Flashcards
Core 1 Formulae
Cards in this deck (15)
- 1If ax^2 + bx + c = 0, what is the quadratic formula which will find all answers of x?
- 2When differentiating, what is the derivative of the function x^n?nx^(n-1)
- 3When integrating, what is the integral of the function x^n?(x^(n + 1))/(n + 1) + c
- 4What is the formula for completing the square?x^2 + bx = (x + b/2)^2 - (b/2)^2
- 5What is the discriminant?b^2 - 4ac
- 6In what form can a quadratic equation be written by completing the square?y = p[(x-q)^2 + r]
- 7What can the equation y = p[(x-q)^2 + r] tell us about a graph of y = ax^2 + bx + c?Turning point = (q, pr)
Axis of symmetry = q
It's the graph of y = x^2 translated q places horizontally and r places vertically - 8How do you rationalise n/x where x is an irrational denominator?n/x * y/y where y = x with all signs reversed
- 9How do numbers in the brackets of a function and outside the brackets of a function translate the curve f(x)?Numbers inside the bracket do the opposite of their sign horizontally, whereas numbers outside do as their sign suggests, vertically
- 10How do you find the gradient of a line passing through a point with a given gradient?y - y1 = m(x - x1)
where y1 and x1 are the coordinates of the point - 11How do you calculate the distance between two given points?Sqrt((x2 - x1)^2 + (y2 - y1)^2)
where x1 and y1 are the coordinates of point 1 and x2 and y2 are the coordinates of point 2 - 12How do you find the midpoint of two given points?((x1 + x2)/2, (y1 + y2)/2)
where x1 and y1 are the coordinates of point 1 and x2 and y2 are the coordinates of point 2 - 13What is the formula for the nth term in an arithmetic progression?Un = a + (n - 1)d
- 14What are the two equations for the sum of an arithmetic sequence?Sn = n/2 * [2a + (n - 1)d]
Sn = n/2 * [a + L] - 15What property of a curve does differentiating find?The gradient of the tangent to the curve