Physics And Maths Tutor Math Solution Bank

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Welcome to our website, Solution Bank. Here you will find all the Chapter and Exercise-questions and their solutions in a PDF format of Edexcel Pure Mathematics Year 1. Due to which all the doubts about your Pure Mathematics Year 1 will be clear. And you will be able to score well in your exam. Moreover, you can also download the pdf of this solution bank on your phone or laptop without any problem.

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Covered so far:

Lecture Topics coveredTextbook chapterMaterials 1 (23/09) Functions, graphs and some examples, vertical line test, piecewise defined functions, domains 0.1 [PDF] 2 (24/09) Natural domain and range of a function. Arithmetic operations on functions, and the corresponding domains. 0.1, 0.2 [PDF] 3 (26/09) Composition of functions. Translations, reflections, scaling, and their effect on graphs. 0.2 [PDF] 4 (30/09) Odd and even functions. Symmetry tests for plane curves. Parametric families: straight lines and power functions. 0.3 [PDF] 5 (01/10) Questions from the first tutorial. Classical types of functions: polynomials and rational functions. Examples. 0.3 [PDF] 6 (03/10) Classical types of functions: trigonometric functions. Inverse functions. Examples, domains and ranges. 0.3, 0.4 [PDF] 7 (07/10) Inverse functions. Computing inverses. Horisontal line test. Summary of the first part of the module. 0.4 [PDF] 8 (08/10) Limits: the informal approach and the formal approach. One-sided limits. Infinite limits. 1.1, 1.4 [PDF] 9 (10/10) Arithmetics of limits. Indeterminate forms of type 0/0. Infinite limits and vertical asymptotes. 1.2 [PDF] 10 (14/10) Limits at infinity and horisontal asymptotes. Infinite limits at infinity. Limit behaviour of polynomials, rational functions, and more complicated expressions. 1.3 [PDF] 11 (15/10) Continuous functions. Continuity on open and closed interval. Continuity and arithmetic operations and composition. Intermediate Value Theorem. 1.5 [PDF] 12 (17/10) Continuity of inverse functions. Continuity of trigonometric functions. Limit of sin(x)/x at x=0. 1.6 [PDF] 13 (21/10) No lecture on October 21 N/A N/A 14 (22/10) Historical remarks on calculus. Slope of the tangent line to a graph. Instantaneous velocity and rate of change. The derivative function. Differentiability at a point or on an open interval. 2.1, 2.2 [PDF] 15 (24/10) Differentiability and continuity. Differentiability on a closed interval. Other notation for derivatives. Derivatives and scalar factors, sums, and differences. Formula an-bn=(a-b)(an-1+an-2b+...+abn-2+bn-1) and derivatives of power functions with positive integer exponents. Derivatives of polynomials. 2.2, 2.3 [PDF] 16 (28/10) October Bank Holiday, no lecture. N/A N/A 17 (29/10) The binomial formula, and derivatives of power functions with positive integer exponents. Product rule. Derivative of 1/g and of the quotient f/g. Derivatives of trigonometric functions. 2.3, 2.4, 2.5 [PDF] 18 (31/10) Derivatives of power functions with negative integer exponents. Chain rule. Implicit differentiation, derivatives of inverse functions. Derivatives of power functions with fractional exponents. 2.6, Appendix D [PDF] Study Week (November 4-10): make sure to use it wisely! 19 (11/11) Implicit differentiation: examples. Higher derivatives. Derivatives of increasing/decreasing functions. 2.6, 3.1 [PDF] 20 (12/11) Derivatives of increasing/decreasing functions. Relative maxima and minima. First and second derivative tests; critical points, stationary points, points of non-differentiability. 3.1, 3.2 [PDF] 21 (14/11) Concavity up and down, inflection points. Multiplicity of roots of polynomials, and its geometric meaning. 3.2 [PDF] 22 (18/11) No lecture on November 18 N/A N/A 23 (19/11) Graphing rational functions. Differential calculus and Extreme Value Theorem / Intermediate Value Theorem. Newton's method. 3.3, 3.4, 3.7 [PDF] 24 (21/11) Newton's method: examples. Exponential and logarithmic function; their derivatives. Using logarithms to simplify functions for differentiation. Summary of differential calculus. Antiderivatives. 3.7, 4.2, 6.1, 6.2, 6.3 [PDF] 25 (25/11) Antiderivatives. Rules for antiderivatives (linear combinations, u-substitution, integration by parts). Examples. 4.2, 4.3, 7.2 [PDF] 26 (26/11) Mnemonics for antiderivatives using dy=f'(x)dx. More examples for the u-substitution and for the integration by parts. 4.3, 7.1, 7.2 [PDF] 27 (28/11) No lecture on November 28 N/A N/A 28 (02/12) Areas under curves. Example of y=x2. Net signed area under the curve. Riemann sums and integrability. Definite integral and its basic properties: exchange of limits of integration is compensated by a factor (-1), linearity of the definite integral, integral over [a,a] vanishes. 4.1, 4.4, 4.5 [PDF] 29 (03/12) Fundamental theorem of calculus. Mean-Value theorems for derivatives and integrals. 4.5, 4.6 [PDF] 30 (05/12) Using u-substitution in definite integrals. Examples. Summary of integral calculus. 4.9 [PDF] 31 (09/12) Applications of definite integrals in geometry. Area between two curves. Arc length of a curve. Volume of a solid of revolution; area of a surface of revolution. 5.1, 5.2, 5.4, 5.5 [PDF] 32 (10/12) Applications of definite integrals in physics and engineering. Work, energy, centre of gravity. 5.6, 5.7 [PDF] 33 (12/12) No lecture on December 12. Attempt sample exam problems. [PDF] Solutions to sample exam problems are available. [PDF] Tutorials:

Tutorials (exercise classes contributing to the final mark) will start in the second week of teaching. Group lists for tutorials will be available in due course on the noticeboard next to the School of Maths entrance on the ground floor of the Hamilton building.

Tutorial times and venues:

group AA1: Thu 12 - 1, M4, Museum Building (tutor: Robert Murtagh)

group AA2: Thu 4 - 5, Salmon Lecture Theatre, Hamilton Building (tutor: Gemma Foley)

group AA3: Thu 12 - 1, Synge Lecture Theatre, Hamilton Building (tutor: Mairead Grogan)

group AA4: Thu 4 - 5, Chemistry Building Large Lecture Theatre (tutor: Brendan Bulfin)

group AA5: Wed 1 - 2, Salmon Lecture Theatre, Hamilton Building (tutor: Gemma Foley)

group AA6: Fri 2 - 3, Synge Lecture Theatre, Hamilton Building (tutor: Brendan Bulfin)

group AA7: Fri 12 - 1, Salmon Lecture Theatre, Hamilton Building (tutor: Gemma Foley)

group AA8: Tue 9 - 10, Synge Lecture Theatre, Hamilton Building (tutor: Mairead Grogan)

Tutorial sheets:

By the weekend of each week, a tutorial sheet for the next week will be posted here, as well as solutions to the previous tutorial sheet. Tutorial 1 (Week 2, Michaelmas 2013): Problem sheet [PDF] Solutions [PDF]

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