1994 HKCEE MATHS Paper II

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1 99 HKCEE MATHS Paper II P. If f ( x) = x + x, then f ( x ) = 99 HKCEE MATHS Paper II 6 If x ( x + ) < ( x + ), then x x x + x x + x x + x If x y =, then x = x + + y + y + y + y y The L.M. of ( ) x y + y ( x ) ( x + )( x + x + ) ( x ) ( x + )( x + x + ) ( x ) ( x + )( x x + ) ( x )( x + )( x + x + ) If a = +, then a = a 0 y y x, x and x is + In the figure, (x, y)is a point in the shaded region (including the boundary) and x, y are integers. Find the greatest value of x + y. x < x < or x > x < or x > < x < < x < 7 Which of the following is/are an identity 8 /identities? I. ( x + )( x ) = x II. ( x + )( x ) = 0 III. ( x + ) = x + 8 I only II only I and III only III only II and III only α hα b = 0 Ifα β and, then α + β = β hβ b = 0 b b h h h 9 Mr. Chan bought a car for $ 900. If the value of the car goes down by 0% each year, find its value at the end of the third year. (Give your answer correct to the nearest hundred dollars.) $9 00 $ $0 900 $ 00

99 HKCEE MATHS Paper II P. $6 600 0 A wholesaler sells an article to a retailer at a profit of 0%. The retailer sells it to a customer for $ 600 at a profit of $70.

2 99 HKCEE MATHS Paper II P. $ A wholesaler sells an article to a retailer at a profit of 0%. The retailer sells it to a customer for $ 600 at a profit of $70. Find the original cost of the article to the wholesaler. $ 0 $ 00 $ 000 $ 880 $ 6 The bearing of A from B is 07º. What is the In the figure, the paper cup in the form of a circular cone contains 0ml of water. How many ml of water must be added to fill up the paper cup? bearing of B from A? 0º 07º 9º 0º º If the sum to infinity of a G.S. is 8 and its second term is 9, the common ratio is 9 In the figure, ABCD is a rectangular field of length p metres and width q metres. The path around the field is of width metres. Find the area of the path. ( p + q) m ( p + q + ) m ( p + q + 6) m ( p + q + 6) m ( + p + q + 6) pq m In the figure, OACB is a sector of radius r. If AOB= π, find the area of the shaded part. π 6 r π r 6 π r

3 99 HKCEE MATHS Paper II P. π r 6 π r r = sinθ + sinθ 9 In the figure, ABCD is a cyclic quadrilateral with AB =, BC = and ADC =0º. Find AC. tanθ 0 tanθ Which of the following figures shows the graph of y = + sin x? 9 0 In the figure, PC is a vertical pole standing on the horizontal plane AB If ABC =90º, BAC =0º, AC =6 and PC =, find tanθ sin( 80 + θ ) cos( 90 θ ) = In the figure, O is the center of the circle. If AC= and 6 π BAC =, 6 find the diameter A tanθ

4 99 HKCEE MATHS Paper II P. In the figure, x, y and z are the exterior angles of AB If x : y : z = : : 6, then BAC= In the figure, PA is tangent to the circle at A, CAP=8º and BA=B Find x. 8º 8º 6º 6º 76º In the figure, O is the center of the inscribed circle of AB If OAC=0º and OCA=º, find AB 6 The points A(,), B(, ) and C (x, ) lie on a straight line. Find x. 0º º 60º 6.º 70º 0 7 In the figure, the shaded part is bounded by the axes, the lines x = and x + y =. Find its area. In the figure, AB=AD and BC=C If BAD=80º and ADC=6º, then BCD= 00º 0º º 0º 60º AB is a diameter of the circle x + y x y 8 = 0. If A is (,), then B is (, )

5 99 HKCEE MATHS Paper II P. (, ) (, 7) (, ) (7, 9) 9 The equations of two circles x are x + y + y x 6y = 0 + x + 6y = 0 Which of the following is/are true? I. The two circles have the same center. II. The two circles have equal radii. III. The two circles pass through the origin. I only II only I and III only III only II and III only 0 In the figure, the pie chart shows the monthly expenditure of a family. If the family spends $800 monthly on rent, what is the monthly expenditure on entertainment? The mean, standard deviation and interquartile range of n numbers are m, s and q respectively. If is added to each of the n numbers, what will be their new mean, standard deviation and interquartile range? Standard Interquartile Mean Deviation Range m s q m s + q + m + s q m + s q + m + s + q + ( x ) = ( x ) x+ 6 x x 9 x $0 $600 $70 $ 800 $ 000 If log = a and log9 = b, then log= b a + b a + a + b A box contains eggs, of which are rotten. If eggs are chosen at random, find the probability that exactly one of them is rotten. a + b a b 6 Factorize a ab + b a + b. ( a b)( a b ) ( a b)( a b +)

6 99 HKCEE MATHS Paper II P.6 6 ( a b)( a + b ) ( a + b)( a b +) ( a b ) x y y x x y y x = y + x y x y + x y x 9 If x =, y = satisfy the simultaneous ax + by = equations, find the values bx ay = of a and b. a = 0, b = a = 0, b = a =, b = 6 7 a =, b = 9 a =, b = 7 P(x) is a polynomial. When P(x) is divided by ( x ), the remainder is R. If P(x) is divided by (x), then the remainder is R R R 8 In the figure, the line y = mx + k cuts the curve y = x + bx + c at x = α and x = β. Find the value of αβ. b c m b k c c k 0 From the table, which of the following intervals must contain a root of ( x) x = 0 <x< f? x f ( x) <x<0 <x< 0 <x< <x< If the product of the first n terms of the sequence 0, 0, 0,, 0 n exceeds 0, find the minimum value of n

7 99 HKCEE MATHS Paper II P.7 If a : b = :, a : c = : and a : d = :, then b : c : d = :: :: 8:6: :6:0 0::8 Let x vary inversely as y. If y is increased by 69%, then x will be increased by.%( sig. fig.) increased by 0% decreased by.%( sig. fig.) decreased by 0% decreased by 76.9%( sig. Fig) In the figure, CDEF is a sector of a circle which touches AB at If AB= and BC=, find the radius of the sector. : : : : 6:6 6 In the figure, area of ABC:area of square BCDE =:. Find PQ:BC : : : : : In the figure, AD:DB =:, AE:EC=:. 7 For 0 x 60, how many roots does the equation sin x ( cos x + ) = 0 have? 0 Area of E:Area of ABC= 8 The largest value of ( cos ) + θ is

8 99 HKCEE MATHS Paper II P In the figure, sina : sinb : sin C = : : 6. If AB=8, find A In the figure, AB= p, ACB=θ. Find C p sinθ In the figure, OABCD is a sector of a circle. If AB = BC = CD, then x = 0º 0º º º 0º In the figure, AB//DC and DAB= DB Which of the following is/are true? p psinθ cos θ psin θ p cos θ sinθ In the figure, ABCD is a semi-circle, CDE and BAE are straight lines. If C=0º and DEA=º, find x. I. II. III. AB = AB = AD = DC AD BC CD I only II only I and II only III only II and III only

UNC Charlotte 2005 Comprehensive March 7, 2005

UNC Charlotte 2005 Comprehensive March 7, 2005 March 7, 2005 1 The numbers x and y satisfy 2 x = 15 and 15 y = 32 What is the value xy? (A) 3 (B) 4 (C) 5 (D) 6 (E) none of A, B, C or D 2 Suppose x, y, z, and w are real numbers satisfying x/y = 4/7,