Figure shows a rectangle OABC in which OA = a and OC = c. F is the midpoint of CB and D is the point on AB such that AD : DB = 2:3
_ _ _ _ _ __ (i) CF in terms of a
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (ii) AD in terms of c
The lines OD and AF intersect at the point X Given that...
Figure shows six identical circles inside a rectangle.
The radius of each circle is 24 cm. The radius of the circles is the greatest possible radius so that the circles fit inside the rectangle. The six circles form the pattern shown in Figure so that
• each circle touches at least two other...
A bag contains x beads. 6 of the beads are red and the rest are blue. Ravish is going to take at random 2 beads from the bag. The probability that the 2 beads will be of the same colour is $9 /17$
Using algebra calculate the value of x. ( show sworking if possible)
(a) Solve the inequality 5(3x + 1) <11x, Show clear algebraic working. (2)
(b) Solve the simultaneous equations 3x 2 + y 2 – 7 = 0, y – 3x – 5 = 0 Show clear algebraic working. (4)
(c) Hence find the value of x for which 5(x + 1) < x and 3x 2 + y 2 – 7 = 0 and y – 3x – 5 = 0
The function h is defined as h : x x 2 – 8x – 9 where x ≥4
(a) h(x) can be written in the form (x+a) 2 +b, find the value of ‘a’ and ‘b’
(b) Express the inverse function h –1 in the form h –1 : x ...
(c) Find the range of function ‘h’.