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
2.1 Two classes wrote a Mathematics test that had a maximum mark of 60. The results of each class are summarised in the box and whisker diagrams below. 2.1.1 Comment on the skewness of the results in class X. (1) 2.1.2 In which class is the standard deviation of the marks bigger? (1) 2.1.3 Comment … Read more