Maths — Pure Mathematics 4

Underground Mathematics

Cambridge's Underground Mathematics Combining Functions, Introducing Calculus, Product Rule & Integration by Parts, Chain Rule & Integration by Substitution, Exponentials & Logarithms, Sequences, Counting & Binomials, Divisibility & Induction, Calculus Of Powers, Calculus Meets Functions, Power Series, Polynomials & Rational Functions, Combining Vectors, Hyperbolic Functions and Vector Geometry collections for Edexcel IAL Maths — 119 resources mapped across 18 specification points, each with suggestions and worked solutions.

Source & rights

18 specification points

1.1 · Proof by contradiction bra and functions: • Including proof of the irrationality of 2 and the infinity of primes, and application to unfamiliar proofs.

57 resources

What (approximately) is the square root of $26$ ? recommendedReview question

Underground Mathematics

1.1 · Proof by contradiction bra and functions: • Including proof of the irrationality of 2 and the infinity of primes, and application to unfamiliar proofs.

Underground Mathematics

1.1 · Proof by contradiction bra and functions: • Including proof of the irrationality of 2 and the infinity of primes, and application to unfamiliar proofs.

3.1 · Parametric equations of curves and conversion between cartesian and parametric forms.

4.1 · Binomial Series for any rational n. Differentiation: • For | x | < b⁄a, students should be able to obtain the expansion of (ax + b)ⁿ, and the expansion of rational functions by decomposition into partial fractions.

5.1 · Differentiation of simple functions defined implicitly or parametrically. The finding of equations of tangents and normals to curves given parametrically or implicitly is required.

5.2 · Formation of simple differential equations. Questions involving connected rates of change may be set.

6.1 · Evaluation of volume of revolution.: • π∫y²dx is required, but not π∫x²dy. Students should be able to find a volume of revolution, given parametric equations.

6.4 · Analytical solution of simple first order differential equations with separable variables. General and particular solutions will be required.

6.5 · Use integration to find the area under a curve given its parametric equations. Students should be able to find the area under a curve given its parametric equations. Students will not be expected to sketch a curve from its parametric equations.

7.1 · Vectors in two and three dimensions.

7.2 · Magnitude of a vector.: • Students should be able to find a unit vector in the direction of a, and be familiar with | a |.

7.3 · Algebraic operations of vector addition and multiplication by scalars, and their geometrical interpretations.   

7.4 · Position vectors.: • OB − OA = AB = b − a

7.5 · The distance between two points. The distance d between two points ( x 1 , y 1 , z 1 ) and ( x 2 , y 2 , z 2 ) is given by d 2 = ( x 1 – x 2 ) 2 + ( y 1 – y 2 ) 2 + ( z 1 – z 2 ) 2

7.6 · Vector equations of lines.: • To include the forms r = a + t b and r = c + t (d – c) Conditions for two lines to be parallel, intersecting or skew.