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Hits: 30 Question a. On the same axes sketch the graphs of the curves with equations i. y=x2(x –2), ii. y=x(6 –x), and indicate on your sketches the coordinates of all the points where the curves cross the x-axis. b. Use algebra to find the coordinates of the points where the graphs intersect. Solution a. […]
Hits: 243 Question Ann has some sticks that are all of the same length. She arranges them in squares and has made the following 3 rows of patterns: She notices that 4 sticks are required to make the single square in the first row, 7 sticks to make 2 squares in the second row and in the […]
Hits: 159 Question The curve C has equation , x > 0. a. Find an expression for . b. Show that the point P (4, 8) lies on C. c. Show that an equation of the normal to C at the point P is 3y=x + 20. The normal to C at P cuts the […]
Hits: 54 Question The curve C has equation y= f(x), x ≠ 0, and the point P(2,1) lies on C. Given that; a. find f(x). b. Find an equation for the tangent to C at the point P, giving your answer in the form y =mx + c, where m and c are integers. Solution a. […]
Hits: 8 Question a. Show that can be written as , where k is a constant to be found. b. Find Solution a. We are given; We have algebraic formula; b. We are required to find; From (a), we know that; Therefore; Rule for integration of is: Rule for integration of is: Rule for integration […]
Hits: 5 Question The equation , where k is a constant, has no real roots. Find the set of possible values of k. Solution We are given; We are given that given equation has equal roots. For a quadratic equation , the expression for solution is; Where is called discriminant. If , the equation will have […]
Hits: 6 Question Solve the simultaneous equations Solution We are given simultaneous equations; Substituting this for from first equation in the second equation; We have the algebraic formula; Therefore; Now we have two options. By substituting one-by-one these values of in first equation, we can find corresponding values of . For For Hence, there are following two solutions of the […]
Hits: 17 Question Given that , x ≠0, a. Sketch the graph of y=f(x)+3 and state the equations of the asymptotes. b. Find the coordinates of the point where y=f(x)+3 crosses a coordinate axis. Solution a. We are given that; We are required to sketch y=f(x)+3. Translation through vector represents the move, units in the x-direction and […]
Hits: 8 Question a. Express in the form , where a is an integer. b. Express in the form , where b and c are integers to be found. Solution a. We are given; Since ; b. We are given; We have algebraic formula;
Hits: 11 Question Given that , Find . Solution We are required to differentiate; We are required to find . Rule for differentiation of is: Rule for differentiation of is: Rule for differentiation is of is: