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Stationary Points & Curve Sketching, and the Second Derivative Test open new vistas in understanding the nature of graphs. As you master Simultaneous Linear Equations, you're not just solving problems; you're unlocking a new perspective on mathematical relationships. The Essential Revision at the end is your bridge to excellence, consolidating your knowledge and skills. Learning Outcomes Develop a foundational understanding of key mathematical concepts and functions. Master the intricacies of quadratic equations and co-ordinate geometry. Explore and apply the principles of sequences, series, and the binomial theorem. Gain proficiency in differentiation and its practical applications in tangents and normals. Understand and implement techniques in curve sketching, stationary points, and optimisation. Why choose this High School Math (Pure Mathematics 1) course? Unlimited access to the course for a lifetime. 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Career path Mathematician: £30,000 - £60,000 Data Analyst: £25,000 - £50,000 Actuarial Analyst: £28,000 - £55,000 Research Scientist (Mathematics): £32,000 - £60,000 Engineering Consultant: £27,000 - £55,000 Academic Tutor (Mathematics): £24,000 - £40,000 Prerequisites This High School Math (Pure Mathematics 1) does not require you to have any prior qualifications or experience. You can just enrol and start learning.This High School Math (Pure Mathematics 1) was made by professionals and it is compatible with all PC's, Mac's, tablets and smartphones. You will be able to access the course from anywhere at any time as long as you have a good enough internet connection. Certification After studying the course materials, there will be a written assignment test which you can take at the end of the course. After successfully passing the test you will be able to claim the pdf certificate for £4.99 Original Hard Copy certificates need to be ordered at an additional cost of £8. Course Curriculum Introduction Introduction 00:03:00 Functions What is Function? 00:07:00 Vertical Line Test 00:04:00 Value of a Function Graphically 00:08:00 Domain Range of a function Algebraically 00:13:00 Domain Range of a function Graphically 00:06:00 Even & Odd Functions 00:07:00 One to one Function 00:05:00 Composite Functions 00:09:00 How to draw Rational Functions- 1 00:04:00 How to draw Rational Functions- 2 00:10:00 Inverse of a function Algebraically 00:05:00 Inverse of a function Graphically 00:09:00 Practice Problems 00:15:00 Practice Problems 00:11:00 Resources Downloads 00:40:00 Quadratic Equations Introduction to Quadratic Equations 00:04:00 Solving Quadratic Equations by Factorization method 00:10:00 Writing in completed square form 00:08:00 Solving by completed square method 00:08:00 Sketching of Quadratic Graphs 00:11:00 Quadratic graphs using Transformations 00:06:00 Quadratic inequalities 00:11:00 Deriving Quadratic formula 00:05:00 Solving problems using Quadratic Formula 00:06:00 Equations reducible to Quadratic 00:07:00 Nature of Roots of Quadratic Equations 00:04:00 Nature of roots continues 00:12:00 Quadratic Equations (Resources) 00:50:00 Co-ordinate Geometry Distance formula 00:15:00 Mid point formula 00:05:00 Gradient of a line 00:10:00 Graphing using gradient and y intercept 00:02:00 Some standard lines 00:04:00 Slope intercept form y = m x +c 00:05:00 Point slope form and two point form 00:10:00 Intersection of line and parabola 00:09:00 Practice Problems from past papers (part 3) 00:12:00 Sequence and series Sequence and series ( video) 00:08:00 Arithmetic Sequence 00:10:00 General term of an A.P. 00:07:00 Finding given term is which term? 00:05:00 Writing sequence when two terms are known 00:08:00 Condition for three terms to be in A.P. 00:05:00 Sum to n terms of A.P. 00:06:00 Practice Problems 1 (A.P.) 00:08:00 Practice problems 3 (A.P.) 00:07:00 Practice problems 4 (A.P.) 00:10:00 Geometric Progressions 00:11:00 Sum to n terms in G.P. 00:14:00 Sum to infinite Terms in G.P. 00:13:00 Practice Problems 1 (GP) 00:13:00 Practice Problems 2 (GP) 00:06:00 Practice Problems based on AP and GP both 00:15:00 Sequence and series Text 1 00:40:00 Sequence and series Text 2 00:55:00 Binomial Theorem What is Factorial? 00:06:00 n-choose -r problems 00:06:00 Properties of n - choose -r 00:05:00 Expanding using Binomial Theorem 00:11:00 Finding the indicated term in the Binomial expansion 00:10:00 Finding the indicated term from end 00:09:00 Finding the coefficient for given exponent (index) of the variable 00:08:00 Finding the term independent of variable 00:05:00 Expanding in increasing and decreasing powers of x 00:09:00 Practice problems 1 00:12:00 Practice Problems 2 00:09:00 Practice problems 3 00:10:00 Past papers problems 1 00:15:00 Past Paper problems 2 00:13:00 Past Paper problems 3 00:09:00 Resources in this section 00:50:00 Differentiation What is Derivative? 00:07:00 Derivation of formula for Derivative 00:06:00 Differentiation by definition or First Principle 00:06:00 Power Rule 00:20:00 Practice Problems on Power Rule 1 00:07:00 Practice Problems on Power Rule 2 00:07:00 Practice Problems on Power Rule 3 00:05:00 Practice Problems on Power Rule 4 00:11:00 Practice Problems on Power Rule 5 00:07:00 Tangents and Normals Tangents and Normals- Basics 00:12:00 Practice- Tangents and Normals Part 1 00:16:00 Practice- Tangents and Normals Part 2 00:13:00 Practice- Tangents and Normals Part 3 00:11:00 Practice- Tangents and Normals Part 4 00:14:00 Stationary Points & Curve Sketching Stationary Points - Basics 00:13:00 Practice- Increasing Decreasing & Maxima Minima part 1 00:11:00 Practice- Increasing Decreasing & Maxima Minima part 2 00:12:00 Practice- Increasing Decreasing & Maxima Minima part 3 00:10:00 Second Derivative Test (Maximum & Minimum Points) Concavity-Basics 00:02:00 Concavity & Second Derivative 00:08:00 Second Derivative Test 00:09:00 Practice Problems on second derivative 00:04:00 Practice Problem of Maxima Minima using second derivative test Part 1 00:17:00 Practice Problem of Maxima Minima using second derivative test Part 2 00:10:00 Practice Problem of Maxima Minima using second derivative test Part 3 00:07:00 Practice Problem of Maxima Minima using second derivative test Part 4 00:07:00 Applications of Maxima and Minima Part 1 00:09:00 Applications of Maxima and Minima Part 2 00:07:00 Applications of Maxima and Minima Part 3 00:10:00 Applications of Maxima and Minima Part 4 00:09:00 Applications of Maxima and Minima Part 5 00:10:00 Applications of Maxima and Minima Part 6 00:08:00 Past Paper Problems on applications of maxima and minima Part 1 00:09:00 Past Paper Problems on applications of maxima and minima Part 2 00:09:00 Past Paper Problems on applications of maxima and minima Part 3 00:08:00 Past Paper Problems on applications of maxima and minima Part 4 00:07:00 Chain Rule 00:12:00 Rate of change part 1 00:05:00 Rate of change part 2 00:10:00 Rate of change part 3 00:07:00 Past Paper Problems using chain rule -1 00:06:00 Past Paper Problems using chain rule - 2 00:07:00 Past Paper Problems using chain rule 3 00:07:00 Past Paper Problems using chain rule -4 00:04:00 Simultaneous Linear equations Graphical Method of solving pair of linear equations 00:10:00 Video lecture on Graphical method 00:05:00 Method of elimination by substitution 00:10:00 Video lecture on substitution method 00:06:00 Method of elimination by equating the coefficients 00:10:00 Video lecture on equating coefficients method 00:09:00 Practice Problems on Linear equation 00:20:00 Essential Revision How to take up this course? 00:10:00 Background of Algebra 00:10:00 Language of Alg ebra 00:10:00 Finding Values of algebraic expressions 00:14:00 Fractional Indices 00:10:00 Higher Indices 00:07:00 Rules of Brackets 00:04:00 Simplification by removing brackets (BODMAS) 00:11:00 Simplifications of Algebraic Fractions 00:07:00 Solving complex Linear Equations in one variable 00:10:00 Factorization by taking out common factor 00:10:00 Factorization by grouping the terms 00:09:00 Factorize using identity a ² - b ² 00:07:00 Factorization by middle term split 00:12:00