Class XII maths

Here is a list of all of the maths skills students learn in class XII! These skills are organised into categories, and you can move your mouse over any skill name to preview the skill. 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.3Find the slope of a linear function
4. A.4Graph a linear function
5. A.5Write the equation of a linear function
6. A.6Evaluate functions
7. A.7Find values using function graphs
8. A.8Complete a table for a function graph
9. A.9Add, subtract, multiply and divide functions
10. A.10Composition of functions
11. A.11Identify inverse functions
12. A.12Find values of inverse functions from tables
13. A.13Find values of inverse functions from graphs
14. A.14Find 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

Nonlinear inequalities

1. E.1Graph solutions to quadratic inequalities
2. E.2Solve quadratic inequalities
3. E.3Graph solutions to higher-degree inequalities
4. E.4Solve higher-degree inequalities

Matrices

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

Trigonometry

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

Trigonometric functions

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

   Trigonometric identities

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

   Conic sections

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

   Complex numbers

   1. K.1Add and subtract complex numbers
   2. K.2Complex conjugates
   3. K.3Multiply and divide complex numbers
   4. K.4Add, subtract, multiply and divide complex numbers
   5. K.5Absolute values of complex numbers
   6. K.6Powers of i

   Argand plane

   1. L.1Introduction to the Argand plane
   2. L.2Graph complex numbers
   3. L.3Addition in the Argand plane
   4. L.4Subtraction in the Argand plane
   5. L.5Graph complex conjugates
   6. L.6Absolute value in the Argand plane
   7. L.7Midpoints in the Argand plane
   8. L.8Distance in the Argand plane

   Polar form

   1. M.1Find the modulus and argument of a complex number
   2. M.2Convert complex numbers from rectangular to polar form
   3. M.3Convert complex numbers from polar to rectangular form
   4. M.4Convert complex numbers between rectangular and polar form
   5. M.5Match polar equations and graphs

   Two-dimensional vectors

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

   Three-dimensional vectors

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

   Sequences and series

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

   Continuity

   1. Q.1Identify graphs of continuous functions
   2. Q.2Determine continuity using graphs
   3. Q.3Determine one-sided continuity using graphs
   4. Q.4Find and analyse points of discontinuity using graphs
   5. Q.5Determine continuity on an interval using graphs
   6. Q.6Determine the continuity of a piecewise function at a point
   7. Q.7Make a piecewise function continuous
   8. Q.8Intermediate Value Theorem
      

      Introduction to derivatives

      1. R.1Average rate of change I
      2. R.2Average rate of change II
      3. R.3Find instantaneous rates of change
      4. R.4Velocity as a rate of change
      5. R.5Find values of derivatives using limits
      6. R.6Find the slope of a tangent line using limits
      7. R.7Find equations of tangent lines using limits

      Derivative rules

      1. S.1Sum and difference rules
      2. S.2Product rule
      3. S.3Quotient rule
      4. S.4Power rule I
      5. S.5Power rule II
      6. S.6Chain rule
      7. S.7Inverse function rule

      Calculate derivatives

      1. T.1Find derivatives of polynomials
      2. T.2Find derivatives of rational functions
      3. T.3Find derivatives of trigonometric functions I
      4. T.4Find derivatives of trigonometric functions II
      5. T.5Find derivatives of exponential functions
      6. T.6Find derivatives of logarithmic functions
      7. T.7Find derivatives of inverse trigonometric functions
      8. T.8Find derivatives of radical functions
      9. T.9Find derivatives using the product rule I
      10. T.10Find derivatives using the product rule II
      11. T.11Find derivatives using the quotient rule I
      12. T.12Find derivatives using the quotient rule II
      13. T.13Find derivatives using the chain rule I
      14. T.14Find derivatives using the chain rule II

      Derivative strategies

      1. U.1Find derivatives using implicit differentiation
      2. U.2Find tangent lines using implicit differentiation
      3. U.3Find derivatives using logarithmic differentiation

      Calculate higher derivatives

      1. V.1Find higher derivatives of polynomials
      2. V.2Find higher derivatives of rational and radical functions
      3. V.3Find second derivatives of trigonometric, exponential and logarithmic functions
      4. V.4Find higher derivatives using patterns

      Probability

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

      Probability distributions

      1. X.1Identify discrete and continuous random variables
      2. X.2Write a discrete probability distribution
      3. X.3Graph a discrete probability distribution
      4. X.4Expected values of random variables
      5. X.5Variance of random variables
      6. X.6Standard deviation of random variables
      7. X.7Write the probability distribution for a game of chance
      8. X.8Expected values for a game of chance
      9. X.9Choose the better bet
      10. X.10Find probabilities using the binomial distribution
      11. X.11Mean, variance and standard deviation of binomial distributions
      12. X.12Find probabilities using the normal distribution
      13. X.13Find z-values
      14. X.14Find values of normal variables
      15. X.15Distributions of sample means
      16. X.16The Central Limit Theorem
      17. X.17Use normal distributions to approximate binomial distributions

      Statistics

      1. Y.1Match correlation coefficients to scatter plots
      2. Y.2Calculate correlation coefficients
      3. Y.3Find the equation of a regression line
      4. Y.4Interpret regression lines
      5. Y.5Analyse a regression line of a data set
      6. Y.6Analyse a regression line using statistics of a data set