The sketch below shows the graph of the function f(𝑥) = a𝑥2 + b𝑥 +c. The straight line with equation 3y = 𝑥 – 5 intersects f at B. The points A(-2;0) and B are the 𝑥-intercepts of f . Point D(-1;3)is a point on f . 9.1 Determine the coordinates of B.(2) 9.2 Determine … Read more
Given and 5.1 Determine 𝑓(-3). (1) 5.2 Determine 𝑥 if 𝑔(𝑥) = 4. (2) 5.3 Write down the asymptotes of 𝑓. (2) 5.4 Write down the range of 𝑔. (1) 5.5 Determine the coordinates of the 𝑥- and 𝑦- intercepts of 𝑓. (5) 5.6 Determine the equation of the axis of symmetry of 𝑓 which … Read more
The sketch below shows the graph of f(x) = 2 x ax – 1. The point A(1; 5) is a point on the graph. 8.1 Show that a = 3. (2) 8.2 Determine the y-intercept of f . (2) 8.3 Write down the range of f . (1) 8.4 Determine f (0,23), rounded off to … Read more
Given the following two functions: 7.1 Determine the 𝑥-intercept of h.(3) 7.2 Sketch neat graphs of h and g on the same set of axes. Clearly show all interceptswith the axes as well as asymptotes. (5) 7.3 Write down the equation of the vertical asymptote of h.(1) 7.4 Determine the coordinates of the points of … Read more
6.1 The price of a new school bus is R540 000. The value of the bus decreases at 11% per annum according to the diminishing-balance method. Calculate the value of the bus after 8 years. (2) 6.2 Determine the effective interest rate if an investment earns interest at a nominal interest rate of 11,5% per … Read more
Given the quadratic pattern: 244 ; 193 ; 148 ; 109 ; … 4.1 Write down the next term of the pattern (2) 4.2 Determine a formula for the 𝑛th term of the pattern (4) 4.3 Which term of the pattern will have a value of 508 ? (4) 4.4 Between which TWO consecutive terms … Read more
3.1 Given the finite linear pattern: 12 ; 17 ; 22 ; … ; 172 3.1.1 Determine a formula for the 𝑛th term of the pattern. (2) 3.1.2 Calculator the value of 𝑇12 . (2) 3.1.3 Determine the number of terms in the pattern. (2) 3.2 Given the first four terms of a linear pattern: … Read more
5.1 The following number pattern has a constant second difference. 5.1.1 Write down the value of the constant second difference. (1) 5.1.2 Determine an expression for the n-th term of the number pattern. (4) 5.1.3 The first forty terms of the number pattern are all prime numbers. Determine the forty-first term and show that it … Read more
The first term of a linear number pattern is 92 and the constant difference is -4.4.1 Write down the values of the second and third terms of the number pattern. (1) 4.2 Determine an expression for the n-th term of the number pattern. (2) 4.3 Determine the value of the eighteenth term. (2) 4.4 If … Read more
O is the centre of the bigger circle. O lies on the circumference of the smaller circle. OWVU are points on the circumference of the smaller circle. TSVU are points on the circumference of the bigger circle. 10.1 Name FOUR other angles each equal to 𝑥 with reasons. (8) 10.2 Determine the size of Ŵ2 … Read more