8 40. Mark your answers in the M.C. answer sheet. 1. Simplify 5 5 C. 5. D Factorize 8a 3 27b 3. A. 2a 3b 4a 2 6ab 9b 2. B. 2a 3b 4a 2 6ab 9b 2

Size: px

Start display at page:

Download "8 40. Mark your answers in the M.C. answer sheet. 1. Simplify 5 5 C. 5. D Factorize 8a 3 27b 3. A. 2a 3b 4a 2 6ab 9b 2. B. 2a 3b 4a 2 6ab 9b 2"

Phillip Shepherd
5 years ago
Views:

1 Section. Simplify D. 5. Multiple hoice: Mark your answers in the M.. answer sheet Factorize 8a 7b.. a b 4a 6ab 9b.. a b 4a 6ab 9b.. a b 4a 6ab 9b. D. a b 4a 6ab 9b = D In the figure, D is a trapezium. Which of the following must be true? I. ED is an equilateral triangle II. ED is a parallelogram III. = D. I only. II only. I and II only D. I and III only [ ]

2 5. The point of intersection of the three altitudes of a triangle is called the. centroid.. circumcentre.. incentre. D. orthocentre. 6. In the figure, the solid consists of a cylinder and a right circular cone with a common base which is a circle of radius cm. The height of the cylinder is 0 cm and the slant height of the cone is 5 cm. Find the total surface area of the solid.. 74 cm. 84 cm. 94 cm D. 04 cm 7. The figure shows a frustum of a right circular cone. The radii of the upper face and the base are cm and cm respectively. If the height is cm, find the volume.. 5 cm.. 9 cm.. 7 cm. D. cm. 8. The figure shows a right prism DEF with a right-angled triangle as the cross-section. The angle between D and the plane DEF is. DE.. DF.. DF. D. DE. 9. Refer to the figure. The whole circle bearing of from is 0. Find the whole circle bearing of from D N N 0 [ ]

0. Which of the solids has the following orthographic projections? Front Left Top... D.. The diagram shows part of a contour map drawn to the scale of : 0000.

3 0. Which of the solids has the following orthographic projections? Front Left Top... D.. The diagram shows part of a contour map drawn to the scale of : If equals to cm in the map, what is the gradient of the road? m m.. D. cannot be determined. 800 m. In the figure, D is a rectangle. Find F.. a b sin cm.. a b cos cm.. asin bcos cm. D. acos bsin cm. [ ]

4 . In the figure, PQRS is a parallelogram. Which of the following is true?. The length of QR is 7.. The length of RS is5.. The slope of QR is. D. The slope of RS is. 4. The points (4, -), (-, ) and (x, 5) lie on a straight line. Find x D.. 5. If the price of a movie ticket is increased from $60 to $75, then the percentage increase is. 0%.. 5%.. 80%. D. 5%. 6. Find the interest on $ 000 for years at 0% p.a., compounded half-yearly.. $ $440.. $464.. D. $0. 7. fair coin is tossed four times. The probability of getting at least two heads is D.. [ 4 ]

5 8. What is the probability that the first day of a month is Sunday?... D Given that a b and b > 0, which of the following(s) is/are incorrect? I. ab 0 II. a b III. a b. II only. III only. I and III D. II and III 0. The numbers of bedrooms in the families of 80 students are listed below. Number of bedrooms 4 Frequency Find the mean of the numbers of bedrooms D. [ 5 ]

6 . If a and b are non-zero numbers, then 8 a.. b. a. b. 8 a. b D. a. b ( a b ) ( a b ( a ) ) 7 0 =. Factorize a + 5ab b.. (a b)(a b). (a + b)(a b). (a + b)(a b) D. (a b)(a + b). In the figure, PQRS is a trapezium. Find x D. 5 P Q 5x 5x S R 4. The base diameter and height of a right circular cone are 0 cm and cm respectively. Find the curved surface area of this cone.. 65 cm. 78 cm. 8 cm D. 56 cm [ 6 ]

7 5. Which of the following is the front view of the given object? top... D. front side 6. ccording to the following front, top and side views of a solid, choose the corresponding -D object. front top side.. top top front side front side. D. top top front side front side [ 7 ]

8 7. Refer to the figure. The whole circle bearing of from is 0. Find the reduced bearing of from.. S40 W. S50 W. N40 E D. N50 E N N 0 8. The figure shows a part of a contour map. Suppose the gradient of the straight path is : 8. Find the horizontal distance between and m. 600 m. 760 m D. 800 m 700 m 750 m 800 m 9. From a point R on the ground, the angle of elevation of the top P of a flagpole is 50. If PQ = 44 m and O is the mid-point of PQ, find the angle of elevation of O from R correct to the nearest degree.. 9 P. 0. D. R 50 O Q 44 m 0. Given two points P( 7, 4) and Q(, ) and a line L that is parallel to PQ, find the slope of L.... D [ 8 ]

9 . Which of the following represents the solutions of x? D. 0. If a > b and c < 0, which of the following must be correct? I. a c > b c II. a c < b c III. a b c c. I only. III only. I and III only D. I, II and III. Find the greatest integer satisfying the inequality 0 (x + ) > x D. [ 9 ]

10 4. The figure shows two similar solids. Find the value of V D cm 0 cm Volume = 686 cm Volume = V cm 5. letter is chosen randomly from the word HLLENGE. Find the probability that a vowel is chosen.... D $0 000 is deposited in a bank and interest is compounded half-yearly. If the amount received after one year is $0 40, find the interest rate per annum.. %..05%. % D..% 7. In a certain year, the rateable value of a shop is $ If the rates percentage charge is 5% each year, find the quarterly rates of the shop.. $ 50. $ 5. $6 50 D. $ 500 [ 0 ]

11 8. students are randomly chosen from male students and female students. Find the probability of choosing male student and female student.... D The figure below shows a circular target of diameter 0 cm. The bullseye is a square of sides 5 cm. armen throws a dart randomly and hits the target. Find the probability that the dart hits the bullseye.... D. 6π 4π 5 4π 5 π 0 cm 5 cm 40. One letter is selected from each of the names "LEO" and "KEN" at random. Find the probability that the two letters are the same.... D [ ]

12 4. If the mean of the ten numbers 7, 5, 5, 5, 6,, 7, 8, 8, x is 6, find the median of the ten numbers D The table below shows the number of visits that 50 students went to Merry Theme Park last year. Number of visits Frequency 5 9 Find the mean number of visits that these 50 students went to Merry Theme Park last year D Find the volume of the frustum in the figure.. 6 cm. 65 π cm. 6 π cm 6 cm 8 cm D cm M E N 7 cm 8 D. π cm 44. Find x and y in the figure.. x = 0, y =. x = 0, y =. x = 40, y = D. x = 40, y = 4 M 40 y cm 0 6 cm x N [ ]

13 45. Which of the following is not a rational number?.. 0. D Which of the following is/are parallelogram(s)? () rectangle () square () rhombus D () and () only () and () only () and () only ll of the above 47. In the figure, 4 D 5 x [ ]

14 48. Refer to the figure. Which of the following is/are true? () E DE () D () E DE D () only () and () only () and () only ll of the above 49. The figure shows the cube DEFGH of volume 6 cm cm 8 cm D 4 cm 6 cm. The volume of the pyramid DH is [ 4 ]

15 50. (right prism) (cube) (regular tetrahedron) () () () (right prism) (right prism) (4) (5) 5. In which of the above solids is the shaded region a plane of reflection? (), () and (5) only (), (), () and (5) only (), (), (4) and (5) only D ll of the above Which of the following nets can be folded into the above triangular prism? () () [ 5 ]

16 () (4) 5. D () and () only () and (4) only (), () and () only ll of the above The above solid is formed by cutting a corner from a cube. Which of the following must be true? V > E > F V > F > E E > V > F D F > V > E (V - Number of vertices, E - Number of edges, F - Number of faces) 5. The mid-point of the line segment joining (, 4 ) and ( x, y ) is M (, ). Find x and y. 7 (, ) 5 (, ) ( 5, ) D ( 5, ) [ 6 ]

54. If the distance between P( a, ) and Q

17 54. If the distance between P( a, ) and Q ( 4, 9 ) is 5 and a 0, a = 4 D The following shows some -D representations of a solid that is made from identical cubes. Top view Front view Side view Which of the following satisfy the above -D representations? () () () (4) D () only () and () only (), () and (4) only ll of the above [ 7 ]

18 56. Find the value of k if the line joining the points (7,9) and (k,) is perpendicular to a line with slope D road has a gradient of in 0. Find the angle of inclination D From the top of a lighthouse of 0 m high, the angle of depression of a boat is 5. How far is the boat away from the base of the lighthouse, which is at sea-level? D 0 m tan 5 0 m sin 5 0 tan 5 m 0sin 5 m 59. The rateable value of a flat is $ and rates are charged at 5.5% per year. The quarterly payment for rates is $880 $ 760 $ 640 D $ What is the compound interest for the third year on a deposit of $0 000 at 0% p.a., compounded yearly? $ 000 $ 00 $ 400 D $ 40 [ 8 ]

19 6. The number of bacteria in a forest grows 8% per day. fter two days, the number of bacteria becomes 96. What is the original number of bacteria? D If x < 0, which of the following must be correct? () x x (). x x (). 4 7x D () only () only () and () only () and () only 6. The sum of two numbers is 0 and their difference is no less than 8. Find the maximum value of the smaller number. 9 9 D Which of the following cannot be the probability of the happening of an event? D 4 [ 9 ]

20 65. bag contains red, white and 5 black balls. One ball is randomly drawn from the bag at random, find the probability that it is not white. D n unfair die is thrown 00 times and the result is as shown: Outcome Frequency If it is thrown once, find the probability that the number is prime. D group of y numbers has mean x. If the numbers and 5 are removed from the group, the mean of the remaining ( y ) numbers remains unchanged. Find x. 4 D 5 [ 0 ]

21 68. If the median of 5 different integers 4,, 5, x, 9 is x, which of the following is/are the possible(s) value of x? () () 6 () 9 D () only () only () and () only () and () only 69. Solve (4 5x) 8x.... D. 4 x 9 4 x 9 4 x 9 4 x The table below shows the salaries tax rate: Net chargeable income Tax rate On the first $ % On the next $ % On the next $ % Remainder 7% The net chargeable income of Miss heung is $ How much salaries tax should she pay?. $7 00. $ $ 400 D. $0 600 [ ]

It is given that the arithmetic mean, the median and the mode of a set of data are 6, and 40

22 7. Which of the following may NOT be a parallelogram?... D. 7.. Which of the following solids corresponds to the given orthographic views?... D. 7. It is given that the arithmetic mean, the median and the mode of a set of data are 6, and 40 respectively. If each data is divided by, find the new arithmetic mean, median and mode. rithmetic mean Median Mode D [ ]

23 74.. Which of the following can be a formula for volume (V), where a, b and c are linear measurements?. V 4 a ac.. V b b V a D. V ab( c d) c 75. It is given that the slope of L is and L, where the coordinates of and are (, 0) and (0, n) respectively. Find the value of n.... D The figure shows a cylinder, a sphere and a right circular cone. Find the ratio of their volumes.. : 4 : 6. 4 : :. 4 : : 6 D. : 4 : [ ]

77. The figure shows a dartboard consisting of squares of equal area, six of which are marked with numbers. Emily throws a dart randomly and hits the dartboard.

24 77. The figure shows a dartboard consisting of squares of equal area, six of which are marked with numbers. Emily throws a dart randomly and hits the dartboard. What is the probability that the dart hits an even number?... D Suppose letters E, F and V represent the number of edges, faces and vertices of a polyhedron respectively. Which of the following must NOT give a polyhedron?. E = 6, F = 0, V = 8.. E = 44 F = 6, V = 0.. E = 8, F = 8, V =. D. E = 56, F =, V = Find the median of 6, 9, 8, 9, 6 and D. 6 [ 4 ]

25 80. TV camera is photographing May. Find the angle of depression between the camera and the horizontal. May D Find x and y in the figure.. x = 0, y =. x = 0, y = M 40 y cm x N. x = 40, y = D. x = 40, y = cm 8. In the figure, the true bearing of from is 0. Find the compass bearing of from.. S40 W N. S50 W N 0. N40 E D. N50 E [ 5 ]

26 8. The figure shows a pyramid VD with a rectangular base D. V is perpendicular to the plane D. Find the angle between V and the plane V. V D. V.. V D. V 84.. In the figure, D and PQRS are two similar quadrilaterals. If the ratio of the area of D to that of PQRS is 49 : 5, find D cm. 9 cm. 4 cm P Q D. 9.6 cm R 85.. The cumulative frequency curves below show the distribution of the ages of employees in two departments of a company. 0 ges of employees in two departments of a company Department umulative frequency Department ge [ 6 ]

27 Which of the following are correct? I. The total number of employees in Department < the total number of employees in Department II. The median age of employees in Department < the median age of employees in Department III. The rd quartile of the ages of employees in Department < the rd quartile of the ages of employees in Department. I and II only. I and III only. II and III only D. I, II and III 86. Factorize y 8x.. (y x)(y + xy + 4x ). (y x)(y xy + 4x ). (y x)(y + 4xy + 4x ) D. (y x)(y 4xy + 4x ) 87. Which of the following numbers has/have the same value as 50? I II III I only. II only. I and II only D. II and III only [ 7 ]

28 88. In the figure, P(x, y) is a point on such that P : P = :. Find the coordinates of P. y. (, ) ( 5, 7). (, 5). (, 5) P(x, y) D. (, ) O (4, ) x 89. Express in scientific notation D In the figure, D = D, =. Which of the following must be true? D. DE E. DE E E. DE ~ E D. None of the above 9. In the figure, PQRS is a parallelogram and SR = TR. Find QRT.. 70 o P T S. 75 o 05 o. 80 o D. 85 o Q R [ 8 ]

29 9. (5, ), (, 5) and (0, ) are the vertices of. How long is the shortest side of? D balloon consists of three parts: an open hemisphere, an open cylinder and an open circular cone. The heights of the cylinder and the cone are 40 cm and 6 cm respectively. Its diameter is 8 cm. Find the total surface area of the balloon. (Give the answer correct to significant figures.). 080 cm. 0 cm 8 cm. 550 cm D. 870 cm 40 cm 6 cm 94. The figure shows 4 check points of a race. Find the true bearing of U from T. N. 9 R D S 6 T 7 U [ 9 ]

30 95. If D is the angle bisector of, which of the following is/are true? () D D () 45 () D D D () only () and () only () and () only ll of the above 96. Factorize 9 b 4.. ( 4b)( 4b). ( 9 b)(9 b). ( b)( b) D. ( b)( b) 97. Solve 5x x.. x 7. x 7. x 7 D. x Express in scientific notation.... D [ 0 ]

31 D p p p.. p.. 9 p. D. 9p. 0. The monthly salary of John is 5% higher than that of David while the monthly salary of David is 5% lower than that of Victor. It is given that the monthly salary of John is $ 60. The monthly salary of Victor is. $ 75.. $ 60.. $ D. $5 5. [ ]

32 0. sum of $ is deposited at an interest rate of % per annum for 4 years, compounded quarterly. Find the amount correct to the nearest dollar.. $ $ 400. $ 50 D. $ Which of the following is/are rational number(s)? I. 7 II. III. 4. I only. I and II only. I and III only D. I, II and III 04.. dice is tossed 50 times. The results are recorded below: Number Frequency Find the experimental probability of getting the number D [ ]

33 05. bag contains 40 balls whose colours are red or white. ball is chosen at random. The probability that the ball is red is 0.. Find the number of red balls in the bag D. 06. Find the relationship of the magnitude between the mean, median and mode of 0, 0, 0, 70, 40, 55 and 0.. mode median mean. mode median mean. mean median mode D. median mode mean 07. Find the weighted mean of the following set of data. Datum 5 40 Weight D. [ ]

08. In the figure, the solid has a square as its base and four equilateral triangles as its faces. The angle between the line V and plane D is. V.. V.. VV. D. VV. 09.

34 08. In the figure, the solid has a square as its base and four equilateral triangles as its faces. The angle between the line V and plane D is. V.. V.. VV. D. VV. 09. In the figure, PQ is an axis of rotational symmetry of the given solid. What is the order of rotational symmetry for PQ? D. 0. If the slope of the line joining P( 5, y) and Q(, ) is, find y D. 7 [ 4 ]

35 . The coordinates of points, and are ( 7, 4), (, ) and (, k) respectively. If, find the value of k.... D.. Given that the height and the base radius of a right circular cone are cm and 0 cm respectively, find its curved surface area cm. 050 cm. 56 cm D. 6 cm. In the figure, PQRS is a square and PST is an equilateral triangle. Find RQT D. 5 [ 5 ]

36 4. If =, find D In the figure, O is the circumcentre of. Find POQ. (Hint: ircumcentre is the point of intersection of three perpendicular bisectors.) P 76 Q. 4 D. 5 O 6. In the figure, FE and E. Which of the following is correct? F D. F [ 6 ]

37 7. Points, and P lie on a straight line. Given that the coordinates of and are ( 8, 5) and (7, 0) respectively, and P : P = :, find the coordinates of P.. ( 0, 5). (, ). (, 4) D. (5, 0) 8. The ratio of the total surface areas of two similar circular cones is Find the ratio of their volumes D Stanley, whose eye level is.8 m above the ground, finds that the angle of elevation of the top of a flagpole is 5. If he is m from the flagpole, what is the height of the flagpole? (Give the answer correct to 0. m.). 8 m. 7.4 m. 6.6 m D. 5.7 m [ 7 ]

0. Points and are 5 cm apart, whereas points and are 0 cm apart. If, find the true bearing of from.. 05. 075. 05 D. 55.

38 0. Points and are 5 cm apart, whereas points and are 0 cm apart. If, find the true bearing of from D. 55. The figure shows a solid which consists of a right circular cone and a hemisphere. Find the volume of the solid.. 6 r. r. r D. r. In the figure, D is a parallelogram. E is a point lying on D such that E = E. If D 4, then E D. 57. END OF PPER [ 8 ]

39 Solutions to Form Mock (M) Mathematics Final Exam D D D D D D D D D D D D D D D D D D D D D D D D D D D [ 9 ]

40 D D D D D [ 40 ]

Tin Ka Ping Secondary School F.3 Mathematics Teaching Syllabus

Tin Ka Ping Secondary School F.3 Mathematics Teaching Syllabus Tin Ka Ping Secondary School 05-06 F. Mathematics Syllabus Chapter Linear Inequalities in One Unknown Time Guide. Basic Concept of Inequalities A. What are Inequalities? B. Solutions of Inequalities C.