Lesson (Guidance only)

Specification – What students need to learn:

Resources

1 Algebra & functions

1.1 The rules of indices

Laws of indices for all rational exponents. The equivalence of and should be known.

1.1 Algebraic Expression Ext Qs

1.2 Indices & Surds

Use and manipulation of surds.

1.3 Rationalising the denominator

Students should be able to rationalise denominators.

1.3 Surds & Indices Ext Qs

1.4 Factorising

Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, factorisation. Students should be able to use brackets. Factorisation of polynomials of degree n, n ≤ 3, eg .The notation f(x) may be used. (Use of the factor theorem is not required.)

2 Quadratic Functions

2.1 Solving quadratic equations by factorisation

Solution of quadratic equations. Solution of quadratic equations by factorisation and completing the square.

CHE Lesson, Printouts

2.1 Quadratic Equations (Example)

2.1 Quadratic Equations Ext Qs Answers

Ext. Find all real numbers such that

2.2 The quadratic formula and its discriminant

… use of the formula and the discriminant of a quadratic function.

CHE Lesson, Printouts

GeoGebra Resource

2.3 Sketching quadratics and the discriminant

Quadratic functions and their graphs.

The discriminant of a quadratic function.

CHE Lesson, Printouts

Emphasise the teaching of the discriminant. You could use Qs 6 to 9 from:

C1 Solomon Worksheet Algebra G

C1 Solomon Worksheet Algebra G Solutions

3 Equations & inequalities

3.1 Solving linear simultaneous equations

Simultaneous equations: analytical solution by substitution.

CHE Lesson, Printouts

Extension questions involving simultaneous equations with three unknowns are on the 3.2 resource below

3.2 Solving non-linear simultaneous equations

For example, where one equation is linear and one equation is quadratic.

CHE Lesson, Printouts

3.2 Simultaneous Equations (Example)

3.2 Simultaneous Equations Ext Qs

3.3 Quadratics inequalities

Solution of linear and quadratic inequalities. For example, , ,.

CHE Lesson, Printouts

3.4 The discriminant

Edexcel frequently ask questions such as:

The equation x2 + kx + 8 = k has no real solutions for x.

(a) Show that k satisfies k2 + 4k – 32 < 0.

(b) Hence find the set of possible values of k.

CHE Lesson, Printouts

SMP Inequalities and the discriminant

Quadratic Inequalities and the discriminant worksheet Answers

Chapters 1 to 3 Algebra Homework

CHE HW Solutions

Chapters 1 to 3 Algebra Test, [Mark Scheme]

4 Sketching Curves

4.1 Sketching cubics

Graphs of functions; sketching curves defined by simple equations. Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations.

4.2 Reciprocal graphs

Functions to include simple cubic functions and the reciprocal function with .

Knowledge of the term asymptote is expected.

4.3 Transformation of graphs

Knowledge of the effect of simple transformations on the graph of y = f(x) as represented by y = af(x), y = f(x) + a, y = f(x + a), y = f(ax).

Students should be able to apply one of these transformations to any of the above functions (quadratics, cubics, reciprocal) and sketch the resulting graph.

Given the graph of any function y = f(x) students should be able to sketch the graph resulting from one of these transformations.

4.3 Limits & asymptotes (Example)

4.3 Limits & asymptotes Ext Qs

4.4 Review

5 Coordinate geometry in the (x, y) plane

5.1 Finding the equation of a line given it’s gradient and a coordinate

Equation of a straight line, including the forms and .

CHE Lesson, Printouts

5.2 Finding the equation of a line given two coordinates

… the equation of a line through two given points

CHE Lesson, Printouts

5.3 Perpendicular gradients and review

…the equation of a line parallel (or perpendicular) to a given line through a given point. For example, the line perpendicular to the line through the point

(2, 3) has equation…