HKDSE Core Math 2015 Paper 1 - WordPresscom PDF 05-dse-math-2015-paper-1-solution-only.pdf

015 Q 12 (a) Mean = 55 kg, median = 52 kg, range = 39 kg (b) Let kg and kg be the

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HKDSE Core Math 2015 Paper 1 (Solutions)

1 For official marking scheme, please refer to HKEA publications.

1. HKDSE 2015 Q.1

2. HKDSE 2015 Q.2

3. HKDSE 2015 Q.3

4 "" """"-ൌ͵൅-൅ͳ

4. HKDSE 2015 Q.4

5. HKDSE 2015 Q.5

(a) ͹െ͵ݔ

4ǡ- "" " ݔ൐ͳ͵

(b) 4

6. HKDSE 2015 Q.6

HKDSE Core Math 2015 Paper 1 (Solutions)

7. HKDSE 2015 Q.7

Let ݔ be the number of apples owned by Billy.

8. HKDSE 2015 Q.8

ס Aൌס ס Aൌס

Thus, ס

In ȟ, ס൅ס

Thus, ס

ס A൅סAൌס

9. HKDSE 2015 Q.9

(a) Let ߠ Therefore, the angle of the sector is ͹ͷι.

10. HKDSE 2015 Q.10

(a) Let 3ൌܽ൅ܾ݊, where ܽ and ܾ

Solving, we have ܽൌ͸͸-- and ܾ

HKDSE Core Math 2015 Paper 1 (Solutions)

11. HKDSE 2015 Q.11

B- -- െͳെξͷ

Thus, the claim is disagreed.

12. HKDSE 2015 Q.12

(a) Mean ൌͷͷ , median ൌͷ- , range ൌ͵ͻ (b) Let ܽ and ܾ be the weights of the two students, where ܽ൑ܾ

Case 1 : ܽ

Then ܾ

Under this case, ܾ

Then ܽ

Thus, the weights of the two students are 52 kg and 80 kg.

HKDSE Core Math 2015 Paper 1 (Solutions)

13. HKDSE 2015 Q.13

(a) In ȟA and ȟ, ס Aൌס

Aൌ (given)

Aൌ (property of square)

׵ ȟA؆ (b) By (a), we have סAൌס ס Aൌͳͺ-ιെסAെסAൌͻ-ιെס

Thus, ȟ

is a right-angled triangle.

14. HKDSE 2015 Q.14

(a) (i) 3" 01ൌ-͵൅ͳ

Equation of L : ݕെͳͳൌ͵

(ii) Equation of the circle passing through P, Q and R :

Thus, the required diameter is 50.

HKDSE Core Math 2015 Paper 1 (Solutions)

15. HKDSE 2015 Q.15

Relative to other students, David performs better in the Science examination than in the

Mathematics examination.

Thus, the claim is correct.

16. HKDSE 2015 Q.16

(b) 4 "" """"-ൌͳെସଽ൅ଵହൈଷଽ

17. HKDSE 2015 Q.17

Thus, the greatest value of ݊ is 64.

HKDSE Core Math 2015 Paper 1 (Solutions)

18. HKDSE 2015 Q.18

In this case, ST is a vertical line.

So, the perpendicular bisector of ST is a horizontal line. Therefore, the circumcentre of ȟC34 does not lie on the ݔ-axis.

Thus, the claim is incorrect.

HKDSE Core Math 2015 Paper 1 (Solutions)

19. HKDSE 2015 Q.19

The distance between A and C is 42.9 cm.

(ii) ס A" - """ ..."ൌͳ i.e. the area of the paper card varies as ס The area of the paper card is the greatest when ס

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