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EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS

EDEXCEL PUPRE MATHS EXAM PACK|GUARANTEED SUCCESS

22 items

Edexcel A Level Maths - Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Cosine Rule - Know 2 sides, and the angle in between. You want the missing side. a² = b² + c² - 2bcCosA Cosine Rule - Know 3 sides. You want an angle. Cos A = (b² + c² - a²) ÷ 2bc Sine Rule - Know 2 angles and a side. You want the missing side. (a ÷ SinA) = (b ÷ SinB) = (c ...

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Edexcel A Level Maths - Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Equation of a straight line y - y₁ = m(x - x₁) Distance between two points d = √(x₂ - x₁)² + (y₂ - y₁)² Integration by substitution ∫f(x) = ∫f(x) × (dx÷du) Integration by parts ∫u (dv÷dx) = uv - ∫v (du÷dx) Trapezium Rule A = ½h (y₀ + 2(...

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Edexcel Pure Maths: A-Level, Content ideas and Formula|2023 LATEST UPDATE|GUARANTEED SUCCESS

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What are the turning point co-ordinates in f(x)=a(x+p)^2 +q (-p,q) How many roots are there if the discriminent > 0? Two distinct roots How many roots are there if the discriminent = 0? One/repeated root How many roots are there if the discriminent < 0? no real roots ...

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Edexcel Pure Maths A Level|2023 LATEST UPDATE|GUARANTEED SUCCESS

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fg(x) apply g first then f Functions f(x) and f^-1(x) reflections of each other in the line y = x Domain of f(x) Range of f^-1(x) Range of f(x) Domain of f^-1(x) y = |f(x)| reflection of y = f(x) for x>0 in the x-axis y = f(|x|) reflection of y = f(x) for ...

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AS-level Edexcel Pure Maths - Module 1: Algebraic expressions|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Base The number that is going to be raised to a power. Exponent The number that is used as a reference for the power Add the powers Multiplying numbers with powers - rule Subtract the powers Dividing numbers with powers - rule Multiply the powers Multiplying numbers ...

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AS-level Edexcel Pure Maths - Module 2: Quadratics|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Quadratic equation Written as ax²+bx+c=0 where a, b, c and constants. Has 0-2 solutions Roots - The solutions to an equation - The values of x for which f(x)=0 - Find by factorising x Completing the square x²+bx = (x+b÷2)²-(b÷2)² Completing the square when a≠1 - Fa...

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Edexcel A Level Maths - Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Natural Numbers The set of numbers 1, 2, 3, 4, ... Also called counting numbers. Integers The set of whole numbers and their opposites Z⁺ Z⁺₀ Rational Number set of all numbers that can be written as a fraction of two integers Q irrational numbers Numbers that can'...

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AS-level Edexcel Pure Maths - Module 6: Circles|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Midpoint ([x₁+x₂]÷2 , [y₁+y₂]÷2) Perpendicular bisector The line that passes through the midpoint of another line at 90° Finding perpendicular bisectors 1. Find the midpoint of AB 2. Find the gradient of AB 3. Find the negative reciprocal of that 4. Sub the midpoint an...

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Edexcel Maths A Level Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Differentiate tan(kx) ksec^2(kx) Differentiate cos(kx) -ksin(kx) Differentiate sin(kx) kcos(kx) Arithmetic sequence Un = a + (n - 1)d Arithmetic series Sn = n/2 (a + d) Geometric sequences Un = ar^n - 1 Geometric series Sn = a(r^n - 1) / r - 1 ...

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Edexcel A-Level Maths Pure Year 2|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Contradiction A contradiction is a disagreement between two statements, which means that both cannot be true. Proof by contradiction is a powerful technique. Proof by contradiction To prove a statement by contradiction you start by assuming it is not true. You then use logical steps to show...

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AS-level Edexcel Pure Maths - Module 4: Graphs and Transformations|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Cubic A graph where the highest exponent is 3 Cubic function f(x) = ax³+bx²+cx+d Repeated root A function where at least 2 of the roots are equal. The turning point of the graph is on the x-axis E.g. y=(x-3)(x-2)² Point of inflection A function where all the roots are e...

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AS-level Edexcel Pure Maths - Module 5: Straight line graphs|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Study AS-level Edexcel Pure Maths - Module 5: Straight line graphs Share In-class activity Classic Live Checkpoint Self-study activity Flashcards Learn Test Match Profile Picture Created by Badman892 Teacher Terms in this set (13) Original

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AS-level Edexcel Pure Maths - Module 5: Straight line graphs|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Gradient of a line (y₂-y₁) ÷ (x₂-x₁) Distance between 2 points Use pythagoras' theorem √[(∆x)²+(∆y)² Parallel lines - Gradient is equal - Y-intercept is different Perpendicular lines - Gradients multiply to make -1 - Gradients are a negative reciprocal t...

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AS-level Edexcel Pure Maths - Module 8: The binomial expansion|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$24.41

Pascal's triangle A triangle where the the two numbers above to make the number below. - The numbers are the coefficients of the expansion of (a+b)ⁿ - The (n+1)th row gives the coefficients of (a+b)ⁿ Binomial The sum or difference of two terms Expanding brackets Multiply ever...

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Edexcel Pure Maths Chapter 5|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$21.54

How to calculate the gradient of a line joining 2 points y2-y1 / x2-x1 What are two ways of writing the equations of lines? -y=mx+c, where m is the gradient and c is the y intercept -ax+by+c, where a b and c are integers How can you define a straight line? By giving: one point on t...

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Edexcel AS Pure Maths|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Quadratic Formula Domain The set of possible inputs for a function. Range The set of possible outputs of a function. Discriminant b² - 4ac > 0 then two distinct real roots. b² - 4ac = 0 then one repeated real root. b² - 4ac < 0 then a quadratic function has no ...

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AS-level Edexcel Pure Maths - Module 7: Algebraic methods|2023 LATEST UPDATE|GUARANTEED SUCCESS

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Simplifying algebraic fractions - Factorise the numerator and denominator - Collect like terms Binomial An algebraic expression of the sum or the difference of two terms. E.g. x²-y³ Polynomial A finite expression with more than 2 terms. E.g. 6x²+24x+48 Dividend The base ...

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Edexcel Pure Maths Chapter 6|2023 LATEST UPDATEGUARANTEED SUCCCESS

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How to find a midpoint of a line segment Average the x and y coordinates of its end points; (x1+x2/2),(y1+y2/2) What's a line segment A finite part of a straight line with two distinctive end points What's it helpful to do in coordinate geometry? Draw a sketch showing the info giv...

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Edexcel Pure Maths Chapter 9|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$23.69

What's the cosine rule? - correct answer a² = b² + c² - 2bcCosA cosA=? - correct answer b^2+c^2-a^2/2bc Sine rule? - correct answer a/sinA = b/sinB = c/sinC ; as well as the inverse What do you have to watch out for with the sine rule? - correct answer It can sometimes produce 2 possibl...

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Pure Maths A Level|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$22.69

Gradient y2-y1/x2-x1 Length of a line sqrt((x2-x1)^2+(y2-y1)^2) Midpoint (x1+x2/2, y1+y2/2) How do you know if two lines are perpendicular? When you multiply the gradients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to...

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A Level Further Maths: Core Pure|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$19.38

Form of complex numbers a + bi Real and imaginary parts of z = a + bi Re(z) = a, Im(z) = b When two complex numbers are equal, what is true Their real parts are equal and their imaginary parts are equal i² -1 i³ -i i⁴ 1 Determinant for two real roo...

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EDEXCEL A LEVEL MATHS|2023 LATEST UPDATE|GUARANTEED SUCCESS

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CA$23.69

1 + tan2θ = sec2θ cot2θ + 1 = cosec2θ = cosec2θ Sin2θ 2sinθcosθ Cos2θ cos²θ-sin²θ 2cos²θ-1 1-2sin²θ Tan2θ 2tanθ / (1 - tan²θ) How do you write a rational number in a proof? a/b What does y=|f(x)| do? Reflects values below the x-...

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