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Open Global Math Standards 2026™
Global
Standards:
42
Subjects:
1
Stages:
Early Years → 12th Grade
Math
42
11th Grade
(42)
OGM.12.ALG.1
Manipulate polynomials using factorisation, algebraic long division, the Factor Theorem, and the Remainder Theorem; simplify and perform operations on rational algebraic expressions.
OGM.12.ALG.2
Decompose rational functions into partial fractions for denominators with non-repeated and squared linear factors (with at most three linear factors in total).
OGM.12.ALG.3
Solve quadratic equations in a function of the unknown, utilize the discriminant to determine root nature, and complete the square to analyze quadratic forms and optimize objective functions.
OGM.12.ALG.4
Solve simultaneous equations in two variables (including linear-quadratic systems) by substitution and elimination, and solve/graph linear and quadratic inequalities using set and interval notation.
OGM.12.ALG.5
Expand binomial expressions (a + bx)^n using Pascal's triangle, combinatorics (nCr, n!), and the general binomial series for any rational exponent n when |bx/a| < 1, using expansions for numerical approximation.
OGM.12.CAL.1
Understand the derivative f'(x) as the limit of the difference quotient and as the gradient of the tangent; differentiate x^n, sin(x), cos(x) from first principles; compute second derivatives to determine convexity, concavity, and points of inflection.
OGM.12.CAL.2
Differentiate powers (x^n), exponentials (e^(kx), a^(kx)), logarithms (ln x), and trigonometric functions (sin kx, cos kx, tan kx); apply product, quotient, and chain rules to composite and inverse functions, including connected rates of change.
OGM.12.CAL.3
Apply differentiation to find equations of tangents and normals, identify intervals of increase/decrease, locate and classify stationary points (local/global extrema, points of inflection), and differentiate implicitly and parametrically.
OGM.12.CAL.4
Understand the Fundamental Theorem of Calculus and integration as the limit of a Riemann sum; evaluate definite and indefinite integrals of standard algebraic, exponential, reciprocal (1/x), and trigonometric functions; calculate areas under curves and between intersecting curves.
OGM.12.CAL.5
Integrate functions using integration by substitution, integration by parts, and partial fractions with linear denominators.
OGM.12.CAL.6
Construct and solve first-order differential equations with separable variables dy/dx = f(x)g(y); determine general and particular solutions with initial conditions; interpret solutions in kinematics, growth/decay, and physical contexts.
OGM.12.CAL.7
Locate roots using sign-change intervals and analyze failure conditions; solve equations iteratively using fixed-point iteration x_(n+1) = g(x_n) (with cobweb/staircase diagrams) and the Newton-Raphson method; perform numerical integration via the trapezium rule.
OGM.12.EXP.1
Distinguish between linear, polynomial, and exponential growth; understand that exponential growth eventually exceeds polynomial growth; prove constant difference vs. constant ratio growth rates over equal intervals.
OGM.12.EXP.2
Understand the inverse relationship between exponential functions (a^x, e^x) and logarithmic functions (log_a(x), ln(x)); graph both families showing asymptotes and key points.
OGM.12.EXP.3
Apply the laws of logarithms (product, quotient, power, change of base) to simplify expressions and solve exponential and logarithmic equations analytically and with technology.
