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Hits: 44 Question A sketch of part of the curve C with equation , x>0 is shown in Figure. Point A lies on C and has an x coordinate equal to 2 a. Show that the equation of the normal to C at A is y = –2x + 7. The normal to C at A […]
Hits: 319 Question Xin has been given a 14 day training schedule by her coach. Xin will run for A minutes on day 1, where A is a constant. She will then increase her running time by (d + 1) minutes each day, where d is a constant. a. Show that on day 14, Xin will run […]
Hits: 30 Question The curve C has equation . The line L has equation y = 3x + k, where k is a positive constant. a. Sketch C and L on separate diagrams, showing the coordinates of the points at which C and L cut the axes. Given that line L is a tangent to C, b. […]
Hits: 38 Question , Given that y=37 at x=4, 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=37 at x=4 ie (4,37). We are required to find the equation of y in terms of x. We can find equation of […]
Hits: 698 Question Figure 2 shows a right angled triangle LMN. The points L and M have coordinates (–1, 2) and (7, –4) respectively. a. Find an equation for the straight line passing through the points L and M. Give your answer in the form ax + by + c = 0, where a, b and c […]
Hits: 152 Question Figure 1 shows the plan of a garden. The marked angles are right angles. The six edges are straight lines. The lengths shown in the diagram are given in metres. Given that the perimeter of the garden is greater than 40 m, a. show that x > 1.7 Given that the area of the […]
Hits: 10 Question Solve the equation Give your answer in the form where a and b are integers. Solution a. We are given;
Hits: 15 Question Given that , , , find in their simplest form, a. b. . Solution a. We are given; We are required to find . Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: Therefore; Rule for differentiation is of is: Rule for […]
Hits: 21 Question A sequence is defined by , for Where is a constant. a) Find an expression for in terms of k. Given that , b) Find the value of k. Solution a) We are given that sequence is defined by We are required to find . We can utilize the given expression for general terms beyond […]
Hits: 8 Question a. Evaluate . b. Simplify fully . Solution a. b.
Hits: 10 Question Factorise fully Solution We are given; We have algebraic formula; Therefore;