British Columbia

British Columbia flag
Skills available for British Columbia grade 12 math curriculum

IXL's grade 12 skills will be aligned to the British Columbia Learning Outcomes soon! Until then, you can view a complete list of grade 12 objectives below.

Show alignments for:

12.A Students use patterns to describe the world and to solve problems; represent algebraic expressions in multiple ways; and, use algebraic and graphical models to generalize patterns, make predictions, and solve problems.

  • 12.A1 derive and apply expressions to represent general terms for geometric growth and to solve problems

  • 12.A2 derive and apply expressions to represent sums for geometric growth and to solve problems

  • 12.A3 estimate sums of expressions represented by infinite geometric processes where the common ratio, r, is -1 < r < 1

  • 12.A4 solve exponential equations having bases that are powers of one another

  • 12.A5 solve and verify exponential and logarithmic equations

  • 12.A6 solve and verify exponential and logarithmic identities

  • 12.A7 distinguish between degree and radian measure, and solve problems using both

  • 12.A8 determine the exact and the approximate values of trigonometric ratios for any multiples of 0°, 30°, 45°, 60° and 90°, and 0 rad, pi / 6 rad, pi / 4 rad, pi / 3 rad, and pi / 2 rad

  • 12.A9 solve first and second degree trigonometric equations over a specified domain

    • 12.A9.1 algebraically

    • 12.A9.2 graphically

  • 12.A10 determine the general solutions to trigonometric equations where the domain is the set of real numbers

  • 12.A11 analyse trigonometric identities

    • 12.A11.1 graphically

    • 12.A11.2 algebraically for general cases

  • 12.A12 use sum, difference, and double angle identities for sine and cosine to verify and simplify trigonometric expressions

  • 12.A13 change functions from exponential form to logarithmic form and vice versa

  • 12.A14 model, graph, and apply exponential functions to solve problems

  • 12.A15 model, graph, and apply logarithmic functions to solve problems

  • 12.A16 describe the three primary trigonometric functions as circular functions with reference to the unit circle and an angle in standard position

  • 12.A17 sketch and analyse the graphs of sine, cosine, and tangent functions, for

    • 12.A17.1 amplitude, if defined

    • 12.A17.2 period

    • 12.A17.3 domain and range

    • 12.A17.4 asymptotes, if any

    • 12.A17.5 behaviour under transformations

  • 12.A18 use trigonometric functions to model and solve problems

12.B Students perform, analyse, and create transformations of functions and relations that are described by equations or graphs.

  • 12.B1 describe how vertical and horizontal translations of functions affect graphs and their related equations:

    • 12.B1.1 y = f(x – h)

    • 12.B1.2 y – k = f(x)

  • 12.B2 describe how compressions and expansions of functions affect graphs and their related equations:

    • 12.B2.1 y = af(x)

    • 12.B2.2 y = f(kx)

  • 12.B3 describe how reflections of functions in both axes and in the line y = x affect graphs and their related equations:

    • 12.B3.1 y = f(–x)

    • 12.B3.2 y = –f(x)

    • 12.B3.3 y = f to the –1 power (x)

  • 12.B4 using the graph and/or the equation of f(x), describe and sketch 1 / f(x)

  • 12.B5 using the graph and/or the equation of f(x), describe and sketch |f(x)|

  • 12.B6 describe and perform single transformations and combinations of transformations on functions and relations

12.C Students solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations, combinations, and combining of simpler probabilities.

  • 12.C1 use the fundamental counting principle to determine the number of different ways to perform multi-step operations

  • 12.C2 use factorial notation to determine different ways of arranging n distinct objects in a sequence

  • 12.C3 determine the number of permutations of n different objects taken r at a time, and use this to solve problems

  • 12.C4 determine the number of combinations of n different objects taken r at a time, and use this to solve problems

  • 12.C5 solve problems, using the binomial theorem where the exponent n belongs to the set of natural numbers

  • 12.C6 construct a sample space for up to three events

  • 12.C7 classify events as independent or dependent

  • 12.C8 solve problems, using the probabilities of mutually exclusive and complementary events

  • 12.C9 determine the conditional probability of two events

  • 12.C10 solve probability problems involving permutations, combinations, and conditional probability