2024 ACJC JC2 H1 LCP2A QP

ANGLO-CHINESE JUNIOR COLLEGE 2024 H1 MATHEMATICS 8865 [Turn over Name: ______________________________ Tutorial Class: _______________ ANGLO-CHINESE JUNIOR COLLEGE MATHEMATICS DEPARTMENT MATHEMATICS Higher 1 19 March 2024 JC2 LCP2A (25 marks) Time allowed: 45 mins List MF26 Standard discrete distributions Distribution of X P( )Xx= Mean Variance Binomial B(n, p) ( )1 nxxn ppx − − np (1 )np p− 1 Find algebraically the set of values of t for which 223 3 ( 3) 0x tx t t− + − −  for all real values of x. [3] 2 Find (i) ( ) 2231 d x x e xe +  [2] (ii) 1 d 94 x x− [2] 8865

ANGLO-CHINESE JUNIOR COLLEGE 2024 H1 MATHEMATICS 8865 3 The diagram shows the curve C with equation ()y x k x=− , where 4k  and the line L with equation 2yx= . The x-coordinate of point Q where C and L intersect is 2k− . Given that the exact area of the region bounded by C, L and the x-axis is 49 3 , find the value k. [5] 4 Sunrise Company produces lemons and sells them in bags of 6. The 6 lemons are randomly chosen from a large supply. The probability that a lemon is rotten is 0.2. (i) State, in context, two assumptions needed for the number of rotten lemons in a bag to be well modelled by a binomial distribution. [2] Assume now that the number of rotten lemons in a bag follows a binomial distribution. (ii) Find the most likely number of rotten lemons that can be found in a randomly selected bag. [1] (iii) Find the probability that, in a randomly selected bag of lemons, there is more than 2 rotten lemons, given that there is at most 4 rotten lemons. [3] The probability that a lemon is rotten is 0.2. A bag of lemons is discarded if more than 70% of the lemons are rotten. (iv) Find the probability that a randomly selected bag of lemons will be discarded. [2] (v) 30 bags are chosen at random, find the probability that none of the bags of lemons will be discarded. [2] Sunrise Company changed its packaging material to prevent the lemons from rotting. The lemons are still sold in bags of 6 and the new probability that a lemon is rotten is p. (vi) It is given that for a randomly selected bag, the probability that at least one lemon is rotten is 0.7. Write down an equation in terms of p, and find the value of p. [3] L x 0 y C Q

ANGLO-CHINESE JUNIOR COLLEGE 2024 H2 MATHEMATICS 9758 [Turn over Summary of Areas for Improvement Knowledge (K) Careless Mistakes (C) Read/Interpret Qn wrongly (R) Presentation (P)