Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is equal to zero; Therefore, we find the expression for […]
Question The variables x and y satisfy the equation y = Kxa, where K and a are constants. The graph of ln y against ln x is a straight line passing through the points (0.22, 3.96) and (1.32, 2.43), as shown in the diagram. Find the values of K and a, correct to 3 significant […]
Question i. Solve the equation ii. Hence, using logarithms, solve the equation giving the answer correct to 3 significant figures. Solution SOLVING EQUALITION: PIECEWISE i. Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli […]
Question a. Find b. Find the exact value of Show all necessary working. Solution a. We are given that; Rule for integration of is: Rule for integration of is: Rule for integration of is: b. We are required to find the exact value of; Rule for integration of is: Rule for integration of […]
Question Find the equation of the normal to the curve at the point (3, 1). Solution We are given equation of the curve as; We are required to find the equation of normal to the curve at the point (3, 1). To find the equation of the line either we need coordinates of the two […]
Question i. Solve the inequality . ii. Hence find the greatest integer satisfying the inequality Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with […]
Question Show that Solution We are given; Division Rule;
Question The polynomial is defined by where is a constant. It is given that is a factor of i. Find the value of a . ii. Using this value of a, factorise completely. iii. Hence solve the equation , giving the answer correct to 2 significant figures. Solution i. We are […]
Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that […]
Question Find the exact value of Solution We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Question i. Solve the inequality . ii. Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following […]
Question The polynomial is defined by where is a constant. It is given that is a factor of . i. Find the value of . ii. Using this value of a, factorise completely. iii. Hence solve the equation , giving the answer correct to 2 significant figures. Solution i. We […]
Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that […]
Question Find the exact value of Solution We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Question i. Solve the inequality . ii. Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following […]
Question The diagram shows the curve with parametric equations , for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1. i. Show that the value of t at the point P satisfies the equation . ii. Use the iterative formula with t1 =0.7 to […]
Question i. Find the quotient and remainder when is divided by . ii. Hence find the exact value of giving the answer in the form where k and a are constants. Solution i. Hence quotient is and remainder is . ii. We are required to solve; When a polynomial, , […]
Question a. Find the exact value of Show all necessary working. b. Use the trapezium rule with two intervals to find an approximation to Solution a. We are required to show; We know that , therefore; Rule for integration of is: Rule for integration of is: Rule for integration of is: Rule for integration […]
Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is equal to zero; Therefore, we find the expression for gradient […]
Question i. Solve the equation . ii. Hence solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately […]