## Question 12

The solid in the diagram is made up of a rightprism with square base, and a right pyramid ontop of the prism. The length of the prism is 12cm, the side of the base is 6 cm and the heightof the pyramid is 8 cm. 12.1 Calculate the slant height of the triangular face of … Read more

## Question 11

11.1 Complete: Opposite angles of a cyclic quadrilateral … (1) 11.2 In the figure, ABCD is a cyclic quadrilateral. AB ║ DC in circle with centre O. BC and AD produced meet at M. D3 = 𝑥 11.2.1 Show that MC = MD. (5) 11.2.2 If D3 = 𝑥, determine the value of M̂ , … Read more

## Question 10

A, B, C and D are points on the circumference of the circle in the diagram below. ECF is atangent at C, B1 = B2 . 10.1 If B1 = 𝑥, find, with reasons, TWO other angles equal to 𝑥. (4) 10.2 Hence, show that DC bisects AĈF. (2) [6]

## Question 9

9.1 In the diagram O is the centre of the circle and ABC are points on the circle. Use the diagram in your SPECIAL ANSWER BOOK to prove that:AÔB = 2AĈB. (6) 9.2 In the figure below, DĈO = 25° and O is the centre of the circle. A, B, E C and D are … Read more

## Question 8

GIVE REASONS FOR YOUR STATEMENTS AND CALCULATIONS IN QUESTIONS 8, 9, 10 AND 11. 8.1 Complete: The line drawn from the centre of the circle perpendicular to the chord … (1) 8.2 In the figure below, AB and CD are chords of the circle with centre O. OE ┴ AB. CF = FD. OE = … Read more

## Question 7

7.1 Draw the graph of f and g for x ∈ [-90° ; 180°] in the SPECIAL ANSWER BOOK. Show all the turning points and intercepts with the axes. Clearly show the asymptotes using dotted lines. (6) 7.2 Determine the values of x, for ∈ [-90° ; 180°], for which f(x) > g(x). (6) 7.3 … Read more

## Question 6

6.1 COMPLETE: In ∆ABC b2 = … + … – … 6.2 In the diagram below, PQ is a straight line 1 500 m long. RS is a vertical tower158 m high with P, Q and S points in the same horizontal plane. The angles ofelevation of R from P and Q are 25° and … Read more

## Question 5

5.1 In the diagram below, P(1;3) is a point on the Cartesian plane, OP = r and XÔP= θ. 5.1.1 Make use of the diagram to calculate the value of θ. (2) 5.1.2 Calculate the length of OP. Leave the answer in surd form. (2) 5.1.3 Determine the values of the following, without using a … Read more

## Question 4

4.1 Calculate the gradient of NQ. (1) 4.2 Calculate the gradient of MP. (1) 4.3 Calculate the angle of inclination of MP. (3) 4.4 Hence, determine the equation of the line MP. (4) 4.5 Hence, determine the coordinates of P. (4) 4.6 Determine the co-ordinates of R. (3) [16]

## Question 3

The points A(2a – 11; a +2), C(4; -1) and D(4p; p – 7) are the vertices of ∆ACD with B(-2; 3)on AC. 3.1 If points A, B and C are collinear, find the value of a. (4) 3.2 Determine the equation of the line AC. (3) 3.3 Hence, determine the co-ordinates of midpoint M … Read more