# Grade 12 math

Here is a list of all of the math skills students learn in grade 12! These skills are organized into categories, and you can move your mouse over any skill name to view a sample question. To start practising, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Functions

- A.1Domain and range
- A.2Identify functions
- A.3Linear functions
- A.4Linear functions over unit intervals
- A.5Evaluate functions
- A.6Find values using function graphs
- A.7Complete a table for a function graph
- A.8Add, subtract, multiply and divide functions
- A.9Composition of functions
- A.10Identify inverse functions
- A.11Find values of inverse functions from tables
- A.12Find values of inverse functions from graphs
- A.13Find inverse functions and relations
- A.14Identify graphs of continuous functions

## Families of functions

## Quadratic relations

- C.1Characteristics of quadratic functions
- C.2Find the maximum or minimum value of a quadratic function
- C.3Graph a quadratic function
- C.4Match quadratic functions and graphs
- C.5Solve a quadratic equation using square roots
- C.6Solve a quadratic equation by factoring
- C.7Solve a quadratic equation by completing the square
- C.8Solve a quadratic equation using the quadratic formula
- C.9Using the discriminant

## Polynomials

- D.1Divide polynomials using long division
- D.2Write a polynomial from its roots
- D.3Find the roots of factored polynomials
- D.4Rational root theorem
- D.5Complex conjugate theorem
- D.6Conjugate root theorems
- D.7Descartes' Rule of Signs
- D.8Fundamental Theorem of Algebra
- D.9Match polynomials and graphs
- D.10Factor sums and differences of cubes
- D.11Solve equations with sums and differences of cubes
- D.12Factor using a quadratic pattern
- D.13Solve equations using a quadratic pattern
- D.14Pascal's triangle
- D.15Pascal's triangle and the Binomial Theorem
- D.16Binomial Theorem I
- D.17Binomial Theorem II

## Rational functions

## Logarithms

- F.1Convert between exponential and logarithmic form: rational bases
- F.2Evaluate logarithms
- F.3Change of base formula
- F.4Identify properties of logarithms
- F.5Product property of logarithms
- F.6Quotient property of logarithms
- F.7Power property of logarithms
- F.8Properties of logarithms: mixed review
- F.9Evaluate logarithms: mixed review

## Exponential and logarithmic functions

- G.1Domain and range of exponential and logarithmic functions
- G.2Evaluate exponential functions
- G.3Match exponential functions and graphs
- G.4Solve exponential equations by factoring
- G.5Solve exponential equations using common logarithms
- G.6Solve logarithmic equations I
- G.7Solve logarithmic equations II
- G.8Identify linear and exponential functions
- G.9Exponential functions over unit intervals
- G.10Describe linear and exponential growth and decay
- G.11Exponential growth and decay: word problems
- G.12Compound interest: word problems
- G.13Continuously compounded interest: word problems

## Radical functions

## Systems of equations

- J.1Solve a system of equations by graphing
- J.2Solve a system of equations by graphing: word problems
- J.3Classify a system of equations
- J.4Solve a system of equations using substitution
- J.5Solve a system of equations using substitution: word problems
- J.6Solve a system of equations using elimination
- J.7Solve a system of equations using elimination: word problems
- J.8Solve a system of equations in three variables using substitution
- J.9Solve a system of equations in three variables using elimination
- J.10Determine the number of solutions to a system of equations in three variables

## Systems of inequalities

## Nonlinear inequalities

## Matrices

- M.1Matrix vocabulary
- M.2Matrix operation rules
- M.3Add and subtract matrices
- M.4Multiply a matrix by a scalar
- M.5Linear combinations of matrices
- M.6Multiply two matrices
- M.7Simplify matrix expressions
- M.8Solve matrix equations
- M.9Determinant of a matrix
- M.10Is a matrix invertible?
- M.11Inverse of a 2 x 2 matrix
- M.12Inverse of a 3 x 3 matrix
- M.13Identify inverse matrices
- M.14Solve matrix equations using inverses

## Trigonometry

- N.1Convert between radians and degrees
- N.2Radians and arc length
- N.3Quadrants
- N.4Coterminal and reference angles
- N.5Find trigonometric ratios using right triangles
- N.6Find trigonometric ratios using the unit circle
- N.7Find trigonometric ratios using reference angles
- N.8Inverses of trigonometric functions
- N.9Solve trigonometric equations
- N.10Trigonometric ratios: find a side length
- N.11Trigonometric ratios: find an angle measure
- N.12Solve a right triangle
- N.13Law of Sines
- N.14Law of Cosines
- N.15Solve a triangle
- N.16Area of a triangle: sine formula
- N.17Area of a triangle: Heron's formula

## Trigonometric functions

- O.1Find properties of sine functions
- O.2Write equations of sine functions from graphs
- O.3Write equations of sine functions using properties
- O.4Graph sine functions
- O.5Find properties of cosine functions
- O.6Write equations of cosine functions from graphs
- O.7Write equations of cosine functions using properties
- O.8Graph cosine functions
- O.9Graph sine and cosine functions

## Trigonometric identities

## Conic sections

- Q.1Find properties of parabolas
- Q.2Write equations of parabolas in vertex form
- Q.3Graph parabolas
- Q.4Find properties of circles
- Q.5Write equations of circles in standard form
- Q.6Graph circles
- Q.7Find properties of ellipses
- Q.8Find the eccentricity of an ellipse
- Q.9Write equations of ellipses in standard form
- Q.10Find properties of hyperbolas
- Q.11Find the eccentricity of a hyperbola
- Q.12Write equations of hyperbolas in standard form
- Q.13Convert equations of conic sections from general to standard form

## Complex numbers

## Polar form

## Two-dimensional vectors

- U.1Find the magnitude of a vector
- U.2Find the direction angle of a vector
- U.3Find the component form of a vector
- U.4Find the component form of a vector from its magnitude and direction angle
- U.5Find a unit vector
- U.6Add and subtract vectors
- U.7Multiply a vector by a scalar
- U.8Find the magnitude or direction of a vector scalar multiple
- U.9Find the magnitude and direction of a vector sum
- U.10Linear combinations of vectors
- U.11Graph a resultant vector using the triangle method
- U.12Graph a resultant vector using the parallelogram method

## Three-dimensional vectors

## Sequences and series

- W.1Find terms of a sequence
- W.2Find terms of a recursive sequence
- W.3Identify a sequence as explicit or recursive
- W.4Find a recursive formula
- W.5Find recursive and explicit formulas
- W.6Convert a recursive formula to an explicit formula
- W.7Convert an explicit formula to a recursive formula
- W.8Convert between explicit and recursive formulas
- W.9Introduction to sigma notation
- W.10Identify arithmetic and geometric series
- W.11Find the sum of a finite arithmetic or geometric series
- W.12Introduction to partial sums
- W.13Partial sums of arithmetic series
- W.14Partial sums of geometric series
- W.15Partial sums: mixed review
- W.16Convergent and divergent geometric series
- W.17Find the value of an infinite geometric series
- W.18Write a repeating decimal as a fraction

## Logic

## Probability

- Y.1Introduction to probability
- Y.2Calculate probabilities of events
- Y.3Combinations and permutations
- Y.4Find probabilities using combinations and permutations
- Y.5Find probabilities using two-way frequency tables
- Y.6Identify independent events
- Y.7Find conditional probabilities
- Y.8Independence and conditional probability
- Y.9Find conditional probabilities using two-way frequency tables
- Y.10Find probabilities using the addition rule

## Probability distributions

- Z.1Identify discrete and continuous random variables
- Z.2Write a discrete probability distribution
- Z.3Graph a discrete probability distribution
- Z.4Expected values of random variables
- Z.5Variance and standard deviation of random variables
- Z.6Write the probability distribution for a game of chance
- Z.7Expected values for a game of chance
- Z.8Choose the better bet
- Z.9Find probabilities using the binomial distribution
- Z.10Mean, variance and standard deviation of binomial distributions
- Z.11Find probabilities using the normal distribution
- Z.12Find z-values
- Z.13Find values of normal variables
- Z.14Distributions of sample means
- Z.15The Central Limit Theorem
- Z.16Use normal distributions to approximate binomial distributions

## Statistics

- AA.1Identify biased samples
- AA.2Variance and standard deviation
- AA.3Identify an outlier
- AA.4Identify an outlier and describe the effect of removing it
- AA.5Outliers in scatter plots
- AA.6Match correlation coefficients to scatter plots
- AA.7Calculate correlation coefficients
- AA.8Find the equation of a regression line
- AA.9Interpret regression lines
- AA.10Analyze a regression line of a data set
- AA.11Analyze a regression line using statistics of a data set
- AA.12Find confidence intervals for population means
- AA.13Find confidence intervals for population proportions
- AA.14Interpret confidence intervals for population means