mandatory maths
A. Numbers
- ompare and order rational numbers
- Absolute value and opposites
- Number lines
- Convert between decimals and fractions
- Convert between repeating decimals and fractions
- Square roots
- Cube roots
- Sort rational and irrational numbers
- Classify rational and irrational numbers
- Properties of operations on rational and irrational numbers
- Classify numbers
B. Operations
- Add, subtract, multiply, and divide integers
- Evaluate numerical expressions involving integers
- Evaluate variable expressions involving integers
- Add and subtract rational numbers
- Multiply and divide rational numbers
- Simplify complex fractions
- Evaluate numerical expressions involving rational numbers
- Evaluate variable expressions involving rational numbers
C. Ratios, rates, and proportionss
- dentify equivalent ratios
- Write an equivalent ratio
- Unit rates
- Unit prices
- Solve proportions
- Solve proportions: word problems
- Scale drawings: word problems
D. Percents
- Convert between percents, fractions, and decimals
- Solve percent equations
- Percent word problems
- Percent of change
- Percent of change: word problems
- Percent of change: find the original amount word problems
- Percent of a number: tax, discount, and more
- Find the percent: tax, discount, and more
- Multi-step problems with percents
E. Measurement
- Convert rates and measurements: customary units
- Convert rates and measurements: metric units
- Unit prices with unit conversions
- Multi-step problems with unit conversions
- Precision
- Greatest possible error
- Minimum and maximum area and volume
- Percent error
- Percent error: area and volume
F. Geometry
- Perimeter
- Area
- Area and perimeter: word problems
- Volume
- Surface area
- Similar figures: side lengths and angle measures
- Similar triangles and indirect measurement
- Dilations and scale factors
- Area and perimeter of similar figures
- Area between two shapes
- Similar solids
- Volume and surface area of similar solids
- Perimeter and area: changes in scale
- Surface area and volume: changes in scale
- Perimeter, area, and volume: changes in scale
- Pythagorean theorem
- Pythagorean theorem: word problems
- Converse of the Pythagorean theorem: is it a right triangle?
- Special right triangles
G. Coordinate planeG. Coordinate plane
- Coordinate plane review
- Midpoint formula: find the midpoint
- Midpoint formula: find the endpoint
- Distance between two points
H. Properties
- Properties of addition and multiplication
- Distributive property
- Simplify variable expressions using properties
- Properties of equality
- Identify equivalent equations
I. Variable expressions and equations
- Write variable expressions
- Sort factors of variable expressions
- Simplify variable expressions involving like terms and the distributive property
- Identify equivalent linear expressions
- Write variable equations
- Does x satisfy the equation?
- Which x satisfies an equation?
- Solve equations using order of operations
- Does (x, y) satisfy the equation?
- Relate the graph of an equation to its solutions
- Rearrange multi-variable equations
J. Solve linear equations
- Model and solve linear equations using algebra tiles
- Write and solve linear equations that represent diagrams
- Solve one-step linear equations
- Solve two-step linear equations
- Solve advanced linear equations
- Solve linear equations with variables on both sides
- Solve linear equations: complete the solution
- Find the number of solutions to a linear equation
- Create linear equations with no solutions or infinitely many solutions
- Solve one-step and two-step linear equations: word problems
- Solve linear equations: mixed review
K. Single-variable linear inequalities
- Graph inequalities
- Write inequalities from graphs
- Identify solutions to inequalities
- Solve one-step linear inequalities: addition and subtraction
- Solve one-step linear inequalities: multiplication and division
- Solve one-step linear inequalities
- Graph solutions to one-step linear inequalities
- Solve two-step linear inequalities
- Graph solutions to two-step linear inequalities
- Solve advanced linear inequalities
- Graph solutions to advanced linear inequalities
- Graph compound inequalities
- Write compound inequalities from graphs
- Solve compound inequalities
- Graph solutions to compound inequalities
Checkpoint skill Checkpoint: Solve linear equations and inequalities
L. Absolute value equations and inequalities
- Solve absolute value equations
- Graph solutions to absolute value equations
- Solve absolute value inequalities
- Graph solutions to absolute value inequalities
M. Matrices
- Matrix vocabulary
- Matrix operation rules
- Add and subtract matrices
- Multiply a matrix by a scalar
- Add and subtract scalar multiples of matrices
- Multiply two matrices
- Properties of matrices
N. Data and graphs
- Interpret line plots
- Create line plots
- Interpret histograms
- Create histograms
- Interpret bar graphs, line graphs, and histograms
- Create bar graphs, line graphs, and histograms
- Interpret circle graphs
- Interpret stem-and-leaf plots
- Box plots
Checkpoint skill Checkpoint: Line plots, histograms, and box plots
O. Problem solvin
- Word problems: mixed review
- Word problems with money
- Consecutive integer problems
- Rate of travel: word problems
- Weighted averages: word problems
Checkpoint skill Checkpoint: Units and quantities
P. Number sequences
- Identify arithmetic and geometric sequences
- Arithmetic sequences
- Geometric sequences
- Evaluate variable expressions for number sequences
- Evaluate recursive formulas for sequences
- Identify a sequence as explicit or recursive
- Write variable expressions for arithmetic sequences
- Write variable expressions for geometric sequences
- Write a formula for a recursive sequence
- Convert a recursive formula to an explicit formula
- Convert an explicit formula to a recursive formula
- Number sequences: mixed review
Checkpoint skill Checkpoint: Sequences
Q. Relations and functions
- Relations: convert between tables, graphs, mappings, and lists of points
- Domain and range of relations
- Identify independent and dependent variables
- Identify functions
- Identify functions: vertical line test
- Find values using function graphs
- Evaluate a function
- Evaluate a function: plug in an expression
- Add and subtract functions
- Multiply functions
- Find the inverse of a function
- Complete a function table from a graph
- Complete a function table from an equation
- Find solutions using a table
- Approximate solutions using a table
- Interpret the graph of a function: word problems
- Interpret functions using everyday language
• New! Identify graphs: word problems - Rate of change: tables
- Rate of change: graphs
Checkpoint skill Checkpoint: Function concepts
Checkpoint skill Checkpoint: Average rate of change
Checkpoint skill Checkpoint: Solve equations using graphs and table
R. Piecewise-defined functions
- Evaluate piecewise-defined functions
- Graph piecewise-defined functions
S. Direct and inverse variation
- Identify proportional relationships
- Find the constant of variation
- Graph a proportional relationship
- Write direct variation equations
- Write and solve direct variation equations
- Identify direct variation and inverse variation
- Write inverse variation equations
- Write and solve inverse variation equations
T. Linear functions
- Identify linear functions from graphs and equations
- Identify linear functions from tables
- Find the slope of a graph
- Find the slope from two points
- Find a missing coordinate using slope
- Slope-intercept form: find the slope and y-intercept
- Slope-intercept form: graph an equation
- Slope-intercept form: write an equation from a graph
- Slope-intercept form: write an equation
- Slope-intercept form: write an equation from a table
- Slope-intercept form: write an equation from a word problem
- Linear equations: solve for y
- Write and solve two-variable linear equations: word problems
- Complete a table and graph a linear function
- Compare linear functions: graphs and equations
- Compare linear functions: tables, graphs, and equations
- Interpret the slope and y-intercept of a linear function
- Write equations in standard form
- Standard form: find x- and y-intercepts
- Standard form: graph an equation
- Equations of horizontal and vertical lines
- Graph a horizontal or vertical line
- Point-slope form: graph an equation
- Point-slope form: write an equation
- Point-slope form: write an equation from a graph
- Find the slope and intercepts from an equation
- Slopes of parallel and perpendicular lines
- Write an equation for a parallel or perpendicular line
- Transformations of linear functions
U. Two-variable linear inequalities
- Does (x, y) satisfy the inequality?
- Linear inequalities: solve for y
- Graph a two-variable linear inequality
- Write a linear inequality from a graph
- Write two-variable inequalities: word problems
- Is (x, y) a solution to the system of linear inequalities?
- Solve systems of linear inequalities by graphing
V. Systems of linear equations
- Is (x, y) a solution to the system of equations?
- Solve a system of equations by graphing
- Solve a system of equations by graphing: word problems
- Find the number of solutions to a system of equations by graphing
- Find the number of solutions to a system of equations
- Classify a system of equations by graphing
- Classify a system of equations
- Solve a system of equations using substitution
- Solve a system of equations using substitution: word problems
- Solve a system of equations using elimination
- Solve a system of equations using elimination: word problems
- Solve a system of equations using augmented matrices
- Solve a system of equations using augmented matrices: word problems
- Solve a system of equations using any method
- Solve a system of equations using any method: word problems
Checkpoint skill Checkpoint: Systems of equations and inequalities
Checkpoint skill Checkpoint: Represent constraint
W. Exponents
- Exponents with integer bases
- Exponents with decimal and fractional bases
- Negative exponents
- Multiplication with exponents
- Division with exponents
- Multiplication and division with exponents
- Power rule
- Evaluate expressions using properties of exponents
- Identify equivalent expressions involving exponents I
- Identify equivalent expressions involving exponents II
- Evaluate integers raised to positive rational exponents
- Evaluate integers raised to rational exponents
- Multiplication with rational exponents
- Division with rational exponents
- Power rule with rational exponents
- Simplify expressions involving rational exponents
X. Scientific notation
- Convert between standard and scientific notation
- Compare numbers written in scientific notation
- Add and subtract numbers written in scientific notation
- Multiply numbers written in scientific notation
- Divide numbers written in scientific notation
Y. Exponential functions
- Evaluate an exponential function
- Graph exponential functions
- Match exponential functions and graphs I
- Match exponential functions and graphs II
- Domain and range of exponential functions: graphs
- Domain and range of exponential functions: equations
• New! Write exponential functions: word problems - Exponential growth and decay: word problems
- Compound interest: word problems
Z. Monomials
- Identify monomials
- Multiply monomials
- Divide monomials
- Multiply and divide monomials
- Powers of monomials
AA. Polynomials
- Polynomial vocabulary
- Model polynomials with algebra tiles
- Add and subtract polynomials using algebra tiles
- Add and subtract polynomials
- Add polynomials to find perimeter
- Multiply a polynomial by a monomial
- Multiply two binomials using algebra tiles
- Multiply two binomials
- Multiply two binomials: special cases
- Multiply polynomials using area models
- Multiply polynomials
- Multiply polynomials to find area
Checkpoint skill Checkpoint: Polynomial operations
BB. Factoring
- GCF of monomials
- Factor out a monomial
- Factor quadratics using algebra tiles
- Factor quadratics with leading coefficient 1
- Factor quadratics with other leading coefficients
- Factor quadratics: special cases
- Factor by grouping
- Factor using a quadratic pattern
- Factor polynomials
CC. Quadratic equations
- Characteristics of quadratic functions: graphs
- Characteristics of quadratic functions: equations
- Complete a function table: quadratic functions
- Transformations of quadratic functions
- Graph quadratic functions in vertex form
- Solve a quadratic equation using square roots
- Solve a quadratic equation using the zero product property
- Solve a quadratic equation by factoring
- Complete the square
- Solve a quadratic equation by completing the square
- Solve a quadratic equation using the quadratic formula
• New! Solve quadratic equations: word problems - Using the discriminant
- Write a quadratic function in vertex form
- Graph quadratic functions in standard form
- Match quadratic functions and graphs
• New! Domain and range of quadratic functions: graphs - Domain and range of quadratic functions: equations
- Write a quadratic function from its vertex and another point
• New! Interpret parts of quadratic expressions: word problems - Solve a system of linear and quadratic equations by graphing
- Solve a system of linear and quadratic equations
Checkpoint skill Checkpoint: Quadratic equations
Checkpoint skill Checkpoint: Write and interpret equivalent expressions
DD. Functions: linear, quadratic, exponential
- Identify linear and exponential functions from graphs
- Identify linear, quadratic, and exponential functions from graphs
- Identify linear and exponential functions from tables
- Identify linear, quadratic, and exponential functions from tables
- Write linear and exponential functions: word problems
- Write linear and exponential functions from tables
- Write linear, quadratic, and exponential functions from tables
- Linear functions over unit intervals
- Exponential functions over unit intervals
- Describe linear and exponential growth and decay
- Compare linear and exponential growth
- Compare linear, exponential, and quadratic growth
Checkpoint skill Checkpoint: Problem solving with equations and inequalities
Checkpoint skill Checkpoint: Features of functions
Checkpoint skill Checkpoint: Compare linear and exponential functions
Checkpoint skill Checkpoint: Build functions
EE. Absolute value and function families
- Complete a function table: absolute value functions
- Graph an absolute value function
- Domain and range of absolute value functions: graphs
- Domain and range of absolute value functions: equations
- Transformations of absolute value functions: translations and reflections
- Transformations of absolute value functions: translations, reflections, and dilations
- Function transformation rules
- Translations of functions
- Reflections of functions
- Dilations of functions
- Transformations of functions
- Describe function transformations
Checkpoint skill Checkpoint: Graph and analyze functions
Checkpoint skill Checkpoint: Function transformations
FF. Radical expressions
- Simplify radical expressions
- Simplify radical expressions with variables
- Simplify radical expressions involving fractions
- Multiply radical expressions
- Add and subtract radical expressions
- Simplify radical expressions using the distributive property
- Simplify radical expressions using conjugates
- Simplify radical expressions: mixed review
Checkpoint skill Checkpoint: Radicals and rational exponents
GG. Radical functions and equation
- Evaluate square root functions
- Domain and range of square root functions: graphs
- Domain and range of square root functions: equations
- Graph square root functions
- Solve radical equations I
- Solve radical equations II
HH. Rational functions and expressions
- Rational functions: asymptotes and excluded values
- Simplify rational expressions
- Multiply and divide rational expressions
- Divide polynomials by monomials
- Divide polynomials using long division
- Add and subtract rational expressions
- Simplify mixed rational expressions
- Solve rational equations
- Evaluate rational expressions
II. Trigonometry
- Trigonometric ratios: sin, cos, and tan
- Find trigonometric ratios using a calculator
- Inverses of trigonometric functions
- Trigonometric ratios: find a side length
- Trigonometric ratios: find an angle measure
- Solve a right triangle
JJ. Sets
- Sets, subsets, and complements
- Set-builder notation
- Interval notation
• New! Unions and intersections of sets
KK. Logic
- Identify hypotheses and conclusions
- Counterexamples
LL. Probability
- Theoretical probability
- Experimental probability
- Find probabilities using two-way frequency tables
- Find conditional probabilities using two-way frequency tables
- Outcomes of compound events
- Identify independent and dependent events
- Probability of independent and dependent events
- Counting principle
- Permutations
- Permutation and combination notation
Checkpoint skill Checkpoint: Two-way frequency tables
MM. Statistics
- Identify biased samples
- Mean, median, mode, and range
- Calculate quartiles and interquartile range
- Identify an outlier
- Identify an outlier and describe the effect of removing it
- Mean absolute deviation
- Variance and standard deviation
- Interpret a scatter plot
- Outliers in scatter plots
- Match correlation coefficients to scatter plots
- Calculate correlation coefficients
- Write equations for lines of best fit
- Find the equation of a regression line
- Interpret regression lines
- Analyze a regression line of a data set
- Correlation and causation
Checkpoint skill Checkpoint: Compare data sets
Checkpoint skill Checkpoint: Linear modeling
