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Hits: 80 Question a. Find the values of the constants a and b. b. In the space provided below, sketch the graph of , indicating clearly the coordinates of any intersections with the coordinate axes. c. Find the value of the discriminant of . Explain how the sign of the discriminant relates to your sketch in […]
Hits: 274 Question Figure 2 shows part of the curve C with equation The curve cuts the x-axis at the points P, (1, 0) and Q, as shown in Figure 2. a. Write down the x-coordinate of P, and the x-coordinate of Q. b. Show that . c. Show that y=x+7 is an equation of the […]
Hits: 46 Question The curve with equation y=f (x) passes through the point (1,6). Given that , , find f(x) and simplify your answer. Solution We are required to find f(x), when; We are also given that , and the curve passes through the point (1,6). Clearly it is the case of finding equation from its derivative. We can find […]
Hits: 413 Question On Alice’s 11th birthday she started to receive an annual allowance. The first annual allowance was £500 and on each following birthday the allowance was increased by £200. a. Show that, immediately after her 12th birthday, the total of the allowances that Alice had received was £1200. b. Find the amount of Alice’s annual allowance […]
Hits: 44 Question Figure 1 shows a sketch of the curve with equation y=f(x). The curve passes through the points (0,3) and (4,0) and touches the x-axis at point (1,0). On separate diagrams sketch the curve with equation a. y=f(x+1), b. y=2f(x), c. On each diagram show clearly the coordinates of all the points where the curve […]
Hits: 14 Question a. Write in the form , where a is an integer. b. Express in the form , where b and c are integers. Solution a. We are given; Since ; b. We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator […]
Hits: 26 Question Given that , , a. Find b. Find Solution a. We are given; We are required to find . Rule for differentiation of is: Rule for differentiation of is: b. We are given; We are required to find . Rule for integration of is: Rule for integration of is: Rule for integration of […]
Hits: 298 Question The line L has equation y=5 – 2x. a. Show that the point P (3, –1) lies on L. b. Find an equation of the line perpendicular to L, which passes through P. Give your answer in the form ax + by + c = 0, where a, b and c […]
Hits: 29 Question The sequence of positive numbers , , , … is given by: , a. Find , and . b. Write down the value of . Solution a. We are given that (n+1)th term of arithmetic series is represented by; Therefore, to find nth term we substitute (n-1) for n in the given […]
Hits: 55 Question Factorise completely Solution