Section C: Specification Content

5Specification Content

TopicCompetence Statement

Algebra

Manipulation of algebraic expressions
The remainder theorem
The factor theorem
Solution of equations
Inequalities
The binomial expansion
Application to probability / a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
a16 / Be able to simplify expressions including algebraic fractions, square
roots and polynomials.
Be able to find the remainder of a polynomial up to order 3 when divided by a linear factor.
Be able to find linear factors of a polynomial up to order 3.
Be confident in the use of brackets.
Be able to solve a linear equation in one unknown.
Be able to solve quadratic equations by factorisation, the use of the formula and by completing the square.
Be able to solve a cubic equation by factorisation.
Be able to solve two linear simultaneous equations in 2 unknowns.
Be able to solve two simultaneous equations in 2 unknowns where one equation is linear and the other is quadratic.
Be able to set up and solve problems leading to linear, quadratic and cubic equations in one unknown, and to simultaneous linear equations in two unknowns.
Be able to manipulate inequalities.
Be able to solve linear and quadratic inequalities algebraically and graphically.
Understand and be able to apply the binomial expansion of (a + b)n where n is a positive integer.
Recognise probability situations which give rise to the binomial distribution.
Be able to identify the binomial parameter, p, the probability of success.
Be able to calculate probabilities using the binomial distribution.

TopicCompetence Statement

Coordinate Geometry (2 dimensions only)

The Straight line
The co-ordinate geometry of circles
Inequalities
Applications to linear programming / g1
g2
g3
g4
g5
g6
g7
g8
g9
g10
g11
g12 / Know the definition of the gradient of a line.
Know the relationship between the gradients of parallel and perpendicular lines.
Be able to calculate the distance between two points.
Be able to find the mid-point of a line segment.
Be able to form the equation of a straight line.
Be able to draw a straight line given its equation.
Be able to solve simultaneous equations graphically.
Know that the equation of a circle, centre (0,0), radius r is x2 + y2 = r2.
Know that (x – a)2 + (y – b)2 = r2 is the equation of a circle with centre
(a, b) and radius r.
Be able to illustrate linear inequalities in two variables.
Be able to express real situations in terms of linear inequalities.
Be able to use graphs of linear inequalities to solve 2-dimensional maximisation and minimisation problems, know the definition of objective function and be able to find it in 2-dimensional cases.

TopicCompetence Statement

Trigonometry

Ratios of any angles and their graphs / t1
t2
t3
t4
t5
t6
t7
t8 / Be able to use the definitions of sin, cos and tan for any angle (measured in degrees only).
Be able to apply trigonometry to right angled triangles.
Know the sine and cosine rules and be able to apply them.
Be able to apply trigonometry to triangles with any angles.
Know and be able to use the identity that
Know and be able to use the identity sin2 + cos2 = 1.
Be able to solve simple trigonometrical equations in given intervals.
Be able to apply trigonometry to 2 and 3 dimensional problems.

TopicCompetence Statement

Calculus

Differentiation
Integration
Definite integrals
Application to kinematics / c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
c14
c15
c16
c17
c18 / Be able to differentiate kxn where n is a positive integer or 0, and the sum of such functions.
Know that the gradient function gives the gradient of the curve
and measures the rate of change of y with x.
Know that the gradient of the function is the gradient of the tangent at that point.
Be able to find the equation of a tangent and normal at any point on a curve.
Be able to use differentiation to find stationary points on a curve.
Be able to determine the nature of a stationary point.
Be able to sketch a curve with known stationary points.
Be aware that integration is the reverse of differentiation.
Be able to integrate kxn where n is a positive integer or 0, and the sum of such functions.
Be able to find a constant of integration.
Be able to find the equation of a curve, given its gradient function and one point.
Know what is meant by an indefinite and a definite integral.
Be able to evaluate definite integrals.
Be able to find the area between a curve, two ordinates and the x-axis.
Be able to find the area between two curves.
Be able to use differentiation and integration with respect to time to solve simple problems involving variable acceleration.
Be able to recognise the special case where the use of constant acceleration formulae is appropriate.
Be able to solve problems using these formulae.

Competence Statements. Additional Mathematics. Page 1