Maths — Pure 1

Underground Mathematics

Cambridge's Underground Mathematics Quadratics, Combining Functions, Geometry of Equations, Circles, Thinking about Geometry, Introducing Calculus, Product Rule & Integration by Parts, Chain Rule & Integration by Substitution, Trigonometry: Triangles to Functions, Trigonometry: Compound Angles, Introducing Calculus, Exponentials & Logarithms, Sequences, Counting & Binomials, Chain Rule & Integration by Substitution, Thinking about Algebra, Divisibility & Induction, Exponentials & Logarithms, Introducing Calculus, Product Rule & Integration by Parts, Introducing Calculus, Calculus Of Powers, Chain Rule, Calculus Meets Functions, Calculus Trig Log, Product Rule, Power Series, Calculus meets Functions, Chain Rule & Integration by Substitution and Product Rule & Integration by Parts collections for Cambridge International A-Level Mathematics — 348 resources mapped across 30 specification points, each with suggestions and worked solutions.

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30 specification points

1.1.1 · carry out the process of completing the square for a quadratic polynomial ax + bx + c and use y a completed square form

8 resources

Name that graph recommendedPackage of problems · Developing

Beyond these specification points131 in the library

These Quadratics, Combining Functions, Geometry of Equations, Circles, Thinking about Geometry, Introducing Calculus, Product Rule & Integration by Parts, Chain Rule & Integration by Substitution, Trigonometry: Triangles to Functions, Trigonometry: Compound Angles, Introducing Calculus, Exponentials & Logarithms, Sequences, Counting & Binomials, Chain Rule & Integration by Substitution, Thinking about Algebra, Divisibility & Induction, Exponentials & Logarithms, Introducing Calculus, Product Rule & Integration by Parts, Introducing Calculus, Calculus Of Powers, Chain Rule, Calculus Meets Functions, Calculus Trig Log, Product Rule, Power Series, Calculus meets Functions, Chain Rule & Integration by Substitution and Product Rule & Integration by Parts resources are kept for extra maths practice — they are not tied to the specification points above, and each one says why.

Beyond these specification points131 in the library

Underground Mathematics

1.1.1 · carry out the process of completing the square for a quadratic polynomial ax + bx + c and use y a completed square form

Beyond these specification points131 in the library

Underground Mathematics

1.1.1 · carry out the process of completing the square for a quadratic polynomial ax + bx + c and use y a completed square form

Beyond these specification points131 in the library

1.1.2 · find the discriminant of a quadratic polynomial ax + bx + c and use the discriminant ‘repeated root’ is included.

1.1.3 · solve quadratic equations, and quadratic By factorising, completing the square and using the inequalities, in one unknown formula.

1.1.4 · solve by substitution a pair of simultaneous e.g. equations of which one is linear and one is 2 quadratic

1.1.5 · recognise and solve equations in x which are quadratic in some function of x . tan

1.2.1 · understand the terms function, domain, range, one-one function, inverse function and composition of functions

1.2.2 · identify the range of a given function in simple cases, and find the composition of two given functions condition that a composite function

1.2.3 · determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases

1.2.4 · illustrate in graphical terms the relation between Sketches should include an indication of the mirror a one-one function and its inverse line

1.3.1 · find the equation of a straight line given e.g. given two points, or one point and the gradient. sufficient information

1.3.2 · interpret and use any of the forms y = mx + c , y – y = m ( x – x ) , ax + by + c = 0 in solving

1.4.1 · understand the definition of a radian, and use the relationship between radians and degrees

1.5.1 · sketch and use graphs of the sine, cosine and tangent functions (for angles of any size, and using either degrees or radians)

1.5.2 · use the exact values of the sine, cosine and tangent of 30°, 45°, 60°, and related angles

1.5.3 · use the notations sin⁻¹x, cos⁻¹x, tan⁻¹x to denote the principal values of the inverse trigonometric functions

1.5.4 · use the identities tan θ ≡ sin θ / cos θ and sin²θ + cos²θ ≡ 1

1.5.5 · find all the solutions of simple trigonometrical equations lying in a specified interval (general forms of solution are not included)

1.6.1 · use the expansion of (a + b)^n, where n is a positive integer

1.6.2 · recognise arithmetic and geometric progressions

1.6.3 · use the formulae for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric progressions

1.6.4 · use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression

1.7.1 · understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations dy/dx, f'(x), f''(x) for first and second derivatives

1.7.2 · use the derivative of x^n (for any rational n), together with constant multiples, sums and differences of functions, and of composite functions using the chain rule

1.7.3 · apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change

1.7.4 · locate stationary points and determine their nature, and use information about stationary points in sketching graphs

1.8.1 · understand integration as the reverse process of differentiation, and integrate (ax + b)^n for any rational n except -1, together with constant multiples, sums and differences

1.8.2 · solve problems involving the evaluation of a constant of integration

1.8.3 · evaluate definite integrals

1.8.4 · use definite integration to find lines parallel to the axes, or between a curve and a line or between two curves: the area of a region bounded by a curve and a volume of revolution about one of the axes