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Hits: 51 Question The curve C has equation , a. Find , giving each term in its simplest form. The point P on C has x-coordinate equal to . b. Find the equation of the tangent to C at P, giving your answer in the form y = ax + b, where a and b are […]
Hits: 16 Question a. Find the values of the constants a, b and c. b. On the axes on page 27, sketch the curve with equation y = 4×2 + 8x + 3, showing clearly the coordinates of any points where the curve crosses the coordinate axes. Solution a. We are given that; In order to find […]
Hits: 17 Question The equation (k + 3)x2 + 6x + k = 5, where k is a constant, has two distinct real solutions for x. a. Show that k satisfies k2 – 2k – 24 < 0 b. Hence, find the set of possible values of k. Solution a. We are given that; We are given that given […]
Hits: 7 Question , Given that y=7 at x=1, find y in terms of x, giving each term in its simplest form. Solution We are given that; We are given coordinates of appoint that is y=7 at x=1 ie (1,7). We are required to find the equation of y in terms of x. We can find equation of […]
Hits: 298 Question Lewis played a game of space invaders. He scored points for each spaceship that he captured. Lewis scored 140 points for capturing his first spaceship. He scored 160 points for capturing his second spaceship, 180 points for capturing his third spaceship, and so on. The number of points scored for capturing each successive spaceship formed an arithmetic […]
Hits: 44 Question Figure 1 shows a sketch of the curve with equation , x ≠ 0. The curve C has equation , x ≠ 0, and the line has equation y = 4x + 2. a. Sketch and clearly label the graphs of C and on a single diagram. On your diagram, show clearly the coordinates […]
Hits: 34 Question The line L1 has equation y = -2x+3. The line L2 is perpendicular to L1 and passes through the point (5, 6). a. Find an equation for L2 in the form ax + by + c = 0, where a, b and c are integers. The line L2 crosses the x-axis at the point A and […]
Hits: 11 Question A sequence satisfies , , Given that , a) Find the value of and the value of . b) Evaluate . Solution a) We are given that sequence is defined by We are given that and required to find . We can utilize the given expression for general terms beyond first term as; Similarly, we can find […]
Hits: 12 Question i. Express in the form , where a and b are integers. ii. Express in the form , where c is an integer. Solution i. We are given; Since ; Since ; ii. We are given; Since ;
Hits: 11 Question Express 82x+3 in the form 2y , stating y in terms of x. Solution We are given; Hence, comparing it with 2y gives;
Hits: 15 Question Factorise completely Solution We are given;