11.1 The Venn-diagram below shows two independent events, M and N. Determine the values of probabilities x and y. Show all calculations.(5) 11.2 The following contingency table shows information on the drivers’ tests of 100 drivers tested at a test centre in Port Elizabeth. A driver is randomly selected from the 100 drivers. 11.2.1 Determine … Read more
A survey regarding their favourite magazine(s) was conducted among 84 high school girls. Three magazines, namely Teen Vogue (T), Drum (D) and People’s Magazine (P) were used in the survey. The results are as follows: 41 read Teen Vogue. 34 read People’s Magazine. 40 read Drum. 18 read Teen Vogue and Drum. 8 read all … Read more
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
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
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
3.1 Solve for 𝑥 and 𝑦 in the following simultaneous equations. (6) 𝑥 + 𝑦 +2 = 0 and 𝑥2 + 𝑦2 = 4 3.2 Determine the nature of the roots of the quadratic equation a𝑥2 + b𝑥 + c = 0 if the following conditions are given: 3.2.1 a < 0, b > 0 and … Read more