## Question 12

12.1 Name, with reasons, FOUR other angles equal to x. (7) 12.3 Determine the numerical value of x+y, if it is given that DCTP is a cyclic quadrilateral. (4) [15] TOTAL: 150

12.1 Name, with reasons, FOUR other angles equal to x. (7) 12.3 Determine the numerical value of x+y, if it is given that DCTP is a cyclic quadrilateral. (4) [15] TOTAL: 150

In the diagram below, O is the centre of the circle. CDE is a tangent to the circle at D. 11.1 Prove that BC ∥ OD. (4) [7]

M is the centre of the circle SVQR having equal chords SV and QR. [9]

Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12. 9.1 In the diagram below, O is the centre of the circle and point T lies on chord RS. Prove the theorem which states that if OT ⊥ RTS then RT = TS. (5) 9.2 In the diagram, O is the … Read more

A pyramid with a square base with a side length of 16 cm is sketched below. P lies on the square base directly below A. The volume of the pyramid is 640 cm3. 8.1 Show that the perpendicular height of the pyramid, AP, is 7.5 cm. (2) 8.2 Hence, determine the total surface area of … Read more

In Δ PQR, QR = 3 units, PR = x units, PQ = 2x units and PQR = θ.

6.1 Determine the general solution for sin(x – 30°) = cos 2x 6.2 Consider the function f (x)= sin(x – 30°) and g(x) = cos 2x 6.2.1 Write down the period of g 6.2.2 State the range of f 6.2.3 On the grid provided in the ANSWER BOOK, draw a graph of f and g … Read more

5.1 Simplify fully : sin(90° – x). cos(180° + x) + tanx. cosx. sin(x – 180°) 5.2 Prove, WITHOUT using a calculator, that (6) (6) 5.3 In the diagram below, R is a point in the first quadrant such that TOR = α .RO is extended to P such that OP = 2 RO and … Read more

C, a point of the x-axis, A (-5; -3) and B (4; 12) are the vertices of a triangle.AB intersect the x-axis at E.ABC = θ and BEC = α . 4.1 Calculate the gradient of AB. 4.2 Determine the coordinates of point E. 4.3 Determine the size of α. Round off to the nearest … Read more

A (-2 ; -5), B, C and D are the vertices of quadrilateral ABCD such as the diagonal AC is perpendicular to diagonal BD at T. The equation of BTD is given by 2y + x = 18 and AB =15 units. 3.1 Determine the gradient of a line AC 3.2 Determine the equation of … Read more