u 2 or GCE A Level H1 Maths Solution Paper 1 2(i) Given 4x 2y i.e. 2x y (i) And..(ii) From (i), substitute y 40 2x into (ii):

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1 GCE A Level H Maths Solution Paper e e u u u u u or e or (N.A.) ln (i) Given y i.e. y... (i) And y( )..(ii) From (i), substitute y into (ii): shown (ii) From or (N.A) since When, y. Thus y. Therefore, length of HF is cm. (i) (ii) Substitute y k into y k : k k k k k or which are the -coordinates of points of intersection of C & L. k Area Area of under the curve from to k Area of the rectangle with sides and k Note: Alternatively, the area can be epressed as k k k d k

2 k k d k k k k 8 k k k k 6 k (i)(a) d ln = 6 d (i)(b) d 8 = 8 d (ii) d d ln 6 ln 8 ln ln 5(i) y y Note: In general, there is a modulus for the ln in d ln C.767 O Points of intersection with the aes are.767,,.,,,, and 5(ii) From GC, the gradient of C at.5 is.986 =.95 correct to d.p. 5(iii) When.5, y Equation of tangent to C is Note: Equation of a straight line is y m c or we can

3 y y y That is, y correct to d.p. consider the form which is used y y m. here: 5 (iv) At y -ais, coordinates of A,.77 At y B.8,.8 coordinates of Length of AB correct to s.f. 6(i) 6(ii) Systematic sampling is a method of selecting members from an ordered sampling frame in such a way that the first member of the sample is randomly selected out of the first k members in the ordered sampling frame, followed by selecting every subsequent k th member from the ordered sampling frame for inclusion in the sample. number of members in sampling frame Here, k. sample size Advantage This method is cost effective. That is, it takes less time and effort to carry out. 6(iii) Disadvantage Not all adults will go to the supermarket at midday due to various reasons such as work etc. Thus the sample collected may not be representative of the town people. One possible way to carry out a more appropriate systematic sampling is to obtain the list of all adults in that particular town, apply systematic sampling on it and call the adults selected in the sample to do the survey. Note: Since the objective is to survey on usage time on computer, the choice of doing survey outside the supermarket is irrelevant. 7(i) P A B P A PB P A B p p p A & B are independent. 9 p 5 5 p or 9p 8p 5 9

4 7(ii) From (i), p or 5 (N.A.) 8 P A B p 8(i) A M.5 P (ii) P( F ) = A B C M F M F M F 8(iii) 9 (i) P( C M ) = 5 y P C M.5. P M (ii) r.98 Since r.98 (correct to s.f.) is close to, it suggests there is a strong negative linear correlation between the advertised price and the age of Pluto cars. 9(iii) From GC, y That is, y correct to d.p. 9(iv) When, y 6.8 Thus, the estimated advertised price is $6. When 9, y. Thus, the estimated advertised price is $.

5 9(v) Since is within the data range, the estimate obtained in (a) is reliable but 9 is not within the given range of data ( we are doing etrapolation), hence the estimate obtained in (b) is unreliable. Let X be the number of Sunbrite plants that flower out of plants. X ~ B,.8. Then (i) P X.87.8 correct to s.f. (ii) P X 8 X P correct to s.f. (iii) (iv) Let Y be the number of Sunbrite plants that flower out of 96 plants (8 trays). Y ~ B 96,.8. Then n = 96 is large, np & nq 9. 5 Y C.C. ~ N 76.8,5.6 appro. Thus required probability is P Y 75 P Y correct to s.f. Let T be the number of gardeners who have more than 75 of their plants flower. T ~ B,.699. Then T P T P correct to s.f. (i) n, ( ) n ( ) s ( ) n n (ii) Let be the mean length of string in a ball. H : against H : at the 5% significance level X Test statistic, Z S Note: In the manager s claim that the average length is at least m, we test H : 5

6 Using z -test, from GC, p -value.7 correct to s.f. Since p -value =.7 <.5, we reject H at 5% level of significance and conclude that there is sufficient evidence to conclude that. Hence the manager s claim is not valid. (iii) H : against H : at the % significance level. k Test statistic, Z. For manager s claim to be valid, we have H not to be rejected. k Thus Z k (.855) k least k correct to d.p. Let X and Y be the masses of grapefruit of type A and B respectively. N.5,. Y N.5,. Then X and (i) Let the total mass of randomly chosen grapefruit of type A be X X... X. X X... X N.5,. Then X X... X ~ N.5,. Required probability P X X... X correct to s.f. 6

7 (ii) Let M be the total mass of 6 randomly chosen grapefruit of type A and Let M be the total mass of 5 randomly chosen grapefruit of type B. Then M M ~ N , (iii) M M ~ N.5,.69 Required probability is P( M M.) P(. M M.).76.7 correct to s.f. Let $W be the price paid by Mrs Woo. W.5 X X X. Y Y Y Then W ~ N ,.5... W ~ N.65,.85 Let $T be the price paid by Mr Tan. T.5 X X X. Then T T N.75,.9 N.5.5,.5. Therefore, W T N.65.75,.85.9 W T N.5,.75 Note: The phrase type A is within. kg of type B means type A grapefruits weigh at most. kg more than type B and at the same time, type A grapefruits weigh at most. kg less than type B. P( W T) P( W T ).67.6 correct to s.f. 7