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
The graph of g (x) = ax3 + bx2+ cx, a cubic function having a y-intercept of 0, is drawn below. The x-coordinates of the turning points of g are -1 and 2. 8.1 For which values of x will g increase? (2) 8.2 Write down the x-coordinate of the point of inflection of g. (2) … Read more
6.1 On 31 January 2020, Tshepo made the first of his monthly deposits of RI 000 into a savings account. He continues to make monthly deposits of RI 000 at the end of each month up until 31 January 2032. The interest rate was fixed at 7,5% p.a., compounded monthly 6.1.1 What will the investment … Read more
The graph of f (x) = 3x-1 is sketched below. A is the y-intercept of f.B is the point of intersection of f and the line y = 9. [12]