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6.1 In the diagram, P(—5 ; 12) and T lies on the positive x-axis. PÔT = 0 Answer the following without using a calculator: 6.1.1 Write down the value of tan0 (1) 6.1.2 Calculate the value of cos0 (3) 6.1.3 S(a, b) is a point in the third quadrant such that TÔS = 0 + … Read more

The graphs of    f(x)1/2 cos x and   g(x) = sin(x + 30°) , for the interval x E [0°; 180°], are drawn below. A(130,9° ; 0,33) is the approximate point of intersection of the two graphs. 5.1 Write down the period of g. (1) 5.2 Write down the amplitude of f (1) 5.3 Determine the value of … Read more

M(—3 ; 4) is the centre of the large circle and a point on the small circle having centre O(0; 0). From N(—11 ; p), a tangent is drawn to touch the large circle at T with NT is parallel to the y-axis. NM is a tangent to the smaller circle at M with MOS … Read more

The number of aircraft landing at the King Shaka International Airport and the Port Elizabeth Airport for the period starting in April 2017 and ending in March 2018, is shown in the double bar graph below. 2.1 The number of aircraft landing at the Port Elizabeth Airport exceeds the number of aircraft landing at the … Read more

A Mathematics teacher was curious to establish if her learners’ Mathematics marks influenced their Physical Sciences marks. In the table below, the Mathematics and Physical Sciences marks of 15 learners in her class are given as percentages (%). 1.1 Determine the equation of the least squares regression line for the data. (3) 1.2 Draw the … Read more

Harry shoots arrows at a target board. He has a 50% chance of hitting the bull’s eye on each shot. 11.1 Calculate the probability that Harry will hit the bull’s eye in his first shot and his second shot. (2) 11.2 Calculate the probability that Harry will hit the bull’s eye at least twice in … Read more

In a certain country, 10-digit telephone numbers with the following format were introduced: Digits may be repeated. 10.1 How many possible 10-digit telephone numbers could be formed? 10.2 Certain restrictions were placed on the groups of digits: Area code: must be 3 digits and the first digit can NOT be 0 or 1 Exchange code: … Read more

A closed rectangular box has to be constructed as follows: Dimensions: length (f), width (w) and height (h). The length (l) of the base has to be 3 times its width (w). The volume has to be 5 m3. The material for the top and the bottom parts costs R15 per square metre and the … Read more