IGCSE 數學 0580 Paper 2（Extended）模擬卷｜70 分・1 小時 30 分・可用計算機

練習卷 · IGCSE 數學 0580 Paper 2（Extended）

IGCSE 數學 0580 Paper 2（Extended）模擬卷：20 題共 70 分、1 小時 30 分、可用計算機，涵蓋數字與代數、圖形與空間、數據與概率三大範疇，每題附答案與完整計算步驟，題目版與答案版 PDF 可即時下載，方便家長即時對答案。全部題目原創，非歷屆試題。

卷面資料　年級：IGCSE（Extended）　｜　科目：數學　｜　時限：90 分鐘　｜　總分：70 分　｜　題數：20

甲部數字與代數（28 分）

全部題目必須作答，須展示計算步驟。

#	題目	答案與評分要點
1	Expand and simplify 5(2x − 3) − 2(x − 4).	10x − 15 − 2x + 8 = 8x − 7
2	Solve 3x + 7 = 4x − 5.	3x + 7 = 4x − 5 gives x = 12; check 3 × 12 + 7 = 43 = 4 × 12 − 5
3	In a sale a jacket is reduced by 15 per cent and now costs $680. Work out the original price.	680 ÷ 0.85 = $800
4	Expand and simplify (x + 6)(x − 4).	x² + 2x − 24
5	Factorise completely 6x² + 15x.	3x(2x + 5)
6	y is directly proportional to x². When x = 7, y = 98. Find y when x = 11.	k = 98 ÷ 49 = 2, so y = 2 × 121 = 242
7	Work out (4.2 × 10⁵) × (3.5 × 10⁻³), giving your answer in standard form.	14.7 × 10² = 1.47 × 10³
8	$4,500 is invested at 3.2 per cent per year compound interest. Find the value after 3 years, to the nearest cent.	4500 × 1.032³ = $4,945.97
9	Simplify (x² − 9) ÷ (x² + x − 12).	(x − 3)(x + 3) ÷ (x − 3)(x + 4) = (x + 3)/(x + 4) for x ≠ 3

如無特別說明，答案須附單位。

#	題目	答案與評分要點
10	A right-angled triangle has legs 9 cm and 12 cm. Work out the length of the hypotenuse and the area of the triangle.	hypotenuse = √(81 + 144) = 15 cm; area = ½ × 9 × 12 = 54 cm²
11	A sector of a circle of radius 7 cm has angle 120°. Using π = 3.142, work out the arc length.	120/360 × 2 × 3.142 × 7 = 14.66 cm
12	A cone has base radius 6 cm and height 10 cm. Using π = 3.142, work out its volume.	⅓ × 3.142 × 36 × 10 = 377.04 cm³
13	Two triangles are similar. The area of the smaller is 50 cm² and the ratio of corresponding lengths is 5 : 7. Find the area of the larger triangle.	50 × 49 ÷ 25 = 98 cm²
14	A ladder 6.5 m long leans against a vertical wall with its foot 2.5 m from the wall. Work out the height reached and the angle the ladder makes with the ground.	height = √(42.25 − 6.25) = 6.0 m; angle = cos⁻¹(2.5 ÷ 6.5) = 67.4°
15	Work out the interior angle of a regular 12-sided polygon.	(12 − 2) × 180 ÷ 12 = 150°

概率可用分數或小數作答。

#	題目	答案與評分要點
16	Five test scores are 12, 15, 9, 18 and 21. Work out the mean score.	total 75 ÷ 5 = 15
17	The ages of 10 club members are 3, 5, 7, 8, 8, 10, 12, 14, 15 and 18. Work out the median age.	median = (8 + 10) ÷ 2 = 9
18	A bag holds 5 red, 3 blue and 2 green counters. One counter is taken at random. (a) Work out the probability that it is not red. (b) Two counters are then taken without replacement; work out the probability that both are red.	(a) 5 of the 10 counters are not red, so 1/2. (b) 5/10 × 4/9 = 2/9 ≈ 0.222
19	A scatter graph of 20 students plots height against shoe size, with the points rising from left to right. Describe the correlation and say what it means.	Positive correlation: taller students tend to have larger shoe sizes
20	The probability that a component is faulty is 0.04. In a batch of 500 components, work out the expected number of faulty components.	500 × 0.04 = 20

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