maths

Class XII

Here is a list of all of the skills students learn in class XII! These skills are organised 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

1. A.1Domain and range
2. A.2Identify functions
3. A.3Linear functions
4. A.4Evaluate functions
5. A.5Add, subtract, multiply, and divide functions
6. A.6Composition of functions
7. A.7Identify inverse functions
8. A.8Find values of inverse functions from tables
9. A.9Find values of inverse functions from graphs
10. A.10Find inverse functions and relations

Families of functions

1. B.1Translations of functions
2. B.2Reflections of functions
3. B.3Dilations of functions
4. B.4Transformations of functions
5. B.5Function transformation rules
6. B.6Describe function transformations

Polynomials

1. C.1Divide polynomials using long division
2. C.2Divide polynomials using synthetic division
3. C.3Evaluate polynomials using synthetic division
4. C.4Write a polynomial from its roots
5. C.5Find the roots of factorised polynomials
6. C.6Rational root theorem
7. C.7Complex conjugate theorem
8. C.8Conjugate root theorems
9. C.9Descartes' Rule of Signs
10. C.10Fundamental Theorem of Algebra
11. C.11Match polynomials and graphs
12. C.12Factorise sums and differences of cubes
13. C.13Solve equations with sums and differences of cubes
14. C.14Factorise using a quadratic pattern
15. C.15Solve equations using a quadratic pattern
16. C.16Pascal's triangle
17. C.17Pascal's triangle and the Binomial Theorem
18. C.18Binomial Theorem I
19. C.19Binomial Theorem II

Systems of inequalities

1. D.1Solve systems of linear inequalities by graphing
2. D.2Solve systems of linear and absolute value inequalities by graphing
3. D.3Find the vertices of a solution set
4. D.4Linear programming
5. D.5Graph solutions to quadratic inequalities
6. D.6Solve quadratic inequalities

Matrices

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

Trigonometry

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

Trigonometric functions

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

Trigonometric identities

1. H.1Complementary angles
2. H.2Symmetry and periodicity of trigonometric functions
3. H.3Trigonometric identities I
4. H.4Trigonometric identities II

Two-dimensional vectors

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

Three-dimensional vectors

1. J.1Find the magnitude of a three-dimensional vector
2. J.2Find the component form of a three-dimensional vector
3. J.3Find a three-dimensional unit vector
4. J.4Add and subtract three-dimensional vectors
5. J.5Scalar multiples of three-dimensional vectors
6. J.6Linear combinations of three-dimensional vectors

Sequences and series

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

Probability

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

Probability distributions

1. M.1Identify discrete and continuous random variables
2. M.2Write a discrete probability distribution
3. M.3Graph a discrete probability distribution
4. M.4Expected values of random variables
5. M.5Variance and standard deviation of random variables
6. M.6Write the probability distribution for a game of chance
7. M.7Expected values for a game of chance
8. M.8Choose the better bet
9. M.9Find probabilities using the binomial distribution
10. M.10Mean, variance, and standard deviation of binomial distributions
11. M.11Find probabilities using the normal distribution
12. M.12Use normal distributions to approximate binomial distributions