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Unformatted text preview: f the curve y = a (x – h)2 + k, where a, h, k ∈ . y 20
(a) 1 2 3 4 5 6 x . The vertex is at the point (3, 1). Write down the value of h and of k.
(2) (b) The point P(5, 9) is on the graph. Show that a = 2.
(3) (c) Hence show that the equation of the curve can be written as
y = 2x2 – 12x + 19.
(1) (d) (i) Find dy
dx A tangent is drawn to the curve at P (5, 9).
(ii) Calculate the gradient of this tangent, (iii) Find the equation of this tangent.
(Total 10 marks) 351 7
10 526. The diagram shows a parallelogram OPQR in which OP = , OQ = . 3
1 y P
R (a) Find the vector OR .
(3) (b) ˆ
Use the scalar product of two vectors to show that cos OPQ = – 15 . 754
(4) (c) (i) ˆ
Explain why cos PQR = –cos OPQ. (ii) ˆ
Hence show that sin PQR = 23 . 754
(iii) Calculate the area of the parallelogram OPQR, giving your answer as an integer.
(Total 14 marks) 352 527. In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not study either
subject. This information is represented in the following Venn diagram. E(32) H(28) a (a) b c Calculate the values a, b, c.
(4) (b) A student is selected at random.
(i) Calculate the probability that he studies both economics and history. (ii) Given that he studies economics, calculate the probability that he does not study
(3) (c) A group of three students is selected at random from the school.
(i) Calculate the probability that none of these students studies economics. (ii) Calculate the probability that at least one of these students studies economics.
(Total 12 marks) 528. An aircraft lands on a runway. Its velocity v ms–1 at time t seconds after landing is given by the
equation v = 50 + 50e–0.5t, where 0 ≤ t ≤ 4.
(a) Find the velocity of the aircraft
(i) when it lands; (ii) when t = 4.
(4) 353 (b) Write down an integral which represents the distance travelled in the first four seconds.
(3) (c) Calculate the distance travelled in the first four seconds.
(2) After four seconds, the aircraft slows down (decelerates) at a constant rate and comes to rest
when t = 11.
(d) Sketch a graph of velocity against time for 0 ≤ t ≤ 11. Clearly label the axes and mark on
the graph the point where t = 4.
(5) (e) Find the constant rate at which the aircraft is slowing down (decelerating) between t = 4
and t = 11.
(2) (f) Calculate the distance travelled by the aircraft between t = 4 and t = 11.
(Total 18 marks) 529. The points P, Q, R are three markers on level ground, joined by straight paths PQ, QR, PR as
shown in the diagram. QR = 9km, PQR = 35°, PRQ = 25°.
(a) 35° 25°
9 km R Find the length PR.
(3) (b) Tom sets out to walk from Q to P at a steady speed of 8 km h–1. At the same time, Alan
sets out to jog from R to P at a steady speed of a km h–1. They reach P at the same time.
Calculate the value of a.
(7) 354 (c) The point S is on [PQ], such that RS = 2QS, as shown in the diagram. P
Q R Find the length QS.
(Total 16 marks) 530. A...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.
- Fall '13
- The Land