OCR a-level maths Question Fully Solved.

- Sn = n/2 (2a + (n-1)d) - Sn = n/2 (a + l) where a is the first term and l is the last term - correct answer formula of an arithmetic series the sum of the terms of an arithmetic sequence - correct answer what is an arithmetic series - Un = a + (n-1)d - a = the first term - d = the common difference - correct answer nth term of an arithmetic sequence - Un = ar^(n-1) - a = first term - r = common ratio - correct answer nth term of a geometric sequence - Sn = a(1-r^n) / 1-r - Sn = a(r^n - 1) / r-1 where r does not equal 1 - correct answer formula of first n terms of a geometric sequence the sum of the values tend towards infinity - correct answer divergent sequence - the sum of the values tend towards a specific number - it is only convergent if |r|<1 - correct answer convergent sequence a / 1-r - correct answer sum to infinity of a geometric series - correct answer series can be shown using sigma notation - 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 - correct answer recurrence relation of form Un+1 = f(Un) it is decreasing - correct answer if Un+1 < Un for all n ∈ ℕ, what is true of the sequence - it is periodic - means that the terms repeat in a cycle - k = the order of the sequence (how often the terms repeat) - correct answer if Un+k = Un for all n ∈ ℕ, what is true of the sequence (x+y)(x-y) - correct answer x^2-y^2 * (a-sqrt(b) / a-sqrt(b)) - correct answer rationalising the denominator of e.g. 1/sqrt(b)+a 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 - correct answer using the discriminant to find number of roots if f(x) = a(x+p)^2 + q, then the turning point is (-p,q) - correct answer completing the square to find the turning point < is dotted line ≤ is solid line - correct answer using lines to represent < and ≤ x=0 and y=0 - correct answer where are the asymptotes of y = k/x translation up by a units - correct answer y = f(x) + a translation left by a units - correct answer y = f(x+a) stretch vertically by scale factor a - correct answer y = af(x) stretch by scale factor 1/a horizontally - correct answer y = f(ax) reflection in x-axis - correct answer y = -f(x) reflection in y-axis - correct answer y = f(-x) m = (y2 - y1)/(x2 - x1) - correct answer calculating the gradient with 2 points y-y1=m(x-x1) - correct answer another way to calculate equation of a line y= -(1/m)x - correct answer equation of line perpendicular to y = mx Sqrt ((x2 - x1)^2 + (y2 - y1)^2 ) - correct answer distance between (x1,y1) and (x2,y2) x^2 + y^2 = r^2 - correct answer equation of circle centre (0,0) (x-a)^2 + (y-b)^2 = r^2 - correct answer equation of circle centre (a,b) centre: (-f,-g) radius: sqrt (f^2 + g^2 -c) - correct answer centre and radius of x^2 + y^2 + 2fx + 2gy + c = 0 perpendicular - correct answer a tangent to a circle is ...... to the radius of the circle at the point of intersection the centre of a circle - correct answer the perpendicular bisector of a chord will go through.....