A tow truck pulls a car along a gravel road. The force applied by the engine of the tow truck is 9 000 N. The mass of the tow truck is 1 300 kg and the mass of the car is 950 kg. The vehicles are connected to each other by an inelastic tow bar … Read more
Learners investigate the relationship between net force and acceleration by pulling a trolley across a surface which is slightly inclined to compensate for friction. The trolley is connected to different masses by a string of negligible mass. The string passes over a frictionless pulley. Refer to the diagram below. Ticker-tape attached to the trolley passes … Read more
Block A, which is at rest on a horizontal rough surface, is used as an anchor to hold block B, with a mass of 56 kg, in the air at a certain height above the ground. The two blocks are connected with rope R, which makes an angle of 35° with the vertical. Block B … Read more
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
The diagram below shows the graphs of 𝑓(𝑥) = -𝑥2 -𝑥 + 6 and 𝑔 (𝑥) = 𝑚𝑥 + 𝑐. A (-2 ; 4) is the point of intersections of the graphs. 6.1 Determine the 𝑥-interceptions 𝑓. (4) 6.2 Write down the equation of the axis of symmetry of 𝑓. (2) 6.3 Determine the range … 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
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