C1 Revision

Quadratic functions:  If f(x)=ax^2+bx+c, the discriminant is b^2-4acFor f(x)=0, b^2-4ac>0  = two real, distinct roots,b^2-4ac=o   = two real, equal roots,b^2-4ac<0    = no distinct real roots.Factorising, completing the square, using the formula.        Sketching quadratic functions:a) find the point of intersection with the y-axis: put x=0 in y=f(x).b) find the points of intersection with the x-axis: solve f(x)=0.c)find the maximum/minimum point: use completing the square, symmetry or solve       f '(x)=0.

C1 Algebra and Functions

Other curves: reciprocal (y = 1/x), cubics.Expanding brackets, collecting like terms, factorising.Simultaneous equations (including one linear and one quadratic).Linear and quadratic inequalities.Transformation   Descriptiony=f(x)+a   a>0      Translation of y=f(x)  (0/a)y=f(x+a)   a>0      Translation of y=f(x)  (-a/0)y=af(x)     a>0      Stretch in x, SF ay=f(ax)     a>0      Stretch in y, SF 1/a 

C1 Coordinate Geometry

P(x1,y1) and Q(x2,y2)Gradient PQ = y2-y1 / x2-x1Distance PQ = square root: (x2-x1)^2 + (y2-y1)^2Equation of a straight line: (i) Given gradient + y intercept:  y=mx+c(ii) Given point(x1,y1) on line and m: y-y1=m(x-x1)(iii) Given P(x1,y1) + Q(x2,y2) on line: y-y1 / y2-y1 = x-x1 / x2-x1Midpoint of PQ = (x1+x2 / 2 , y1+y2 / 2)Gradient of line l1 is m1, gradient of l2 is m2If l1 is parallel to l2, then m1=m2If l1 is perpendicular to l2, then m1 x m2 = -1

C1 Sequences and Series

Sigma notation, e.g. E^4-r=1    (2r+5) = 7 + 9 + 11 + 13Un+1 = 3Un+5, n>_1, u1=-2  The first 5 terms of this sequence are -2, -1, 2, 11 and 38An arithmetic series is a series in which each term is obtained from the previous term by adding a constant called the common difference, dnth term = a + (n-1)dSn = n/2 [2a + (n-1) d]  or  Sn = n/2 (a+l) where last term l = a + (n-1)dSum of the first n natural numbers: 1 + 2 + 3 + 4 + ..... + n:    Sn = n/2 (n+1)

C1 Differentiation

Notation:If y=f(x)  then  dy/dx = f'(x)  and d^2y/dx^2 = f'(x)y                               dy/dxax^n                          anx^n-1   (a is constant)f(x) +/- g(x)                 f'(x) +/- g'(x)Equation of tangents and normals: Use the following facts:a) Gradient of a tangent to a curve = dy/dxb) The normal to a curve at a particular point is perpendicular to the tangent at that pointc) If two perpendicular lines have gradients m1 and m2 then m1xm2 = -1d) The equation of a line through (x1,y1) with gradient m is y-y1 = m(x-x1)

C1 Integration

/ax^ndx = ax^n+1/n+1 +c           provided n =/ -1 /(f'(x) + g '(x))   dx = f(x) + g(x) + c