Preparation for HKDSE (S1 – S3) Full Solutions

**Preparation for HKDSE (S1 – S3) Full Solutions**

HKDSE Mastering Mathematics 6 © Pearson Education Asia Limited 2013

Preparation for HKDSE (S1 – S3) Full Solutions

**STRUCTURAL QUESTIONS**

**Suggested Solutions Marks Remarks**

1.

1M

1M

1A

2.

1M

1M

1A

3. (a)

1A

(b)

1M

1A

4. (a) The selling price of a bag of Potato cat food

1M + 1M

1A

(b) The new selling price of a bag of Potato cat food

∴ The show owner will not make a profit. 1A f.t.

5. Let x g and y g be the weights of a pen and a ruler respectively.

So, we have and . 1A + 1A

Therefore, 1M

i.e. x = 12

∴ The required weight

1A

6. AC = 2(2) cm = 4 cm

In △ABC,

(Pyth. theorem) 1M

(∵ AB = BC)

cm 1A

∴ The required area

1M

1A

7. (a)

1M

∴ OA is perpendicular to OB. 1A f.t.

(b) ∵ AOC is a straight line.

∴ Polar angle of C

1A

∵ Area of △ABC = 18 square units

∴ 1M

1A

∴ The polar coordinates of C are (6,).

8. (a) Coordinates of Y 1A

Coordinates of Z 1A

(b) XY

XZ

∵ 1M

∴ △XYZ is not an equilateral triangle. 1A f.t.

9. (a) (∠s at a pt.) 1M

1A

(b) Total number of students in the school before the new students join

1A

Let q be the angle of the sector representing cat.

1M

∴ The angle of the sector representing cat is not an integer. 1A f.t.

10. (a) The volume of the cone

1M

1A

(b) (i) Let h cm be the height of the frustum under the plane surface of

the hemisphere, and V cm3 be the volume of the cone which has

been cut away.

Refer to the figure below, we have

1M

= 24

∵ The original cone and the removed cone are similar.

∴ 1M

Alternative solution:

Let r cm be the base radius of the cone which has been cut away.

By the property of similar triangles, we have

1M

∴

∴ The required volume iscm3. 1A

(ii) The number of cubes that can be made

1M

∴ Kenny’s claim is agreed. 1A f.t.

11. (a) (i) ∵ The mode of the weights of the group is 58 kg.

∴ 1A

∵ The median of the weights of the group is 58 kg.

∴

1A

(ii) The mean weight

kg

1A

(b) (i) P(the weight of the selected student is the same as the mode)

1M

1A

(ii) P(the weight of the selected student is greater than the mean weight)

1M

1A

12. (a) In △ABD and △EBC,

AB = EB 1M

BD = BC

(prop. of equil.△) 1M

∴ △ABD△EBC (SAS) 1

(b) (i) ∵ (prop. of equil.△) 1A

∴ (corr.∠s, ~△s) 1A

∴ (corr.∠s,△s) 1A

(ii) ∵

∴

∴ (corr.∠s,△s) 1A

In △EBC,

(∠sum of △)

∵

∴ BE = CE (sides opp. equal∠s)

∴ △BCE is an isosceles triangle. 1A f.t.

**MULTIPLE CHOICE QUESTIONS**

13. CD

14. CC

In △ADE,

∵ AD = AE

∴ (base∠s, isos.△)

(∠sum of △)

(int.∠s, AD // BC)

15. CD

For I:

The interior angle of a regular 8-sided polygon

(∠sum of polygon)

∴ I is true.

For II:

∵ A regular 8-sided polygon repeats itself 8 times in one complete revolution.

∴ The order of rotational symmetry is 8.

∴ II is true.

For III:

Refer to the figure below.

∴ III is true.

∴ The answer is D.

16. CA

HKDSE Mastering Mathematics 6 © Pearson Education Asia Limited 2013