HKDSE Core Math 2015 Paper 1 (Solutions)
For official marking scheme please refer to HKEA publications. 1. HKDSE 2015 Q.1. 9. ( 3 ?7)5. =.
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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) െ͵ݔ4ǡ- "" " ݔͳ͵
(b) 46. HKDSE 2015 Q.6
HKDSE Core Math 2015 Paper 1 (Solutions)
27. HKDSE 2015 Q.7
Let ݔ be the number of apples owned by Billy.
8. HKDSE 2015 Q.8
ס Aൌס ס AൌסThus, ס
In ȟ, סס
Thus, ס
ס AסAൌס9. HKDSE 2015 Q.9
(a) Let ߠ Therefore, the angle of the sector is ͷι.10. HKDSE 2015 Q.10
(a) Let 3ൌܾܽ݊, where ܽ and ܾSolving, we have ܽൌ-- and ܾ
HKDSE Core Math 2015 Paper 1 (Solutions)
311. 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)
413. HKDSE 2015 Q.13
(a) In ȟA and ȟ, ס AൌסAൌ (given)
Aൌ (property of square)
ȟA؆ (b) By (a), we have סAൌס ס Aൌͳͺ-ιെסAെסAൌͻ-ιെסThus, ȟ
is a right-angled triangle.14. HKDSE 2015 Q.14
(a) (i) 3" 01ൌ-͵ͳEquation 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)
515. HKDSE 2015 Q.15
Relative to other students, David performs better in the Science examination than in theMathematics examination.
Thus, the claim is correct.
16. HKDSE 2015 Q.16
(b) 4 "" """"-ൌͳെସଽଵହൈଷଽ
17. HKDSE 2015 Q.17
Thus, the greatest value of ݊ is 64.
HKDSE Core Math 2015 Paper 1 (Solutions)
618. 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)
719. 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 סWhen סAൌͻ-ι, we have ס
When ס
When ס
(b) Let M be the mid-point of CD. ൌA...סAൌAס
Volume of the pyramid ABCD
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