In the diagram below, the coordinates of ∆ABC are given as A(– 2 ; 4) , B(– 6 ; – 2) andC(8 ; 2). P and Q are the midpoints of AB and BC respectively. 2.1 Calculate the coordinates of P and Q. (4) 2.2 Show that: 2.2.1 PQ // AC (4) 2.2.2 PQ = … Read more
In the diagram, O is the centre of the circle through the points A, B, C, D and T. HC and HT are tangents to the circle at C and T respectively. AD is produced to meet HT at R OC bisects AD at J. Let C3 = x. 11.1 Write down, with a reason, … Read more
10.1 In the diagram below, O is the centre of the circle. P, T and S are points on the circumference of the circle. PS, PT and OT are drawn Prove the theorem which states that SÔT = 2 x SPT. (5) 10.2 In the diagram, O is the centre of the circle. Points A,B,C … Read more
In figure Q, P, T , S and R lie on the circle. M lies on QS such that PM || SR. PTS=145o 9.1 Calculate the size of: 9.1.1 (2) 9.1.2 (2) 9.1.3 (1) 9.2 Why is PR tangent to the circle passing through P, M and Q? (1) [6]
7.1 IN the diagram A , C , E and B are the vertices of a quadrilateral. ABC = 31o , BAC = 106o , BCE = 46o , AC= 4,6 cm, CE = 10 cm and BC = x. 7.1.1 Calculate the length of BC. (3) 7.1.2 Calculate the area of quadrilateral ACEB. (4) … Read more
Sketched below are the graphs of the functions f(x) = cos x+q and   g(x) = 2sin bx for xe [-60° ; 120° ]. 6.1 Write down the coordinates of the maximum turning point of g in the given interval. (1) 6.2 Determine the values of x where f is strictly increasing in the given interval. … Read more
5.1 In the diagram below, P(k ; 24)  is a point in the second quadrant such that OP = 25 units. N is a point on the positive x-axis and PÔN = θ. WITHOUT calculating the size of 0, determine the value of the following: 5.1.1 k (2) 5.1.2 tan θ (1) 5.1.3 sina if θ … Read more
In the diagram, B is a point on the y-axis. A(4 ; y), B, C(3 ; 0) and D(7 ; 6) are the vertices of rectangle ABCD. Diagonals BD and AC are drawn. The inclination of DC is a   and BÂC =θ . 4.1 Determine the gradient of CD. (2) 4.2 Calculate the size of a. … Read more
In the diagram, A(—2 ; 2), B(—4 ; —6), C(4 ; —2) and E(6 ; y) are the vertices of a quadrilateral having AE || BC. D lies on BC such that AD BC and AC is drawn. M(x ; 2) is a point on EC. 3.1 Calculate the gradient of BC. (3) 3.2 If … Read more