grade11

2.1 Simplify fully , WITHOUT using a calculator: (4) 2.2 Solve for 𝑥, WITHOUT using a calculator: 2.2.1 (3) 2.2.2 (4) 2.3 If and , determine the value of ( 𝑥 + 𝑦 )2 (3) 2.4 Show WITHOUT, using a calculator, that (4) [18]

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

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

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]