Tuen Mun Government Secondary School

Summer Supplementary Exercise (S2 to S3)

Instructions:

  1. Use single-lined paper to finish all the following questions.
  2. Show working steps clearly.
  3. Hand in your assignment on 2nd September, 2013.
  4. Please copy the following directory. In case you lose your assignment, you can access it through “School Website > Structure > Subjects > Mathematics website > Assignment”

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Chapter 1: Estimation and Approximation

  1. Estimate the values of the following expressions and state the strategies used.

(a)

(b)

(c)

(d)

  1. Steven Chicken Soup in packs of 298mL and 500mL are sold at $7.5 and $9.9 each respectively.

(a)Estimate whether the average price for 100mL of Steven Chicken Soup for each packaging is more than $2. Explain briefly.

(b)Based on the result of (a), which packaging of Steven Chicken Soup is more economical?

Chapter 2: Measurement and Errors

  1. Find the maximum absolute error of each of the following approximate values, and the upper limit and lower limit of its actual value.

(a)156mL(corr. to the nearest mL)

(b)0.001g(corr. to 1 sig. fig.)

(c)70.0km(corr. to 3 sig. fig.)

  1. Find the maximum absolute error, relative error (in the form of) and percentage error of each of the following approximate values. (Give your answers correct to 3 significant figures if necessary.)

(a)156mL(corr. to the nearest mL)

(b)$20(corr. to the nearest $10)

(c)0.001g(corr. to 1 sig. fig.)

(d)70.0km(corr. to 3 sig. fig.)

Chapter 3: Identities and Factorization

  1. Determine, with a proof, whether each of the following is an identity.

(a) / / (b) /
  1. If, find the constants A, B and C.
  1. Expand the following.

(a) / / (b) / / (c) /
(d) / / (e) / / (e) /
  1. (a)Expand.

(b)By using the result of (a), expand.

  1. Factorize the following.

(a) / / (b) / / (c) /
(d) / / (e) / / (f) /

Chapter 4: Simultaneous Equations

  1. Use the method of substitution to solve the following simultaneous equations.

(a) / / (b) /
  1. Use the method of elimination to solve the following simultaneous equations.

(a) / / (b) /
  1. A farm keeps some ducks and cows. Given that they have 42 heads and 120 feet altogether, find the respective number of ducks and cows in the farm.
  1. A restaurant provides daily lunch set and special lunch set. It is given that the total price of 2 daily lunch sets and 3 special lunch sets is $120, and the total price of 5 daily lunch sets and 2 special lunch sets is $157. What is the price of each kind of lunch sets?
  1. 40 employees of a company are evenly divided into 4 groups where the number of male employees in each group is 2 more than the number of female employees. How many male and female employees are there among the 40 employees?

Chapter 5: Congruent and Similar Triangles

  1. In the figure, AD//BC,. Prove that.
  1. In the figure,and.

(a)Prove that.

(b)Prove that.

(c)Prove that.

  1. In the figure, ABCD, BGE and CGF are straight lines. ABCD, AFBE, FCAD and EDAD.

(a)Prove that.

(b)Prove that AF//BE.

  1. In the figure, ABD and ACE are straight lines. BC//DE.

(a)Prove that.

(b)Find x.

(c)Find y.

  1. In the figure,. D is a point on AC such that.

(a)Prove that.

(b)Find AD.

Chapter 6: Square Roots and Pythagoras' Theorem

  1. In the figure, BDC is a straight line. Find the value of c.
    (Give your answer correct to 3 significant figures.)
  1. In the figure, D is a point on BC and.

(a)Prove that ABC is a right-angled triangle.

(b)Find the value of h.
(Give your answer correct to 3 significant figures.)

  1. In the figure, the lighthouse is 20m high. The topAof the lighthouse is connected to points C and D on the ground by two wires, where CBD is a straight line. If ACAD30m, find the distance betweenC and D. (Give your answer correct to 3 significant figures.)
  1. The length and width of a field are 130m and 74m respectively.

The following are two routes to walk from point A to point C.

Route 1:Walking along the sides of the field (i.e. ABC).

Route 2:Walking diagonally across the field (i.e. AC).

What is the difference in length between the above two routes? (Give your answer correct to 3 significant figures.)

  1. Simplify the following.

(a) / / (b) /
  1. Rationalize the denominators of the following.

(a) / / (b) /
  1. Simplify the following.

(a) / / (b) /

Chapter 7: More about Statistical Graphs

  1. The following frequency polygons show the scores of S2A and S2B students in a Mathematics examination.

(a)Which class has students with scores below 20.5?

(b)If students with scores 80.5 or above willbe awarded, how many students will be awarded in each class?

(c)Which class has a better performance?

(d)Which class needs to put more effort into mathematics?

2. The following cumulative frequency curve shows the time taken by a group of students to do 30 sit-ups.

(a)How many students are there in the group?

(b)How many students have done 30 sit-ups in less than 32s?

(c)For students who have taken 40s or more to finish 30 sit-ups, they need to do another 30 sit-ups. How many students need to do the additional 30 sit-ups?

Chapter 8: Inequalities

  1. Solve each of the following inequalities and represent the solutions graphically.

(a) / / (b) /
  1. Find the smallest value and smallest integral value of x of each of the following inequalities.

(a)(b)(c)

  1. A store bought 250 eggs for $200 and found that 25 of them were cracked. The rest of the eggs will be sold at a percentage profit of not greater than 35%. Find the maximum selling price of each egg.
  1. The ingredients of the nuts of Brand X, Brand Y and Brand Z in percentage are as follows:

Brand
Ingredients / X / Y / Z
Walnut / 30% / 25% / 55%
Almond / 30% / 50% / 30%
Hazelnut / 40% / 25% / 15%

How many kg of nuts from Brand Z should be added to 0.5kg of nuts from Brand X and 1kg of nuts from Brand Y, such that there are not less than 20% of hazelnuts in the mixture?

Chapter 9: Algebraic Fractions and Formulae

  1. Simplify the following expressions.

(a) / / (b) /
(c) / / (d) /
  1. (a)Factorize.

(b)From the result of (a), simplify.

  1. Simplify the following expressions.

(a) / / (b) /
(c) / / (d) /
  1. Given that, find the value of a if,and.
  1. Make the letters in brackets the subjects of the corresponding formulae.

(a) / [q] / (b) / [x]
  1. Miss Cheung deposits a sum of money $P in a bank. The amount $A received after T years is given by the following formula:

(a)If Miss Cheung deposits $5000 in a bank, find the amount received after 4 years.

(b)Make T the subject of the formula.

(c)If Miss Cheung deposits $12000 in the bank, how long does it take for her to receive an amount of $14400?

Chapter 10: Areas and Volumes

  1. Given that AD and CE meet at F, find the area of the shaded region.
  1. Terry jogged around a circular park. Suppose he had completed 4 laps with a total distance of 1250m, find the radius of the park.
  1. In the figure, the ratio of the radii of two circles is 7:9.

(a)Find the ratio of the area of the smaller circle to that of the larger circle.

(b)If the area of the shaded region is, find the area of the smaller circle.

  1. Figure I and Figure II show two containers in the shapes of a cylinder and a square prism respectively. Both the containers are with lids, their heights are both 10cm, and their volumes are both 500cm3. If the material cost of making the containers is $1/cm2, which container has a lower material cost? Explain briefly.

Chapter 11: Introduction to Trigonometric Ratios

[In this exercise, correct your answers to 3 significant figures, if necessary.]

1.In the figure, CDB is a straight line.

(a)Find AD.

(b)Find .

  1. In the figure, ABD and DBC are right-angled triangles.

(a)Find BD.

(b)Find BC.

  1. In the figure, ABC is a sector. Its radius is 10cm and the angle at the centre is 70. D is a point on AC such that BDAC.

(a)Find the area of ABD.

(b)Find the area of the shaded region.

  1. Figure I shows a piece of rectangular paper with thedimensions of. The paper is folded in a way that the vertices of its two opposite angles coincide (see Figure II). Find the value of x.

(a)(i)Express BE in terms of x.

(ii)Hence find the value of x.

(b)Karl thinks that . Do you agree? Explain briefly.

  1. In the figure, ABCD is the rectangular container of the dump truck, where and . The container can rotate about point D, where  is the angle of the container made with the horizontal. D is 1.6m from the ground.

(a)Find BD. (Leave your answer in surd form.)

(b)Find BDC.

(c)The dump truck is going to deliver some sand to a construction site with the maximum height limit of 6m. When the truck unloads the sand,  must be adjusted to 40. Can the dump truck unload the sand in the construction site? Explain briefly.

Chapter 12: Polygons

  1. In the figure, BC//ED.

(a)Find x.

(b)Find y.

  1. If each of the following is the size of an exterior angle of a regular polygon, find the number of sides of the regular polygon.

(a)120(b)36(c)14.4

  1. In the figure, AB, BC and CD are three sides of a regular polygon where BAC18.

(a)Find the size of an exterior angle of this regular polygon.

(b)Find the number of sides of this regular polygon.

Chapter 13: Measures of Central Tendency

  1. The mean time for an athlete to complete 5times of 400mwas 54.16s. If the athlete took 55.2sto complete the 6th time of 400m, what would be the mean time for the athlete to complete6times of 400m? (Give your answer correct to 2 decimal places.)
  1. It is known that the sales volume (in glasses) of soya milk in the past six days were 121, 103, 106, 110, 106 and 113.

(a)Find the median sales volume of soya milk in the past six days.

(b)If 135 glasses of soya milk were sold today, find the median sales volume of soya milk in these seven days.

  1. The following frequency distribution table shows the ages of 200 students in a Japanese language school where x and y are positive integers.

Age / 16-20 / 21-25 / 26-30 / 31-35 / 36-40 / 41-45
Frequency / 30 / 42 / 40x / 34 / y / 19

(a)Can the modal class be 36-40? Explain briefly.

(b)If the modal class is 26-30, write down a set of possible values of x and y.

1