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Cambridge 4 Unit Mathematics Year 12

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Published: 28th September 2000
For Ages: 16 - 17 years old
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Written by highly respected and experienced authors, Cambridge Mathematics 4 Unit Year 12 is a textbook of exceptional quality that can cater for a range of abilities in the maths classroom. It provides engaging and logical resources designed to encourage mathematical imagination, demonstrate the relationships between topics, and reflect the key syllabus emphases for Mathematics Extension 2.

1. Graphs
1.1. Critical points on a curve
1.2. Reflecting graphs on the coordinate axes
1.3. Translation of graphs – addition and subtraction of ordinates
1.4. Multiplication of ordinates
1.5. Reciprocal functions and division of ordinates
1.6. Graphs of the form y=[f(x)]n
1.7. Graphs of the form y=square root of f(x)
1.8. Graphs of composite functions
1.9. Implicit differentiation and curve sketching
1.10. Using graphs
2. Complex numbers
2.1. The arithmetic of complex numbers and the solution of quadratic equations
2.2. Geometrical representation of a complex number as a point in an Argand diagram
2.3. Geometrical representation of a complex number as a vector
2.4. Powers and roots of complex numbers
2.5. Curves and regions in the Argand diagram
3. Conics
3.1. Focus/directrix definitions and Cartesian equations
3.2. Parametric equations for the ellipse and hyperbola
3.3. Tangents and normals to the ellipse and hyperbola
3.4. The rectangular hyperbola
4. Polynomials
4.1. Factors and zeros of polynomials
4.2. Factorisation of polynomials and the fundamental theorem of algebra
4.3. The relationship between the roots and coefficients of a polynomial equation
4.4. Solutions of polynomial equations
4.5. Partial fractions
5. Integration
5.1. Using a table of standard integrals
5.2. Reduction to standard form by algebraic rearrangement of the integrand
5.3. Using substitution to reduce integrals to standard form
5.4. Integrals of trigonometric functions
5.5. Integration by parts
5.6. Further properties of definite integrals
6. Volumes
6.1. Volumes of solids of revolution by slicing
6.2. Volumes of solids by cylindrical shells
6.3. Volumes of solids with parallel cross-sections of similar shapes
7. Mechanics
7.1. Motion of a particle in one dimension
7.2. Motion of a particle moving in a straight line in a resisting medium under gravity
7.3. Motion of a particle in two dimensions
7.4. Circular motion in a horizontal plane
7.5. The conical pendulum
7.6. Motion around a circular banked track
8. Harder 3 Unit topics
8.1. Inequalities between real numbers
8.2. Mathematical induction
8.3. Geometry of the circle

ISBN: 9780521005470
ISBN-10: 0521005477
Audience: Primary / High School
For Ages: 16 - 17 years old