OCR a-level maths
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1. - Sn = n/2 (2a + (n-1)d)
- Sn = n/2 (a + l) where a is the first term and l is the last term: formula of an
arithmetic series
2. the sum of the terms of an arithmetic sequence: what is an arithmetic series
3. - Un = a + (n-1)d
- a = the first term
- d = the common difference: nth term of an arithmetic sequence
4. - Un = ar^(n-1)
- a = first term
- r = common ratio: nth term of a geometric sequence
5. - Sn = a(1-r^n) / 1-r
- Sn = a(r^n - 1) / r-1
where r does not equal 1: formula of first n terms of a geometric sequence
6. the sum of the values tend towards infinity: divergent sequence
7. - the sum of the values tend towards a specific number
- it is only convergent if |r|<1: convergent sequence
8. a / 1-r: sum to infinity of a geometric series
9. : series can be shown using sigma notation
10. - defines each term of a sequence as a function of the previous term
- to find the members of the sequence substitute in n=1, n=2 ... using the
previous terms given: recurrence relation of form Un+1 = f(Un)
11. it is decreasing: if Un+1 < Un for all n , what is true of the sequence
12. - it is periodic
- means that the terms repeat in a cycle
- k = the order of the sequence (how often the terms repeat): if Un+k = Un for
all n , what is true of the sequence
13. (x+y)(x-y): x^2-y^2
14. * (a-sqrt(b) / a-sqrt(b)): rationalising the denominator of e.g. 1/sqrt(b)+a
15. b^2 - 4ac > 0 has 2 distant real roots
B^2 -4ac = 0 has on real repeated root
b^2 - 4ac < 0 has no real roots: using the discriminant to find number of roots
16. if f(x) = a(x+p)^2 + q, then the turning point is (-p,q): completing the square
to find the turning point
, OCR a-level maths
Study online at https://quizlet.com/_79wpbd
17. < is dotted line
dis solid line: using lines to represent < and d
18. x=0 and y=0: where are the asymptotes of y = k/x
19. translation up by a units: y = f(x) + a
20. translation left by a units: y = f(x+a)
21. stretch vertically by scale factor a: y = af(x)
22. stretch by scale factor 1/a horizontally: y = f(ax)
23. reflection in x-axis: y = -f(x)
24. reflection in y-axis: y = f(-x)
25. m = (y2 - y1)/(x2 - x1): calculating the gradient with 2 points
26. y-y1=m(x-x1): another way to calculate equation of a line
27. y= -(1/m)x: equation of line perpendicular to y = mx
28. Sqrt ((x2 - x1)^2 + (y2 - y1)^2 ): distance between (x1,y1) and (x2,y2)
29. x^2 + y^2 = r^2: equation of circle centre (0,0)
30. (x-a)^2 + (y-b)^2 = r^2: equation of circle centre (a,b)
31. centre: (-f,-g)
radius: sqrt (f^2 + g^2 -c): centre and radius of x^2 + y^2 + 2fx + 2gy + c = 0
32. perpendicular: a tangent to a circle is ...... to the radius of the circle at the point
of intersection
33. the centre of a circle: the perpendicular bisector of a chord will go through.....
34. a right angle: the angle in a semicircle is always
35. : if PRQ = 90° then R lies on the circle with diameter PQ
36. -find the equations of the perpendicular bisectors of 2 different chords
-find the coordinates of the intersection of the perpendicular bisectors: find
the centre of a circle given any 3 points
37. if f(p) = 0 then (x-p) is a factor of f(x): factor theorem
38. starting from known facts or definitions then using logical steps to reach
the desired conclusion: proof by deduction
39. breaking the statement into smaller cases and proving each case separate-
ly: proof by exhaustion
40. an example that does not work for the statement: proof by counter-example
41. (n+1)th row: which row of pascal's triangle gives the coefficients of the expan-
sion of (a+b)^n
42. n * (n-1) * (n-2) * ... *3 * 2 * 1: n!
43. n!/r!(n-r)!: nCr
44. a^n + nC1*a^n-1*b + nC2*a^n-2*b^2 + ... + nCr*a^n-r*b^r + ... + b^n: binomial
expansion of (a+b)^n with nCr
45. : if x is small the first few terms in a binomial expansion can be used to find an
approximate value for a complicated expression
Study online at https://quizlet.com/_79wpbd
1. - Sn = n/2 (2a + (n-1)d)
- Sn = n/2 (a + l) where a is the first term and l is the last term: formula of an
arithmetic series
2. the sum of the terms of an arithmetic sequence: what is an arithmetic series
3. - Un = a + (n-1)d
- a = the first term
- d = the common difference: nth term of an arithmetic sequence
4. - Un = ar^(n-1)
- a = first term
- r = common ratio: nth term of a geometric sequence
5. - Sn = a(1-r^n) / 1-r
- Sn = a(r^n - 1) / r-1
where r does not equal 1: formula of first n terms of a geometric sequence
6. the sum of the values tend towards infinity: divergent sequence
7. - the sum of the values tend towards a specific number
- it is only convergent if |r|<1: convergent sequence
8. a / 1-r: sum to infinity of a geometric series
9. : series can be shown using sigma notation
10. - defines each term of a sequence as a function of the previous term
- to find the members of the sequence substitute in n=1, n=2 ... using the
previous terms given: recurrence relation of form Un+1 = f(Un)
11. it is decreasing: if Un+1 < Un for all n , what is true of the sequence
12. - it is periodic
- means that the terms repeat in a cycle
- k = the order of the sequence (how often the terms repeat): if Un+k = Un for
all n , what is true of the sequence
13. (x+y)(x-y): x^2-y^2
14. * (a-sqrt(b) / a-sqrt(b)): rationalising the denominator of e.g. 1/sqrt(b)+a
15. b^2 - 4ac > 0 has 2 distant real roots
B^2 -4ac = 0 has on real repeated root
b^2 - 4ac < 0 has no real roots: using the discriminant to find number of roots
16. if f(x) = a(x+p)^2 + q, then the turning point is (-p,q): completing the square
to find the turning point
, OCR a-level maths
Study online at https://quizlet.com/_79wpbd
17. < is dotted line
dis solid line: using lines to represent < and d
18. x=0 and y=0: where are the asymptotes of y = k/x
19. translation up by a units: y = f(x) + a
20. translation left by a units: y = f(x+a)
21. stretch vertically by scale factor a: y = af(x)
22. stretch by scale factor 1/a horizontally: y = f(ax)
23. reflection in x-axis: y = -f(x)
24. reflection in y-axis: y = f(-x)
25. m = (y2 - y1)/(x2 - x1): calculating the gradient with 2 points
26. y-y1=m(x-x1): another way to calculate equation of a line
27. y= -(1/m)x: equation of line perpendicular to y = mx
28. Sqrt ((x2 - x1)^2 + (y2 - y1)^2 ): distance between (x1,y1) and (x2,y2)
29. x^2 + y^2 = r^2: equation of circle centre (0,0)
30. (x-a)^2 + (y-b)^2 = r^2: equation of circle centre (a,b)
31. centre: (-f,-g)
radius: sqrt (f^2 + g^2 -c): centre and radius of x^2 + y^2 + 2fx + 2gy + c = 0
32. perpendicular: a tangent to a circle is ...... to the radius of the circle at the point
of intersection
33. the centre of a circle: the perpendicular bisector of a chord will go through.....
34. a right angle: the angle in a semicircle is always
35. : if PRQ = 90° then R lies on the circle with diameter PQ
36. -find the equations of the perpendicular bisectors of 2 different chords
-find the coordinates of the intersection of the perpendicular bisectors: find
the centre of a circle given any 3 points
37. if f(p) = 0 then (x-p) is a factor of f(x): factor theorem
38. starting from known facts or definitions then using logical steps to reach
the desired conclusion: proof by deduction
39. breaking the statement into smaller cases and proving each case separate-
ly: proof by exhaustion
40. an example that does not work for the statement: proof by counter-example
41. (n+1)th row: which row of pascal's triangle gives the coefficients of the expan-
sion of (a+b)^n
42. n * (n-1) * (n-2) * ... *3 * 2 * 1: n!
43. n!/r!(n-r)!: nCr
44. a^n + nC1*a^n-1*b + nC2*a^n-2*b^2 + ... + nCr*a^n-r*b^r + ... + b^n: binomial
expansion of (a+b)^n with nCr
45. : if x is small the first few terms in a binomial expansion can be used to find an
approximate value for a complicated expression
