Class XI maths

Here is a list of all of the maths skills students learn in class XI! 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. Prakash Academy will track your score, and the questions will automatically increase in difficulty as you improve!

Consumer maths

1. A.1Simple interest
2. A.2Compound interest
3. A.3Continuously compounded interest
4. A.4Percent of a number: VAT, discount and more
5. A.5Find the percent: discount and mark-up
6. A.6Multi-step problems with percents

Single-variable inequalities

1. B.1Graph inequalities
2. B.2Write inequalities from graphs
3. B.3Identify solutions to inequalities
4. B.4Solve one-step linear inequalities: addition and subtraction
5. B.5Solve one-step linear inequalities: multiplication and division
6. B.6Solve one-step linear inequalities
7. B.7Graph solutions to one-step linear inequalities
8. B.8Solve two-step linear inequalities
9. B.9Graph solutions to two-step linear inequalities
10. B.10Solve advanced linear inequalities
11. B.11Graph solutions to advanced linear inequalities
12. B.12Graph compound inequalities
13. B.13Write compound inequalities from graphs
14. B.14Solve compound inequalities
15. B.15Graph solutions to compound inequalities
16. B.16Graph solutions to quadratic inequalities
17. B.17Solve quadratic inequalities

Relations and functions

1. C.1Relations: convert between tables, graphs, mappings and lists of points
2. C.2Domain and range of relations
3. C.3Identify independent and dependent variables
4. C.4Identify functions
5. C.5Identify functions: vertical line test
6. C.6Find values using function graphs
7. C.7Evaluate a function
8. C.8Evaluate a function: plug in an expression
9. C.9Complete a function table from a graph
10. C.10Complete a function table from an equation
11. C.11Interpret the graph of a function: word problems

Linear functions

1. D.1Find the slope of a graph
2. D.2Find the slope from two points
3. D.3Find a missing coordinate using slope
4. D.4Slope-intercept form: find the slope and y-intercept
5. D.5Slope-intercept form: graph an equation
6. D.6Slope-intercept form: write an equation from a graph
7. D.7Slope-intercept form: write an equation
8. D.8Slope-intercept form: write an equation from a table
9. D.9Slope-intercept form: write an equation from a word problem
10. D.10Write linear functions to solve word problems
11. D.11Complete a table and graph a linear function
12. D.12Write equations in standard form
13. D.13Standard form: find x- and y-intercepts
14. D.14Standard form: graph an equation
15. D.15Equations of horizontal and vertical lines
16. D.16Graph a horizontal or vertical line
17. D.17Slopes of parallel and perpendicular lines
18. D.18Write an equation for a parallel or perpendicular line
19. D.19Transformations of linear functions

Linear inequalities

1. E.1Does (x, y) satisfy the inequality?
2. E.2Linear inequalities: solve for y
3. E.3Graph a linear inequality in the coordinate plane
4. E.4Linear inequalities: word problems
5. E.5Is (x, y) a solution to the system of inequalities?
6. E.6Solve systems of linear inequalities by graphing
7. E.7Solve systems of linear and absolute value inequalities by graphing

Complex numbers

1. F.1Introduction to complex numbers
2. F.2Add and subtract complex numbers
3. F.3Complex conjugates
4. F.4Multiply complex numbers
5. F.5Divide complex numbers
6. F.6Add, subtract, multiply and divide complex numbers
7. F.7Absolute values of complex numbers
8. F.8Powers of i

Argand plane

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

Factorising

1. H.1Factorise out a monomial
2. H.2Factorise quadratic polynomials
3. H.3Factorise quadratics using algebra tiles
4. H.4Factorise using a quadratic pattern
5. H.5Factorise by grouping
6. H.6Factorise sums and differences of cubes
7. H.7Factorise polynomials

Quadratic functions

1. I.1Characteristics of quadratic functions
2. I.2Complete a function table: quadratic functions
3. I.3Find a quadratic function
4. I.4Graph a quadratic function
5. I.5Match quadratic functions and graphs
6. I.6Solve a quadratic equation using square roots
7. I.7Solve a quadratic equation using the zero product property
8. I.8Solve a quadratic equation by factorising
9. I.9Complete the square
10. I.10Solve a quadratic equation using the quadratic formula
11. I.11Using the discriminant

    Polynomials

    1. J.1Polynomial vocabulary
    2. J.2Add and subtract polynomials
    3. J.3Multiply polynomials
    4. J.4Divide polynomials using long division
    5. J.5Divide polynomials using synthetic division
    6. J.6Evaluate polynomials using synthetic division
    7. J.7Solve polynomial equations
    8. J.8Write a polynomial from its roots
    9. J.9Find the roots of factorised polynomials
    10. J.10Rational root theorem
    11. J.11Complex conjugate theorem
    12. J.12Conjugate root theorems
    13. J.13Match polynomials and graphs
    14. J.14Fundamental Theorem of Algebra
    15. J.15Pascal's triangle
    16. J.16Pascal's triangle and the Binomial Theorem
    17. J.17Binomial Theorem I
    18. J.18Binomial Theorem II

    Parabolas

    1. K.1Identify the direction a parabola opens
    2. K.2Find the vertex of a parabola
    3. K.3Find the focus or directrix of a parabola
    4. K.4Find the axis of symmetry of a parabola
    5. K.5Write equations of parabolas in vertex form from graphs
    6. K.6Write equations of parabolas in vertex form using properties
    7. K.7Convert equations of parabolas from general to vertex form
    8. K.8Find properties of a parabola from equations in general form
    9. K.9Graph parabolas

    Circles

    1. L.1Find the centre of a circle
    2. L.2Find the radius or diameter of a circle
    3. L.3Write equations of circles in standard form from graphs
    4. L.4Write equations of circles in standard form using properties
    5. L.5Convert equations of circles from general to standard form
    6. L.6Find properties of circles from equations in general form
    7. L.7Graph circles

    Ellipses

    1. M.1Find the center, vertices, or co-vertices of an ellipse
    2. M.2Find the length of the major or minor axes of an ellipse
    3. M.3Find the foci of an ellipse
    4. M.4Write equations of ellipses in standard form from graphs
    5. M.5Write equations of ellipses in standard form using properties
    6. M.6Convert equations of ellipses from general to standard form
    7. M.7Find properties of ellipses from equations in general form

    Hyperbolas

    1. N.1Find the center of a hyperbola
    2. N.2Find the vertices of a hyperbola
    3. N.3Find the length of the transverse or conjugate axes of a hyperbola
    4. N.4Find the equations for the asymptotes of a hyperbola
    5. N.5Find the foci of a hyperbola
    6. N.6Write equations of hyperbolas in standard form from graphs
    7. N.7Write equations of hyperbolas in standard form using properties
    8. N.8Convert equations of hyperbolas from general to standard form
    9. N.9Find properties of hyperbolas from equations in general form

    Rational functions and expressions

    1. O.1Rational functions: asymptotes and excluded values
    2. O.2Evaluate rational expressions I
    3. O.3Evaluate rational expressions II
    4. O.4Simplify rational expressions
    5. O.5Multiply and divide rational expressions
    6. O.6Add and subtract rational expressions
    7. O.7Solve rational equations

    Function operations

    1. P.1Add and subtract functions
    2. P.2Multiply functions
    3. P.3Divide functions
    4. P.4Composition of linear functions: find a value
    5. P.5Composition of linear functions: find an equation
    6. P.6Composition of linear and quadratic functions: find a value
    7. P.7Composition of linear and quadratic functions: find an equation

    Angle measures

    1. Q.1Convert between radians and degrees
    2. Q.2Radians and arc length
    3. Q.3Quadrants
    4. Q.4Graphs of angles
    5. Q.5Coterminal angles
    6. Q.6Reference angles

    Trigonometry

    1. R.1Pythagoras' Theorem and its converse
    2. R.2Special right triangles
    3. R.3Trigonometric ratios: sin, cos and tan
    4. R.4Trigonometric ratios: csc, sec and cot
    5. R.5Trigonometric ratios in similar right triangles
    6. R.6Find trigonometric ratios using the unit circle
    7. R.7Sin, cos and tan of special angles
    8. R.8Csc, sec and cot of special angles
    9. R.9Find trigonometric functions using a calculator
    10. R.10Inverses of sin, cos and tan
    11. R.11Inverses of csc, sec and cot
    12. R.12Solve trigonometric equations I
    13. R.13Solve trigonometric equations II
    14. R.14Trigonometric ratios: find a side length
    15. R.15Trigonometric ratios: find an angle measure
    16. R.16Solve a right triangle
    17. R.17Law of Sines
    18. R.18Law of Cosines
    19. R.19Solve a triangle
    20. R.20Area of a triangle: sine formula
    21. R.21Area of a triangle: Law of Sines

    Trigonometric functions

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

    Trigonometric identities

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

       Problem solving

       1. U.1Word problems: mixed review
       2. U.2Word problems with money
       3. U.3Consecutive integer problems
       4. U.4Rate of travel: word problems
       5. U.5Weighted averages: word problems

       Logic

       1. V.1Identify hypotheses and conclusions
       2. V.2Counterexamples
       3. V.3Truth tables
       4. V.4Truth values
       5. V.5Conditionals
       6. V.6Negations
       7. V.7Converses, inverses and contrapositives
       8. V.8Biconditionals

       Sequences and series

       1. W.1Classify formulas and sequences
       2. W.2Find terms of an arithmetic sequence
       3. W.3Find terms of a geometric sequence
       4. W.4Find terms of a recursive sequence
       5. W.5Evaluate formulas for sequences
       6. W.6Write a formula for an arithmetic sequence
       7. W.7Write a formula for a geometric sequence
       8. W.8Write a formula for a recursive sequence
       9. W.9Sequences: mixed review
       10. W.10Introduction to sigma notation
       11. W.11Identify arithmetic and geometric series
       12. W.12Find the sum of a finite arithmetic or geometric series
       13. W.13Introduction to partial sums
       14. W.14Partial sums of arithmetic series
       15. W.15Partial sums of geometric series
       16. W.16Partial sums: mixed review
       17. W.17Convergent and divergent geometric series
       18. W.18Find the value of an infinite geometric series
       19. W.19Write a repeating decimal as a fraction

       Introduction to limits

       1. X.1Find limits using graphs
       2. X.2Find one-sided limits using graphs
       3. X.3Determine if a limit exists

       Calculate limits

       1. Y.1Find limits using addition, subtraction and multiplication laws
       2. Y.2Find limits using the division law
       3. Y.3Find limits using power and root laws
       4. Y.4Find limits using limit laws
       5. Y.5Find limits of polynomials and rational functions
       6. Y.6Find limits involving factorisation and rationalisation

       Limits involving infinity

       1. Z.1Find limits at vertical asymptotes using graphs
       2. Z.2Determine end behaviour using graphs
       3. Z.3Determine end behaviour of polynomial and rational functions

       Limits and rational functions

       1. AA.1Find the limit at a vertical asymptote of a rational function I
       2. AA.2Find the limit at a vertical asymptote of a rational function II

       Continuity

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

       Introduction to derivatives

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

       Calculate derivatives

       1. DD.1Sum and difference rules
       2. DD.2Product rule
       3. DD.3Quotient rule
       4. DD.4Power rule I
       5. DD.5Power rule II
       6. DD.6Find derivatives of polynomials
       7. DD.7Find derivatives of rational functions
       8. DD.8Find derivatives of trigonometric functions I
       9. DD.9Find derivatives of trigonometric functions II
       10. DD.10Chain rule
       11. DD.11Find derivatives of radical functions
       12. DD.12Find derivatives using the product rule
       13. DD.13Find derivatives using the quotient rule I
       14. DD.14Find derivatives using the quotient rule II
       15. DD.15Find derivatives using the chain rule I
       16. DD.16Find derivatives using the chain rule II

       Probability

       1. EE.1Introduction to probability
       2. EE.2Theoretical and experimental probability
       3. EE.3Compound events: find the number of outcomes
       4. EE.4Calculate probabilities of events
       5. EE.5Permutations
       6. EE.6Counting principle
       7. EE.7Permutation and combination notation
       8. EE.8Find probabilities using permutations and combinations
       9. EE.9Find probabilities using two-way frequency tables
       10. EE.10Identify independent events
       11. EE.11Probability of independent and dependent events
       12. EE.12Geometric probability
       13. EE.13Find conditional probabilities
       14. EE.14Independence and conditional probability
       15. EE.15Find conditional probabilities using two-way frequency tables
       16. EE.16Find probabilities using the addition rule
       17. EE.17Find probabilities using the normal distribution

       Statistics

       1. FF.1Mean, median, mode and range
       2. FF.2Quartiles
       3. FF.3Identify biased samples
       4. FF.4Mean absolute deviation
       5. FF.5Variance and standard deviation