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Pui Ying College Supplementary Exercise for Chapter 1 Simple Introduction to Deductive Geometry

Name : Class : F.2( ) No.:

Pui Ying College Supplementary Exercise for Chapter 2 Pythagoras’ Theorem Name : Class : F.2( ) No.: 1. Find the value of the unknown in the following figures. (Correct the answers to 2 decimal places.) 2. Prove that the triangle is right-angled.

3. Find the value of the unknown in the following figure.

4. Find the values of the unknowns in the following figure.

5. The figure shows a rectangular tool box of length 50 cm, width 30 cm and height 20 cm. What is the maximum length of the tool that the tool box can hold? (Correct the answer to the nearest 0.01 cm.)

6. In the figure, ABDE is a square of area 81 cm 2 . Find the area of the equilateral triangle BCD. (Correct the answer to 2 decimal places.) 7. In the figure, ABCD is a rectangle. E is a point on CD so that ∠AEB = 90 It is also given that AE = 8 and BE = 6. (a) Find AB.

(b) Find the area of AEB.

(c) Using the results in (a) and (b), find the length of the other side of the rectangle, i.e. AD.

8. A lamp-post is fixed by two cables AB and AC which are of the same length. B and C are 8 m apart, and A is 6 m above the ground. If the cost of the cable used is $50 per metre, how much does it cost to fix 8 lamp-posts? (Correct the answer to the nearest dollar.)

9. A boat is tied to a fixed post on the pier with a rope. The knot A on the post is 4x m above the sea level. The knot B on the boat is 3x m from the pier. The length of the rope between knots A and B is 25 m. (a) Find the value of x.

(b) If the sea level rises by 1.5 m and the distance between the pier and the boat remains unchanged, what should be the new length (in m) of the rope between knots A and B? (Correct the answer to 2 decimal places.)

10. In the figure, ABCD is a rectangle with AD = 12 m and AB = 6 m. If line segments AF and AE divide the rectangle into 3 parts of equal areas, find the lengths of

AF and AE. (Leave in your answer.)

Pui Ying College Supplementary Exercise for Chapter 3 Formulas Name : Class : F.2( ) No.:

Pui Ying College Supplementary Exercise for Chapter 4 Equation s and identities Name : Class : F.2( ) No.: Determine whether each of the following equations is an identity? 1. (x  4)(x  4)  (x  4)2  8(4  x) 2. x 2  25  (x  5)2

3. x  1 2x 1 4x  7   1 3 6 6

Find the constant A and B in each of the following identities. 4. (Ax  2) 2  9x 2 12x  B 5. x 2  2ax  b  (x  2)(x  3)

Expand each of the following expression 6. (a  2b) 2  (a  2b) 2 b 7. (a  ) 2 2

8. (xy  yz  xz) 2 9. (x  1)(x 1)(x 2  1)

10. (2  3w)(4  6w  9w2 ) Pui Ying College Supplementary Exercise for Chapter 5 More about Percentages Name : Class : F.2( ) No.: