6 marks 490 the tangent to the curve y fx at the point

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ………………………….. (Total 6 marks) 343 517. Consider events A, B such that P(A) ≠ 0, P(A) ≠ 1, P(B) ≠ 0, and P(B) ≠ 1. In each of the situations (a), (b), (c) below state whether A and B are mutually exclusive (M); independent (I); neither (N). (a) P(A|B) = P(A) (b) P(A ∩ B) = 0 (c) P(A ∩ B) = P(A) Working: Answers: (a) ………………………………………….. (b) ……………………………………….. (c) .................................................................. (Total 6 marks) 344 3 518. Given that ∫ g ( x)dx = 10, deduce the value of 1 3 (a) 1 ∫ 2 g ( x)dx; 1 3 (b) ∫ ( g ( x) + 4)dx. 1 Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 345 519. Given that log5 x = y, express each of the following in terms of y. (a) log5x2 (b) log5 1 x (c) log25x Working: Answers: (a) ………………………………………….. (b) ………………………………………….. (b) .................................................................. (Total 6 marks) 346 520. Let f(x) = e–x, and g(x) = (a) f–1(x) (b) x , x ≠ –1. Find 1+ x (g ° f)(x). Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 521. Consider the vectors c = 3i + 4j and d = 5i – 12j. Calculate the scalar product c ⋅ d. Working: Answers: ………………………………………….. (Total 2 marks) 347 522. A family of functions is given by f(x) = x2 + 3x + k, where k ∈ {1, 2, 3, 4, 5, 6, 7}. One of these functions is chosen at random. Calculate the probability that the curve of this function crosses the x-axis. Working: Answer: ………………………………………….. (Total 6 marks) 348 523. The diagram below shows a triangle and two arcs of circles. The triangle ABC is a right-angled isosceles triangle, with AB = AC = 2. The point P is the midpoint of [BC]. The arc BDC is part of a circle with centre A. The arc BEC is part of a circle with centre P. E B D 2 A P C 2 (a) Calculate the area of the segment BDCP. (b) Calculate the area of the shaded region BECD. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 6 marks) 349 524. Consider the following relations between two variables x and y. A. y = sin x B. y is directly proportional to x C. y = 1 + tan x D. speed y as a function of time x, constant acceleration E. y = 2x F. distance y as a function of time x, velocity decreasing Each sketch below could represent exactly two of the above relations on a certain interval. (i) y (ii) (iii) y x y x x Complete the table below, by writing the letter for the two relations that each sketch could represent. sketch relation letters (i) (ii) (iii) 350 525. The diagram shows part of the graph o...
View Full Document

Ask a homework question - tutors are online