P1.1 - Algebra and functions

Laws of indices for all rational am × an = am + n, am ÷ an = am − n, (am)n = amn exponents. m The equivalence of a n and n am should be known.

Use laws of indices to connect the rule to the data and decision in the question.

This matters because laws of indices determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply laws of indices to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Laws of indices is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Use and manipulation of surds.; Students should be able to rationalise denominators.

Use use and manipulate surds to connect the rule to the data and decision in the question.

This matters because use and manipulate surds determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply use and manipulate surds to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Use and manipulate surds is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Quadratic functions and their graphs.

Use quadratic functions and their graphs to connect the rule to the data and decision in the question.

This matters because quadratic functions and their graphs determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply quadratic functions and their graphs to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Quadratic functions and their graphs is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The discriminant of a quadratic function.; Know and use b² − 4ac > 0, b² − 4ac = 0 and b² − 4ac < 0.

Use discriminant of a quadratic to connect the rule to the data and decision in the question.

This matters because discriminant of a quadratic determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply discriminant of a quadratic to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Discriminant of a quadratic is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Completing the square and solving quadratic equations.; Solve quadratic equations by factorisation, formula, calculator methods and completing the square.

Use completing the square to connect the rule to the data and decision in the question.

This matters because completing the square determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply completing the square to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Completing the square is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Solve simultaneous equations; analytical solution by substitution.

Use solve simultaneous equations to connect the rule to the data and decision in the question.

This matters because solve simultaneous equations determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply solve simultaneous equations to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

Interpret linear and quadratic inequalities graphically and algebraically, including inequalities with brackets or fractions reducible to linear or quadratic form; identify solution ranges from intersections of curves and lines.

Use interpreting linear and quadratic inequalities to connect the rule to the data and decision in the question.

This matters because interpreting linear and quadratic inequalities determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply interpreting linear and quadratic inequalities to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Interpreting linear and quadratic inequalities is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Represent linear and quadratic inequalities graphically, such as y > x + r and y > ax² + bx + c.; Use shading and dotted/solid line conventions.

Use graphing linear and quadratic inequalities to connect the rule to the data and decision in the question.

This matters because graphing linear and quadratic inequalities determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply graphing linear and quadratic inequalities to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Graphing linear and quadratic inequalities is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Solve linear and quadratic inequalities, including comparisons between a quadratic expression and a linear expression.

Use solving linear and quadratic inequalities to connect the rule to the data and decision in the question.

This matters because solving linear and quadratic inequalities determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply solving linear and quadratic inequalities to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Solving linear and quadratic inequalities is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Algebraic manipulation of polynomials.; Expand brackets, collect like terms and factorise polynomials of degree n, n <= 3.; The notation f(x) may be used.

Use algebraic manipulation to connect the rule to the data and decision in the question.

This matters because algebraic manipulation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply algebraic manipulation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Algebraic manipulation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Graphs of functions; sketching Functions to include simple cubic functions and the curves defined by simple equations. reciprocal functions Geometrical interpretation of k k algebraic solution of equations.; Use y = and y = with x ≠ 0. of intersection points of graphs of x x2 functions to solve equations.; Knowledge of the term asymptote is expected.; Also, trigonometric graphs.

Use graphs of functions to connect the rule to the data and decision in the question.

This matters because graphs of functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply graphs of functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Graphs of functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Knowledge of the effect of simple Students should be able to apply one of these transformations on the graph of transformations to any of the above functions (quadratics, cubics, reciprocals, sine, cosine, and tangent) and sketch the y = f(x) as represented by y = af(x), resulting graphs. y = f(x) + a, y = f(x + a), y = f(ax).; Given the graph of any function y = f(x), students should be able to sketch the graph resulting from one of these transformations.

Use effect of simple to connect the rule to the data and decision in the question.

This matters because effect of simple determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply effect of simple to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Effect of simple is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.