Bridging Unit
|
Chapter |
Content |
Time |
Resources |
|
Number and Algebra |
Writing numbers in Standard Form Laws of Indices for Integer exponents Ratio and Proportion Factorising, Algebra in fractions, Simultaneous
equations, Changing the subject of the formula Straight line graphs, gradient and y-intercept. Finding the distance between two points |
3 hours 3 hours 2 hours |
Number and algebra 1 Number and algebra 2 Straight line graphs |
|
Shape and Space |
Basic Trigonometry Sine Rule, Cosine Rule, Area of a
Triangle
Volume and Surface Area of a Cone
and Sphere
Circle theorems: (a)
angle in a
semicircle is a right angle. (b) the perpendicular
drawn from the centre of a circle to a chord bisects the chord. (c) the radius of a
circle drawn to the point of contact of a tangent to the circle is at right
angles to the tangent. |
2 hours 4 hours 1 hour 2 hours |
Trigonometry Sine rule, Cosine rule, areas
of triangles Surface Area and Volume Circles |
Pure Maths 1
|
Chapter |
Content |
Time |
Resources |
|
P1.1. Proof |
Proof by direct methods. Proof by a direct method
including a sequence of logical steps may be required. For example, prove
that the equation x2 + px + q = 0 has distinct real roots if, and only if, p2 > 4q. |
2 hours |
Proof |
|
P1.2. Algebra |
Laws of indices for all rational exponents. The
equivalence of am/n and n√am. Use and manipulate surds including rationalising
denominators. Solution of quadratic equations. The discriminant of a quadratic function. Proof of existence of
roots. Solution by factorisation, formula and completing the square. Proof of the quadratic formula. Algebraic manipulation of polynomials, including
expanding brackets and collecting like terms. Factorising and use
of the Factor Theorem. (If f(x)
= 0 when x = a, then (x a) is a factor of f(x).) Factorisation of polynomials of
degree n, n ≤ 3, eg x3 - 4x2 + 3. The notation f(x). Evaluate f(x) for
specific values of x. Identities.
Algebraic division. Equating coefficients. Quadratic functions and their graphs. Solution of simultaneous equations in particular where
one equation is linear and one equation is quadratic. Solution of linear and quadratic inequalities. For
example, px2 + qx + r ≤ 0. |
2 hour 1 hour 3
hours 1 hour 3 hours 2 hours 2 hours 2 hours |
P1 5A,5B,5C P1 1E P1 2B The Discriminant P1 1A,
Identities P1 1B,1C,1D Long Division Factor Theorem Quadratic Functions & Graphs P1 2C P1 2D |
|
P1.3. Trigonometry |
Radians. Use of the formulas s = rq and A = ½r2q for
arc length and area of sector Trigonometric functions for any angle in radians and
degrees. Their graphs, symmetries and periodicity. Knowledge of graphs of
curves with equations such as y = 3
sin x, y = sin(x + π/6), y = sin 2x will be
required. Knowledge and use of and sin2q + cos2q = 1 to solve trigonometric equations in a given interval. For example, 2sin (x - π/2) = Ύ for 0 < x < 2π cos (2x + 30) = -½ for 180 ≤ x ≤ 180, 6cos2x + sin x 5 = 0 for 0
≤ x ≤ 360, |
2 hours 3 hours 3
hours |
P1 7A P1 7B,7C,7D (Questions 1 & 2) 7E P1 7D Trigonometric equations |
Pure Maths 1
Chapter |
Content |
Time |
Resources |
|
P1.4. Co-ordinate geometry in the (x,y) plane |
Forming the equation of a straight line in forms y = mx + c, y - y1 = m(x - x1) and ax + by
+ c = 0 from either being given a) 2 points or b) a parallel /
perpendicular line and 1 point For example the line perpendicular to the line
3x + 4y = 18 through the point (2,3) has equation y 3 = 4/3(x 2) Conditions for two straight lines to be parallel or
perpendicular to each other. The co-ordinates of the mid-point of a line segment
joining two given points. |
3 hours 1 hour |
P1 4B,4C Perpendicular /
Parallel Lines Equations of Lines |
|
P1.5. Sequences and series |
Sequences, including those given by a formula for the nth term. Arithmetic series, including the formula for the sum
of the first n natural numbers. The
general term and the sum to n terms
of the series are required. The proof
of the sum formula should be known. Geometric series. The general term and the sum to n terms are required. The proof of the sum formula should be
known. The sum to infinity of a
convergent geometric series. Use
of S notation for both Arithmetic and Geometric
series |
1 hour 2 hours 2 hours 1 hour |
P1 6A P1 6D P1 6E P1
6C |
Pure Maths 1
Chapter |
Content |
Time |
Resourses |
|
P1.6. Differentiation |
The derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point; the gradient of the tangent as a limit;
interpretation as a rate of change, i.e. is
the rate of change of y with
respect to x. Knowledge of the
chain rule is not required. Algebraic differentiation of xp , where p is rational. For example, the
ability to differentiate expressions such as (2x + 5)(x - 1) and is
expected. Second
order derivatives. Increasing and decreasing functions. Notation such as will
be needed. Applications to gradients, maxima, minima and
stationary points. Problems involving
finding equations of normals and tangents. Problems involving curve
sketching. Practical problems, for example find maximum volume of a box given
its surface area. |
1 hour 2 hours 4 hours |
Notes from P1 Ch8 P1 8A Differentiation P1 8D Tangents / Normals |
|
P1.7. Integration |
Indefinite integration as
the reverse of differentiation. Integration of xp, where p
is rational, p ≠ -1. The general and particular
solution of Evaluation of definite integrals. Interpretation of the
definite integral as the area under a curve. Evaluation of the area of a region bounded by a curve,
given lines parallel to the y-axis
and the x-axis. Familiarity with the
idea that the area under a curve may be obtained as the limit of a sum of the
areas of rectangles. Both ∫ y dx
and ∫ x dy are required. |
2 hours 3 hours |
P1 9A,9B(question 1) P1 9B,9C Integration and Area |
Mechanics 1
Chapter |
Content |
Time |
Resources |
|
M1.1. Mathematical Modelling in Mechanics |
The basic ideas of mathematical
modelling as applied in mechanics. This should not be taught as a singular
topic, but the ideas should be constantly emphasised during the course
wherever appropriate. Familiarity with terms : particle, lamina, rigid body,
rod (light, uniform, non-uniform), inextensible string, smooth and rough
surface, light smooth pulley, bead, wire, peg. Students should be familiar
with the assumptions made in these models. |
|
|
|
M1.2. Vectors |
Magnitude and direction of a
vector. Properties of vectors. Resultant of vectors. Use i and j notation. Application of vectors to
displacements, velocities, accelerations and forces in a plane. Use of velocity = change of
displacement / time in the case of
constant velocity, and of acceleration = change of
velocity / time in the case of constant acceleration. |
2 hours 2 hours 2 hours |
Notes from M1 p16 M1 2B M1 2C M1 2D |
|
M1.3. Kinematics |
Motion in a straight line with constant acceleration.
Knowledge and use of formulae for constant acceleration will be required. Graphical solutions may be required, including
displacement-time, velocity-time, speed-time and acceleration-time
graphs. Greater emphasis should be
placed on speed-time graphs. |
4 hours 3 hours |
M1 3A, 3B M1 3C Vertical Motion |
|
M1.4. Dynamics |
Newtons laws of motion. Simple applications including the motion of two
connected particles. Problems with smooth fixed pulleys and motion on a rough
or smooth inclined plane. Coefficient of friction. An understanding of F = mR when a particle is
moving. Momentum and impulse. The impulse-momentum principle.
The principle of conservation of momentum applied to two particles colliding
directly. Knowledge of Newtons law of restitution is not required. Problems
will be confined to those of a one-dimensional nature. |
2 hours 6 hours 2 hours |
M1 5A M1 5B, 5C, 5D M1 5I, 5J(ignore questions
relating to energy) |
Mechanics 1
Chapter |
Content |
Time |
Resources |
|
M1.5 Statics |
Forces treated as vectors. Resolution of forces.
Resolving forces into components using sin and cos. Equilibrium of a particle under coplanar forces.
Weight, normal reaction, tension and thrust, friction. Coefficient of friction. An understanding of F £ mR in a situation of
equilibrium. |
4 hours 3 hours 2 hours |
M1 4A, 4B M1 4C, 4D M1 4E |
|
M1.6. Moments |
Moment of a force. Simple
problems involving coplanar parallel forces acting on a body and conditions
for equilibrium in such
situations. |
3 hours |
M1 6A, 6B |
Statistics 1
Chapter |
Content |
Time |
Resources |
|
1. Mathematical models in probability and statistics |
The basic ideas of
mathematical modelling as applied in probability and statistics. |
1 hour |
Information sheet Mathematical modelling in
Probability and Statistics |