Which of the following shows 15 of the figure shaded?
A
B
C
D
看答案和讲解
正确答案：A.
考点分数：图形中表示几分之一（等份） · Fractions: shaded part of a figure in equal parts
思路：要表示 1/5，图形必须分成相等的份数，涂其中的 1/5。(1) 有 25 个相同的小格，涂了 5 格，5/25 = 1/5。(2) 的五条不一样宽，不是等份；(3) 是 5/6；(4) 是 4/5。 Think: The parts must be equal. (1) has 25 equal squares with 5 shaded: 5/25 = 1/5. (2) has unequal strips, (3) shows 5/6, (4) shows 4/5. 小提醒：先检查是不是“等份”。 Tip: Always check that the parts are equal first.
第 2 题分数公教中学(附小) 2025 Prelim Paper 1 第 5 题
In the number line, what is the mixed number represented by A?
A123
B134
C156
D167
看答案和讲解
正确答案：C. 156
考点分数：数线上的带分数 · Fractions: mixed numbers on a number line
思路：1 到 2 之间被分成 6 个相等的小段，每段是 1/6。A 在第 5 个刻度上，所以 A = 1 5/6。 Think: From 1 to 2 there are 6 equal parts, so each part is 1/6. A is at the 5th mark, so A = 1 5/6. 小提醒：数“段”，不要数“刻度线”。 Tip: Count the spaces, not the lines.
第 3 题数据分析公教中学(附小) 2025 Prelim Paper 1 第 10 题
The pie chart shows the number of pupils taking part in various activities at a sports carnival. The same information is shown in a bar graph, but the names of the activities are not shown on the bar graph.
How many pupils took part in Soccer and Hockey altogether?
A120
B130
C150
D170
看答案和讲解
正确答案：C. 150
考点数据分析：饼图与条形图对照 · Data analysis: matching a pie chart with a bar graph
思路：饼图中 Soccer 最大，对应最高的条 100 人；Golf 最小，对应 30 人；Hockey 比 Badminton 小，所以 Hockey 是 50 人，Badminton 是 70 人。Soccer + Hockey = 100 + 50 = 150。 Think: Soccer is the biggest part, so it is the tallest bar (100). Golf is the smallest (30). Hockey is smaller than Badminton, so Hockey = 50 and Badminton = 70. 100 + 50 = 150. 小提醒：按大小顺序把饼图的部分和条形对上。 Tip: Match the parts by size, from biggest to smallest.
第 4 题代数卍慈学校 2025 Prelim Paper 2 第 4(a) 题
The figure below shows a triangle with its three sides given.
Is the statement below true, false or not possible to tell from the information given?
a) The length of Side C is longer than the length of Side B.
思路：C − B = (4x + 2) − (5x − 2) = 4 − x。x 小于 4 时 C 比较长，x = 4 时一样长，x 大于 4 时 B 比较长。题目没给 x 的值，所以无法判断。 Think: C − B = (4x + 2) − (5x − 2) = 4 − x. If x < 4, C is longer; if x = 4 they are equal; if x > 4, B is longer. We do not know x, so it is not possible to tell. 小提醒：可以试两个数，例如 x = 2 和 x = 4，结果不同就"无法判断"。 Tip: Try two values such as x = 2 and x = 4; different results mean "not possible to tell".
第 5 题角与几何图形卍慈学校 2025 Prelim 第 10 题
The figure below shows a rhombus ABCD and ECD is a straight line.
Which of the following is false?
A∠BAC = ∠DAC
B∠ABC = ∠BCE
C∠ADC + ∠BCE = 180°
D∠DCA + ∠BAC + ∠BCE = 180°
看答案和讲解
正确答案：C. ∠ADC + ∠BCE = 180°
考点几何：菱形的性质与平行线 · Geometry: properties of a rhombus
思路：菱形对角线平分顶角，(1) 对；AB ∥ DE，∠ABC = ∠BCE（内错角），(2) 对；∠ADC = ∠ABC = ∠BCE，两个相加不一定是 180°，(3) 错；∠DCA = ∠BCA = ∠BAC，三个角拼在直线 DE 上，和是 180°，(4) 对。 Think: A diagonal of a rhombus bisects the angles, so (1) is true. AB ∥ DE, so ∠ABC = ∠BCE (alternate angles): (2) true. ∠ADC = ∠ABC = ∠BCE, so their sum is not always 180°: (3) false. ∠DCA = ∠BCA = ∠BAC, and the three angles lie on line DE, so they add to 180°: (4) true. 小提醒：找"错误"的一项，四个都要检查。 Tip: The question asks for the FALSE one — check all four.
第 6 题面积与周长卍慈学校 2025 Prelim 第 11 题
Study the shapes shown in the grid.
Which two shapes have the same area?
AA and B
BB and C
CB and D
DC and D
看答案和讲解
正确答案：B. B and C
考点面积：方格中数格子求面积 · Area: counting squares and half squares
思路：每个半格算 0.5。A = 5 + 0.5 = 5.5；B = 4 + 4 × 0.5 = 6；C = 6；D = 9 − 4 × 0.5 = 7。B 和 C 面积相同。 Think: Count each half square as 0.5. A = 5 + 0.5 = 5.5, B = 4 + 4 × 0.5 = 6, C = 6, D = 9 − 4 × 0.5 = 7. B and C have the same area. 小提醒：两个三角形半格拼起来是 1 整格。 Tip: Two half squares make one whole square.
第 7 题八方位与转向卍慈学校 2025 Prelim 第 12 题
The square grid shows the position of A, B, C, D, E and F.
Cathy stood at one of the points facing point F. After she turned 45° anti-clockwise, she faced point C. Which point was Cathy at?
AA
BB
CD
DE
看答案和讲解
正确答案：A. A
考点转向：转 45° 与方向 · Turns: 45° anticlockwise turns on a grid
思路：站在 A 时看 F 是向左下方（西南）；逆时针转 45° 后变成正下方（南），A 正下方就是 C。其他点都对不上。 Think: From A, F is towards the bottom-left (south-west). Turning 45° anticlockwise makes Cathy face straight down (south), and C is straight below A. No other point works. 小提醒：逆时针 = 和钟表指针相反的方向。 Tip: Anticlockwise means the opposite way to the hands of a clock.
第 8 题小数乐赛学校 2025 Prelim 第 12 题
In the number line, what is the value represented by A?
A1.225
B1.250
C1.725
D1.750
看答案和讲解
正确答案：C. 1.725
考点数线：每格代表的数值 · Number line: value of each interval
思路：从 1.1 到 2.1 相差 1，被分成 8 格，每格 = 1 ÷ 8 = 0.125。A 在第 5 格：1.1 + 5 × 0.125 = 1.725，选 (3)。 Think: 1.1 to 2.1 is 1, split into 8 equal parts, so each part is 0.125. A is 5 parts after 1.1: 1.1 + 0.625 = 1.725. 小提醒：数清楚是“格数”，不是刻度线的条数。 Tip: Count the gaps, not the marks.
第 9 题面积与周长乐赛学校 2025 Prelim 第 15 题
The figure below is formed using 2 identical squares, 2 identical large equilateral triangles and 2 identical small equilateral triangles. The length of the square is 4 cm.
What is the perimeter of the figure?
A20 cm
B24 cm
C40 cm
D60 cm
看答案和讲解
正确答案：C. 40 cm
考点周长：由正方形和等边三角形组成的图形 · Perimeter: figure made of squares and equilateral triangles
思路：上下两条边各 4 cm。每边的小三角形和大三角形贴在正方形边上的两条边合起来 = 两个正方形的高 = 8 cm；等边三角形外露的两条边也加起来等于 2 × 8 = 16 cm（每边）。周长 = 4 + 4 + 16 + 16 = 40 cm，选 (3)。 Think: Top and bottom are 4 cm each. On each side, the small and large triangle sides along the squares add up to 8 cm, so their outer sides add up to 16 cm. Perimeter = 4 + 4 + 16 + 16 = 40 cm. 小提醒：等边三角形三条边一样长，不必知道每个三角形的边长。 Tip: All sides of an equilateral triangle are equal, so you do not need each triangle's side.
第 10 题三角形面积乐赛学校 2025 Prelim 第 6 题
The figure below is not drawn to scale. Find the area of triangle ACD.
A48 cm²
B84 cm²
C132 cm²
D144 cm²
看答案和讲解
正确答案：B. 84 cm²
考点三角形面积：底和高（高在三角形外） · Area of triangle: base and height outside the triangle
思路：三角形 ACD 的底 CD = 22 − 8 = 14 cm，高是 AB = 12 cm（从 A 垂直到底边所在直线）。面积 = ½ × 14 × 12 = 84 cm²，选 (2)。 Think: Base CD = 22 − 8 = 14 cm. The height is AB = 12 cm. Area = ½ × 14 × 12 = 84 cm². 小提醒：24 cm 是斜边，不是高，用不上。 Tip: 24 cm is a slanting side, not the height. You do not need it.
