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
In the diagram ∆LNR is drawn with points L and R on the circumference of a circle. NR cuts the circle at M. K is a point on LR with KN the bisector of LN̂R. KN cuts the chord LM at O. LK = LO. LÔK = 65° and KN̂M = 25°. 9.1 Prove that … Read more
Give reasons for ALL statements in QUESTIONS 8, 9 and 10. In the diagram below O is the centre of the circle. Quadrilateral ABCO is drawn with A and C on the circumference. AB is a tangent to the circle at point A and BC is a tangent to circle at point C. D is … Read more
The picture below shows a storage tank in which a farmer stores his grain. The tank is madeup of a right cylinder with a hemisphere on top. The perpendicular height of the tank to thetop is 7 500 cm and the radius of the tank is 10 m. 7.1 Calculate the total surface area of … Read more
6.1 Complete: ···= a2 + b2 – 2ab cosĈ .(1) 6.2 TRS is a secant of the circle, and SU is a tangent at U. TU = 16 cm, TR = 12 cm and T̂ = 41°. Calculate the: 6.2.1 Length of UR, correct to two decimals. (3) 6.2.2 Size of Û2 (3) 6.2.3 Length … Read more
5.1 On the same set of axes draw ƒ(𝑥) = -cos(45° – 𝑥) and g(𝑥) = tan(-𝑥) in the interval of -90° ≤ 𝑥 ≤ -180°. Make use of the grid provided in the SPECIAL ANSWER BOOK. 5.2 For which values of 𝑥 is ƒ(𝑥) – g(𝑥) ≤ 0 for 𝑥 ∈ [−90°; 90°] (2) … Read more
4.1 Given: 𝑝.sin 𝛽 – 4 = 0 and 𝑝.cos 𝛽 + 3 = 0 where 𝑝 > 0 4.1.1 Explain why 𝛽 ∈ [900;1800] (3) 4.1.3 Determine the numerical value of 𝑝. 4.2 Simplify without using a calculator: sin1430.cos1270 – sin530.cos370 [24]
In the diagram below, ∆ PQS is drawn with vertices P (-2 ; 3), Q (3 ; 6) and S in a Cartesian plane. Line QS passes through the origin at O. PS║QR. PŜQ 20,230. 3.1 Calculate the gradient of QS. (2) 3.2 Calculate the size of 𝜃. (2) 3.3 Determine the: 3.3.1 gradient of … Read more
A group of learners wrote a standardised English test that was scored out of 60. The results were represented in a cumulative frequency graph below. 2.1 How many learners wrote the test? (1) 2.2 How many learners scored at least 20 out of 60? (2) 2.3 Using the graph, estimate the median test score. (2) … Read more
Mr Ngwane is the sales manager for a furniture shop. Every month his 15 staff members report on the number of customers who visited during the previous month. The results were given as follows: 12 15 15 19 22 23 26 26 32 33 33 33 33 35 35 1.1 Determine the: 1.1.1 median of … Read more