Here is a list of all of the math skills students should learn in 12th Grade. These skills are organized into categories and topics are organized in them. This list is provided by IXL, a company who is providing an immersive learning experience that provides comprehensive, curriculum-aligned math and English language arts content for junior kindergarten to grade 12.

## IXL Mathematics Grade 12 Skills Complete Curriculum

### Functions

A.1 Domain and range

A.2 Identify functions

A.3 Find the slope of a linear function

A.4 Graph a linear function

A.5 Write the equation of a linear function

A.6 Linear functions over unit intervals

A.7 Evaluate functions

A.8 Find values using function graphs

A.9 Complete a table for a function graph

A.10 Add, subtract, multiply and divide functions

A.11 Composition of functions

A.12 Identify inverse functions

A.13 Find values of inverse functions from tables

A.14 Find values of inverse functions from graphs

A.15 Find inverse functions and relations

A.16 Identify graphs of continuous functions

### Systems of equations

J.1 Solve a system of equations by graphing

J.2 Solve a system of equations by graphing: word problems

J.3 Classify a system of equations

J.4 Solve a system of equations using substitution

J.5 Solve a system of equations using substitution: word problems

J.6 Solve a system of equations using elimination

J.7 Solve a system of equations using elimination: word problems

J.8 Solve a system of equations in three variables using substitution

J.9 Solve a system of equations in three variables using elimination

J.10 Determine the number of solutions to a system of equations in three variables

### Polar form

T.1 Find the modulus and argument of a complex number

T.2 Convert complex numbers from rectangular to polar form

T.3 Convert complex numbers from polar to rectangular form

T.4 Convert complex numbers between rectangular and polar form

T.5 Match polar equations and graphs

### Families of functions

B.1 Translations of functions

B.2 Reflections of functions

B.3 Dilations of functions

B.4 Transformations of functions

B.5 Function transformation rules

B.6 Describe function transformations

### Systems of inequalities

K.1 Solve systems of inequalities by graphing

K.2 Find the vertices of a solution set

K.3 Linear programming

### Two-dimensional vectors

U.1 Find the magnitude of a vector

U.2 Find the direction angle of a vector

U.3 Find the component form of a vector

U.4 Find the component form of a vector from its magnitude and direction angle

U.5 Find a unit vector

U.6 Add and subtract vectors

U.7 Multiply a vector by a scalar

U.8 Find the magnitude or direction of a vector scalar multiple

U.9 Find the magnitude and direction of a vector sum

U.10 Linear combinations of vectors

U.11 Graph a resultant vector using the triangle method

U.12 Graph a resultant vector using the parallelogram method

### Nonlinear inequalities

L.1 Graph solutions to quadratic inequalities

L.2 Solve quadratic inequalities

L.3 Graph solutions to higher-degree inequalities

L.4 Solve higher-degree inequalities

### Quadratic relations

C.1 Characteristics of quadratic functions

C.2 Find the maximum or minimum value of a quadratic function

C.3 Graph a quadratic function

C.4 Match quadratic functions and graphs

C.5 Solve a quadratic equation using square roots

C.6 Solve a quadratic equation by factoring

C.7 Solve a quadratic equation by completing the square

C.8 Solve a quadratic equation using the quadratic formula

C.9 Using the discriminant

### Matrices

M.1 Matrix vocabulary

M.2 Matrix operation rules

M.3 Add and subtract matrices

M.4 Multiply a matrix by a scalar

M.5 Linear combinations of matrices

M.6 Multiply two matrices

M.7 Simplify matrix expressions

M.8 Solve matrix equations

M.9 Determinant of a matrix

M.10 Is a matrix invertible?

M.11 Inverse of a 2 x 2 matrix

M.12 Inverse of a 3 x 3 matrix

M.13 Identify inverse matrices

M.14 Solve matrix equations using inverses

### Three-dimensional vectors

V.1 Find the magnitude of a three-dimensional vector

V.2 Find the component form of a three-dimensional vector

V.3 Find a three-dimensional unit vector

V.4 Add and subtract three-dimensional vectors

V.5 Scalar multiples of three-dimensional vectors

V.6 Linear combinations of three-dimensional vectors

### Polynomials

D.1 Divide polynomials using long division

D.2 Write a polynomial from its roots

D.3 Find the roots of factored polynomials

D.4 Rational root theorem

D.5 Complex conjugate theorem

D.6 Conjugate root theorems

D.7 Descartes’ Rule of Signs

D.8 Fundamental Theorem of Algebra

D.9 Match polynomials and graphs

D.10 Factor sums and differences of cubes

D.11 Solve equations with sums and differences of cubes

D.12 Factor using a quadratic pattern

D.13 Solve equations using a quadratic pattern

D.14 Pascal’s triangle

D.15 Pascal’s triangle and the Binomial Theorem

D.16 Binomial Theorem I

D.17 Binomial Theorem II

### Trigonometry

N.1 Convert between radians and degrees

N.2 Radians and arc length

N.3 Quadrants

N.4 Coterminal and reference angles

N.5 Find trigonometric ratios using right triangles

N.6 Find trigonometric ratios using the unit circle

N.7 Find trigonometric ratios using reference angles

N.8 Inverses of trigonometric functions

N.9 Solve trigonometric equations

N.10 Trigonometric ratios: find a side length

N.11 Trigonometric ratios: find an angle measure

N.12 Solve a right triangle

N.13 Law of Sines

N.14 Law of Cosines

N.15 Solve a triangle

N.16 Area of a triangle: sine formula

N.17 Area of a triangle: Heron’s formula

### Sequences and series

W.1 Find terms of a sequence

W.2 Find terms of a recursive sequence

W.3 Identify a sequence as explicit or recursive

W.4 Find a recursive formula

W.5 Find recursive and explicit formulas

W.6 Convert a recursive formula to an explicit formula

W.7 Convert an explicit formula to a recursive formula

W.8 Convert between explicit and recursive formulas

W.9 Introduction to sigma notation

W.10 Identify arithmetic and geometric series

W.11 Find the sum of a finite arithmetic or geometric series

W.12 Introduction to partial sums

W.13 Partial sums of arithmetic series

W.14 Partial sums of geometric series

W.15 Partial sums: mixed review

W.16 Convergent and divergent geometric series

W.17 Find the value of an infinite geometric series

W.18 Write a repeating decimal as a fraction

### Rational functions

E.1 Rational functions: asymptotes and excluded values

E.2 Solve rational equations

E.3 Check whether two rational functions are inverses

### Logic

X.1 Identify hypotheses and conclusions

X.2 Counterexamples

X.3 Conditionals

X.4 Negations

X.5 Converses, inverses and contrapositives

X.6 Biconditionals

### Logarithms

F.1 Convert between exponential and logarithmic form: rational bases

F.2 Evaluate logarithms

F.3 Change of base formula

F.4 Identify properties of logarithms

F.5 Product property of logarithms

F.6 Quotient property of logarithms

F.7 Power property of logarithms

F.8 Properties of logarithms: mixed review

F.9 Evaluate logarithms: mixed review

### Exponential and logarithmic functions

G.1 Domain and range of exponential and logarithmic functions

G.2 Evaluate exponential functions

G.3 Match exponential functions and graphs

G.4 Solve exponential equations by factoring

G.5 Solve exponential equations using common logarithms

G.6 Solve logarithmic equations I

G.7 Solve logarithmic equations II

G.8 Identify linear and exponential functions

G.9 Exponential functions over unit intervals

G.10 Describe linear and exponential growth and decay

G.11 Exponential growth and decay: word problems

G.12 Compound interest: word problems

G.13 Continuously compounded interest: word problems

### Radical functions

H.1 Domain and range of radical functions

H.2 Solve radical equations

### Roots and rational exponents

I.1 Roots of integers

I.2 Roots of rational numbers

I.3 Find roots using a calculator

I.4 Evaluate rational exponents

I.5 Operations with rational exponents

I.6 Nth roots

I.7 Simplify radical expressions with variables

I.8 Simplify expressions involving rational exponents

### Trigonometric functions

O.1 Find properties of sine functions

O.2 Write equations of sine functions from graphs

O.3 Write equations of sine functions using properties

O.4 Graph sine functions

O.5 Find properties of cosine functions

O.6 Write equations of cosine functions from graphs

O.7 Write equations of cosine functions using properties

O.8 Graph cosine functions

O.9 Graph sine and cosine functions

### Trigonometric identities

P.1 Complementary angle identities

P.2 Symmetry and periodicity of trigonometric functions

P.3 Trigonometric identities I

P.4 Trigonometric identities II

### Conic sections

Q.1 Find properties of parabolas

Q.2 Write equations of parabolas in vertex form

Q.3 Graph parabolas

Q.4 Find properties of circles

Q.5 Write equations of circles in standard form

Q.6 Graph circles

Q.7 Find properties of ellipses

Q.8 Find the eccentricity of an ellipse

Q.9 Write equations of ellipses in standard form

Q.10 Find properties of hyperbolas

Q.11 Find the eccentricity of a hyperbola

Q.12 Write equations of hyperbolas in standard form

Q.13 Convert equations of conic sections from general to standard form

### Complex numbers

R.1 Add and subtract complex numbers

R.2 Complex conjugates

R.3 Multiply and divide complex numbers

R.4 Add, subtract, multiply and divide complex numbers

R.5 Absolute values of complex numbers

R.6 Powers of i

### Complex plane

S.1 Introduction to the complex plane

S.2 Graph complex numbers

S.3 Addition in the complex plane

S.4 Subtraction in the complex plane

S.5 Graph complex conjugates

S.6 Absolute value in the complex plane

S.7 Midpoints in the complex plane

S.8 Distance in the complex plane

### Probability

Y.1 Introduction to probability

Y.2 Calculate probabilities of events

Y.3 Combinations and permutations

Y.4 Find probabilities using combinations and permutations

Y.5 Find probabilities using two-way frequency tables

Y.6 Identify independent events

Y.7 Find conditional probabilities

Y.8 Independence and conditional probability

Y.9 Find conditional probabilities using two-way frequency tables

Y.10 Find probabilities using the addition rule

### Probability distributions

Z.1 Identify discrete and continuous random variables

Z.2 Write a discrete probability distribution

Z.3 Graph a discrete probability distribution

Z.4 Expected values of random variables

Z.5 Variance of random variables

Z.6 Standard deviation of random variables

Z.7 Write the probability distribution for a game of chance

Z.8 Expected values for a game of chance

Z.9 Choose the better bet

Z.10 Find probabilities using the binomial distribution

Z.11 Mean, variance and standard deviation of binomial distributions

Z.12 Find probabilities using the normal distribution

Z.13 Find z-values

Z.14 Find values of normal variables

Z.15 Distributions of sample means

Z.16 The Central Limit Theorem

Z.17 Use normal distributions to approximate binomial distributions

### Statistics

AA.1 Identify biased samples

AA.2 Variance and standard deviation

AA.3 Identify an outlier

AA.4 Identify an outlier and describe the effect of removing it

AA.5 Outliers in scatter plots

AA.6 Match correlation coefficients to scatter plots

AA.7 Calculate correlation coefficients

AA.8 Find the equation of a regression line

AA.9 Interpret regression lines

AA.10 Analyze a regression line of a data set

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

AA.12 Find confidence intervals for population means

AA.13 Find confidence intervals for population proportions

AA.14 Interpret confidence intervals for population means

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