By Hugh Neill, Douglas Quadling, Julian Gilbey
Written to compare the contents of the Cambridge syllabus. natural arithmetic 1 corresponds to unit P1. It covers quadratics, capabilities, coordinate geometry, round degree, trigonometry, vectors, sequence, differentiation and integration.
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Additional info for Advanced Level Mathematics: Pure Mathematics 1
So either x > 0 and y > 0, or x < 0 and y < 0. The point (x,y) therefore lies in either the first or the third quadrant. It is often convenient to describe the direction of the y-axis as 'vertical', and the x-axis as 'horizontal'. But of course if you are drawing the graph on a horizonta! surface like a table, these descriptions are not strictly accurate. The graph of a function f(x) is made up of all the points whose coordinates (x,y) satisfy the equation y =f(x). When you draw such a graph by hand, you choose a few values of x and work out y =f(x) for these.
Leave irrational answers in surd form. If there is no solution, say so. Keep your answers for use in Question 8. f r (b) x 2 -4x-7=0 (c) x 2 +6x+9=0 (d) x 2 +5x+2=0 (e) x 2 +x+l=O (f) 3x 2 -5x-6=0 (g) 2x 2 + 7x + 3 = 0 (h) 8 - 3x - x 2 = 0 (i) 5 + 4x - 6x 2 = 0 (a) x 2 +3x-5=0 2 Use the value of the discriminant b 2 - 4ac to determine whether the followfog equations have two roots, one root or no roots. (a) x 2 -3x-5=0 (b) x 2 +2x+l=O 2 (d) 3x -6x+5=0 (e) 2 (g) 3x +42x+l47=0 (c) x 2 -3x+4=0 2x 2 -7x+3=0 (f) 5x 2 +9x+4=0 2 (h) 3-7x-4x =0 In parts (i) and (j), the values of p and q are positive.
The discriminant is (-2) 2 - 4 x k x (-7) = 4 + 28k. As the equation has two real roots, the value of the discriminant is positive, so 4 + 28k > 0, and k > - ~ . 3 The equation 3x 2 + 2x + k = 0 has a repeated root. Find the value of k . j.. - 4 x 3 x k = 0. This Notice how, in the above examples, there is no need to solve the quadratic equation. You can find all you need to know from the discriminant. Leave irrational answers in surd form. If there is no solution, say so. Keep your answers for use in Question 8.
Advanced Level Mathematics: Pure Mathematics 1 by Hugh Neill, Douglas Quadling, Julian Gilbey