Analysis on the HKCEE/HKDSE questionsephhk.popularworldhk.com/.../pl_sec_maths_mc/c525.pdf · 2014-09-12 · Paper II of the HKDSE mathematics examination consists of two sections:
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Analysis on the HKCEE/HKDSE questions2003 2004 2005 2006 2007
Note: 1. The numbers listed above refer to the question numbers in the HKCEE/HKDSE mathematics Paper II that year. 2. ‘Permutation and Combination’ is a new topic in the HKDSE syllabus.
Paper II of the HKDSE mathematics examination consists of two sections: Sections A and B. There are 30 questions in Section A and 15 questions in Section B. As the time allowed is 75 minutes, students are required to answer one question in about 1.5 minutes on average. In order to spend time in the most effective way, it is essential for candidates to learn some useful strategies in answering multiple-choice questions.
Strategy 1 Direct computationIn questions such as finding interest, area of plane figures or solving equations with quadratic formulas, candidates can apply the related formulas and calculate the answers directly. However, as not all the formulas are provided in the examination paper, candidates should be familiar with some useful formulas.
Example 1A sum of $30 000 is deposited for 1 year at 6% p.a., compounded monthly. Find the interest correct to the nearest dollar.A. $1750B. $1800C. $1850D. $1900
Solution:
Interest = $30 000 × 112
+
6%
12– $30 000
= $1850 (cor. to the nearest dollar)The answer is C.
Compound interest I = P(1 + r%)n – P
Example 2In the figure, the solid consists of a hemisphere and a cylinder. If the base radius and the height of the cylinder are 6 cm and 5 cm respectively, find the volume of the solid.A. 204πB. 324πC. 396πD. 468π
= Cost × (1 – Loss percentage)For example, if Peter bought a computer for $4000 and then sold it ata loss of 20%, then selling price = $4000(1 – 20%) = $3200
5. Let f(x) = 2x3 – 3x2 – x + 1. When f(x) is divided by x + 1, the remainder isA. –6.B. –3.C. 4.D. 7.
6. Solve (x + 2a)2 = 9a2, where a is a constant.A. x = aB. x = –3a or x = 3aC. x = –5a or x = aD. x = –5a or x = 3a
7. Find the range of values of k such that the quadratic equation 2x2 + x + 2k = k – x has real roots.
A. k ≤1
4
B. k ≤1
2
C. k ≥1
4
D. k ≥1
2
8. In the figure, the graph of y = x2 + kx – 3 passes through the vertex (a, –4). Find the equation of the axis of symmetry of the graph.A. x = –2B. x = –1C. x = 1D. x = 2
x
y
0 3
(a, –4)
Section A
1. (16 ⋅ 8n – 1)2 =A. 26n – 1
B. 26n + 2
C. 26n + 3
D. 27n + 1
2. If 23
4xy
− = , then y =
A. 2x – 3.B. 2 – 3x.C. 3(x + 4).D. 6(x – 2).
3. If x + 3y + 2 = y – x = –3, then y =A. 2.B. 1.C. 0.D. –2.
There are 30 questions in Section A and 15 questions in Section B.The diagrams in this paper are not necessarily drawn to scale.Choose the best answer for each question.
y = x2 + kx – 3
1
Solution Guide
3. A
Percentage increase = (110 0) cm
00 cm
3
3
− 10
1× 100%
= 10%
4. B
Percentage change = (40 50) kg
50 kg
−× 100%
= –20%
5. A
6. BLet $x be the sales amount last month. x(1 + 10%) = 60 500 1.1x = 60 500 x = 55 000The sales amount last month was $55 000.
7. ALet l and w be the original length and width of the rectangle respectively. Original area = lwNew area = (1 + 10%)l × (1 – 15%)w = 0.935lw
GuidelinesWhen performing long division of polynomials, add ‘0’s to the missing terms of the dividend can avoid mistakes.
GuidelinesThe difference of squares and the sum and difference of cubes are very common in public examination. Candidates should familiarize with these identities.