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Infection and response
Organisation
Cell biology
Biological molecules
Homeostasis and response
Responding to change (a2 only)
Energy transfers (a2 only)
The control of gene expression (a-level only)
Substance exchange
Bioenergetics
Genetic information & variation
Inheritance, variation and evolution
Genetics & ecosystems (a2 only)
Ecology
Cells
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1f industrialisation and the people: britain, c1783-1885
1c the tudors: england, 1485-1603
Britain & the wider world: 1745 -1901
Inter-war germany
World war one
2n revolution and dictatorship: russia, 1917-1953
World war two & the holocaust
1l the quest for political stability: germany, 1871-1991
The cold war
2j america: a nation divided, c1845-1877
Medieval period: 1066 -1509
The fight for female suffrage
2m wars and welfare: britain in transition, 1906-1957
2d religious conflict and the church in england, c1529-c1570
Britain: 1509 -1745
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10/11/2022
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Chp 1. Algebraic Expressions edexcel. INDEX CAWS: x a a х х • aº а-с x сосаза (ab)c =x d L = d = L ac а Va aª= d√ac² а X x ad atd a-d ac b c D •spee points: PURE - Algebra and functions * index laws only work avith terus that have the same base e.g 23 x 52 cannot be simplified using inders laws WHAT ARE SURDS? n 0 = لاک : a positive integer; not a square number. Sards are irrational numbers • irrational numbers. a number that cannot be written in the form a where a and b are both integers. b a • • lets ↳ The decimal expansion of an irrational number goes on forever, and never recurs. Vab √a x √b こ = = surd you exact form, va √b leave answers in Sa+ √b IS NOT EQUAL то бать 06 √a-√b is NOT EQUAL TO √a-b when simpliquying surds, novembering your saquare numbers is really herpfal RATIONALISING SURDS. • Rationalising a denominator changes a fraction with surds in its denominator, into an equivalent fraction where the denominator is a rational number Cusually an integer) and any surds in the numerator * Rational number = a number that can be written in the form a where a and bave both integers. b * Integer = any number including 0, positive numbers, and negative numbers. NEVER a fraction, a decimal, or a per cent. (1) (2) 1 (3) 1 x √α = va va va √a + √b 土 va-√b 3 cases you need to know to deal with when rationalising denominators: X Va raxva = x √a - √b₂ = √a- √b Va-be atb va а (Sat √b) (Sa-√b) a-vab + √ab-b √a+ √b = √a + √b √a + √b atb Chp 2. Quadratics edexcel spec points • PORE- algebra + ах2 Ax² +bx+c...
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= 0, where a, b, c are real number and fundi function a +0. ● To solve quadratic equations, a given equation must be rewritten in the form or kept in the form of αx²+bx+c = 0. . ax² +bx+c Must be factorised Quadratic formula: x = -b ± √√√b²-4ac 2a COMPLETING THE SQUARE: • x² + bx+c = ( x + b₂² ) ²³ - ( b )² + c 2 Example x²+6x+2 (x+6) ² (€) ²+2 2 (x+3)²-9+2 (x+3)²-7 WAYS TO SOLUE: factorisation ↳ Completing the square ↳ quadratic formula FUNCTIONS • A function can be seen as a machine that takes in an input, converts this value Mathema- tically and gives an output. • Input = denoted with 'x' • Output = represented as f(x) or g(x) For a given function, the set of possible inputs is called domain and the set of possible outputs is called the range Function x f(x) 1x² + x ● 3 QUADRATIC GRAPHS 0 f(x) = ax² + bxctc y = ax² + bx + ( ↳a is positive the shape of the parabola would be Lais negative the shape of the parabola would be H (B) Intersection of the y-axis ACSO: Minimum value of a function is the place where the graph has a verter at its lowest point. Maximum value of a function is the place where the graph has a vertex at its highest point. •A and B roots 62 Turning point are the intersection of the x-axis at these points y=o 3²+x = 11 f(x= (x+b)²-(1)² + c La stationary point ↳ can be found by completing the square :.T.P - (-2,- () ² + c) THE DISCRIMINANT The expression b²-4ac is called the discriminant. 4 • The value obtained using the discriminant expression on a quadratic function will indicate how many roots a function f(x) has. given part of the quadratic formula - b ± √(b) ² - 4 Cac) 20 ● For the quadratic function f(x) = ax² + bx+c. * if the discrimant b²- 4ac >0 then the function f(x) has 2 distinct real roots. * if the discrimant b²- 4ac =0, then the function f(x) has I repeated real root. * If the discriminant b² (ac <0, then the function f(x) has no real roots. EXAMPLE x = - find the range of U for which x² + 2x +h=0 has 2 distinct real roots. x² + 2x + 1 = 0 a = 1, b = 2 7 b²-4ac>0 for 2 distinct real roots 2²- 4 x 1 x 4 >0 2²-4K>0 C = K -4K>-4 K21 HIDDEN QUADRATICS Example Solve x4- 13x² + 36 = 0 f(x) = x², so let y = x ² and substitute into the equation: y) 13y + 36 = as x ² = (x²)² = y² 10 Then, solve by factorising (y- 9) (y-4)= 0 y-9=0 ⇒ y = 9 y - 4 = 0 ⇒ y = 4 (3 marks) x= ± √3 x= ±2