Hits: 75
Hits: 75 Question Given , find the value of when x=8, writing your answer in the form where a is a rational number. Solution 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 […]
Hits: 24 Question a. Simplify Giving your answer in the form , where a is an integer. b. Hence, or otherwise, simplify Giving your answer in the form , where b and c is are integers and . Solution a. We are given; Since ; Since ; b. We are given; We have found in (a) that; Therefore; If we […]
Hits: 29 Question Simplify a. b. giving your answer in the form a + √b , where a and b are integers. Solution a. We are given; b. We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If […]
Hits: 14 Question Solve the equation Give your answer in the form where a and b are integers. Solution a. We are given;
Hits: 18 Question a) Write in the form , where c is a positive constant. A rectangle R has a length of cm and an area of cm2. b) Calculate the width of R in cm. Express your answer in the form , where p and q are integers to be found. Solution a. Since […]
Hits: 25 Question Fully simplify a. b. Solution a. We are given; b. We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator by . ü If the […]
Hits: 5 Question Express in the form , where k is an integer. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator by . ü If the denominator is […]
Hits: 7 Question Simplify giving your answer in the form , where a and b are integers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator […]
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: 13 Question Show that can be written in the form , where a and b are integers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator […]
Hits: 13 Question a. Simplify giving your answer in the form , where is an integer. b. Simplify giving your answer in the form , where b and c are integers. Solution a. We are given; Since ; Since ; b. As demonstrated in (a) we can write the numerator as; If we need a rational number […]
Hits: 32 Question Given that can be written in the form , a. Write down the value of p and the value of q. Given that , and that y=90 when x=4; b. find in terms of x, simplifying the coefficient of each term. Solution a. We are given; b. We are required to […]
Hits: 104 Question The line L1 has equation 2y − 3x − k = 0, where k is a constant. Given that the point A (1, 4) lies on L1, find a. the value of k, b. the gradient of L1. The line L2 passes through A and is perpendicular to L1. c. Find an equation of […]
Hits: 8 Question Simplfy Giving your answer in the form , where p and q are rational numbers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator […]
Hits: 65 Question a. On the axes below sketch the graphs of i. y = x (4 – x) ii. y = x2 (7 – x) showing clearly the coordinates of the points where the curves cross the coordinate axes. b. Show that the x-coordinates of the points of intersection of y = x (4 – x) and […]
Hits: 2 Question Write in the form , where k and x are integers. Solution We are given; Since ; Since;
Hits: 7 Question a. Expand and simplify b. Express in the form , where a and b 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 rationalization” as given below. ü If the denominator is […]
Hits: 54 Question , x>0 a) Show that , where A and B are constants to be found. b) Find c) Evaluate . Solution a) We are given; Utilizing algebraic identity; b) We are given; We are required to find . We can write the given equation/function as; Gradient (slope) of the curve is the […]
Hits: 10 Question Simply a. b. Solution a. We are given; 63 b. We are given; Since ;
Hits: 8 Question Expand and simplify . Solution We are given; We have algebraic formula;