独中线上学堂 | Duzhong Academy | 全马独中生的线上补习平台

1

Answer the following.

(a)

Write the negation of the following statement, then state its truth value. 12 is the highest common factor (HCF) of 28 and 42.

[2 分]

(b)

2

[2 分]

此为作答题,交卷后显示参考答案供自我核对。

2

Diagram 3 is a pie chart showing the number of mangosteens eaten by 4 students.

(图 3:饼状图,四个扇形标示 Ahmad 12、Siva 10、Mandeep 20、Kenny 18。)

Calculate

(a)

the mean number of mangosteens eaten by a student.

[2 分]

(b)

the angle of the sector that represents Kenny.

[2 分]

此为作答题,交卷后显示参考答案供自我核对。

3

In Diagram 4, $O$ is the centre of a circle with a radius of $3$ cm and $ROS$ is a straight line. Given that $\angle ORP = 25^{\circ}$ and $PS$ is the tangent to the circle.

(图 4:圆心 O,R 在圆上左侧,S 在圆外右侧,ROS 为直线;P 在圆下方,OP = 3 cm 为半径,PS 与圆相切于 P; $\angle ORP = 25^{\circ}$ , $\angle x^{\circ}$ 标在 O 处 $\angle POS$ 。)

Find

(a)

x^{\circ}

[1 分]

(b)

RS

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

4

Answer the following.

(a)

Jimmy has an Axia car for personal use in Sabah. His car has never made a claim from the insurance company. Given the car's information is as follows: | Item | Value | |---|---| | Age of car | 3 years | | Engine capacity | 1 500 cc | | NCD | 30% | | The amount to be insured | RM 45 000 | Calculate the gross premium for Jimmy's car under the third party, fire and theft policy if the basic premium for the comprehensive policy is RM 1 113.20.

[3 分]

(b)

Yusri's car hit another car in an accident and he was found at fault. As a result of the accident, both cars were badly damaged and the driver of the car that Yusri hit suffered a broken leg. Yusri wants to make a claim for damages to both cars as well as the cost of treating the driver's injuries. Based on the scenario above, state the claim that Yusri can make to his insurance company if he insures his car under a third-party policy.

[2 分]

此为作答题,交卷后显示参考答案供自我核对。

5

Diagram 7 shows a part of the graph of quadratic function $f(x) = -a(x-m)(x-n)$ with $m < n$ .

(图 7:开口向下的抛物线, $x$ 轴截距为 $-1$ 与 $4$ , $y$ 轴截距为 $4$ 。)

(a(i))

m

[1 分]

(a(ii))

n

[1 分]

(a(iii))

a

[1 分]

(b)

State the equation of axis of symmetry.

[1 分]

此为作答题,交卷后显示参考答案供自我核对。

6

Complete Table 1 for the value of $x = -1$ which satisfies the equation $y = x^{3} - 11x + 2$ . Hence, draw the graph of $y = x^{3} - 11x + 2$ for $-3 \leq x \leq 4$ .

$x$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$3.5$	$4$
$y$	$8$	$16$		$2$	$-8$	$-12$	$-4$	$6.4$	$22$

()

Complete Table 1 and draw the graph.

[4 分]

此为作答题,交卷后显示参考答案供自我核对。

7

Draw a directed graph to represent the roads which connect a few cities based on the given information. Hence, determine the number of degrees of the graph.

$E = \{(K, L), (L, M), (M, N), (M, O), (N, P), (P, Q)\}$

()

Draw the directed graph and state the number of degrees.

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

8

Diagram 9 shows an incomplete tree diagram representing watches produced by Rolax factory. Two watches are selected at random. Given that the probability that a watch is not working, $J$ is $\dfrac{3}{14}$ .

(图 9:概率树图,第一层 Watch 1 分 $J$ (上, $\frac{3}{14}$ )与 $J'$ (下);第二层 Watch 2 各分 $J$ ( $\frac{3}{14}$ )与 $J'$ ;结果栏 $(J,J)$ 、、、 $(J',J')$ 。)

(a)

Complete the tree diagram in Diagram 9 in the answer space.

[2 分]

(b(i))

Calculate the probability that at least one watch is not working.

[2 分]

(b(ii))

Calculate the probability that both watches are working.

[1 分]

此为作答题,交卷后显示参考答案供自我核对。

9

Diagram 10 shows a distance-time graph in km/min, of a car.

(图 10:距离-时间图, $O(0,0) \to A(30,160) \to B(60,160) \to C(120,180) \to D(240,0)$ ;OABC 表示从槟城家到 Ipoh,CD 表示返回。)

Given $OABC$ shows a movement of a car from a house at Penang to Ipoh, Perak. $CD$ is a movement of a car going back to the house.

(a)

State the period of time, in minutes, the car stops at Rest and Relaxation Area.

[1 分]

(b)

\text{km h}^{-1}

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

10

Diagram 11 shows six sphere marbles arranged in horizontal at one straight line.

(图 11:六个球形弹珠水平排成一直线,下方双向箭头表示总水平长度。)

Given that the volume of a marble is $179\frac{2}{3}$ cm $^{3}$ . Calculate the horizontal length, in cm, of six marbles. (Use $\pi = \dfrac{22}{7}$ )

()

Calculate the horizontal length of six marbles.

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

11

(a) Diagram 12 shows point $S$ on Cartesian plane.

(图 12:直角坐标平面,点 $S(4, 2)$ 。)

Transformation $\mathbf{T}$ is a translation $\begin{pmatrix} -4 \\ 2 \end{pmatrix}$ . Transformation $\mathbf{R}$ is a reflection in the line $y = 4$ . Transformation $\mathbf{P}$ is a clockwise rotation of $90^{\circ}$ about the centre $(6, 3)$ .

(b) Diagram 13 shows three pentagons $ABCDE$ , $APQRS$ and $GHIJK$ , drawn on Cartesian plane.

(图 13:坐标平面上三个五边形。 $ABCDE$ : $A(-2,2)$ 、 $B(-2,8)$ 、 $C(-4,14)$ 、 $D(-6,8)$ 、 $E(-8,8)$ 。 $APQRS$ (阴影): $A(-2,2)$ 、 $P(-2,5)$ 、 $Q(-4,8)$ 、 $R(-5,5)$ 、 $S(-6,5)$ 。 $GHIJK$ : $G(2,2)$ 、 $H(2,5)$ 、 $I(4,8)$ 、 $J(4,5)$ 、 $K(5,5)$ 。)

(a(i))

S

[1 分]

(a(ii))

S

[2 分]

(b(i)(a))

GHIJK

[3 分]

(b(i)(b))

\mathbf{S}

[2 分]

(b(ii))

ABCDE

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

12

Answer the following about Puan Hannah.

(a)

11

[2 分]

(b)

The annual value of Puan Hannah's house was RM 30 000 in 2024. The property assessment tax rate that year is 6%. Calculate the property assessment tax that Puan Hannah must pay.

[2 分]

(c(i))

x

[1 分]

(c(ii))

Calculate the total payment not subjected to service tax.

[1 分]

(c(iii))

Calculate the service tax imposed on the electricity bill for December.

[1 分]

此为作答题,交卷后显示参考答案供自我核对。

13

Diagram 14 shows an ogive of distribution of mass, in kg, for 80 students in class 5 Walid.

(图 14:累积频率曲线,横轴 Mass(kg) 刻度 49.5、59.5、69.5、79.5、89.5;描点约 (49.5, 8)、(59.5, 25)、(69.5, 52)、(79.5, 73)、(89.5, 80),起点 (39.5, 0)。)

(a(i))

P_{15}

[1 分]

(a(ii))

Based on the ogive, find the third quartile.

[1 分]

(b)

Based on Diagram 14, complete Table 3 in the answer space. | Mass (kg) | Upper boundary | Midpoint | Frequency | |---|---|---|---| | 30 - 39 | 39.5 | | | | 40 - 49 | 49.5 | | | | 50 - 59 | 59.5 | | | | 60 - 69 | 69.5 | | | | 70 - 79 | 79.5 | | | | 80 - 89 | 89.5 | | |

[2 分]

(c(i))

You must use 2B or BB pencil for this question. Using the scale of 2 cm to 10 kg on the horizontal axis and 2 cm to 5 pupils on the vertical axis, draw a histogram based on the information in Table 3.

[4 分]

(c(ii))

State the shape of the distribution for the histogram.

[1 分]

此为作答题,交卷后显示参考答案供自我核对。

14

On Cooperative Day, the STEM Club sells $x$ souvenirs $A$ and $y$ souvenirs $B$ . Profits of RM 4 and RM 5 respectively are obtained from the sale of each souvenir $A$ and $B$ . The number of souvenirs $A$ sold is at least equal to the number of souvenirs $B$ sold. The total number of souvenirs $A$ and $B$ sold is at most 15. The STEM Club wants to earn a minimum profit of RM 40.

No	Condition	Linear inequality
(i)	The number of souvenirs $A$ sold is at least equal to the number of souvenirs $B$ sold.	$x \geq y$
(ii)		$x + y \leq 15$
(iii)	The minimum profit is RM 40.

(a(i))

Write a condition that represents the linear inequality (ii).

[1 分]

(a(ii))

Write a linear inequality that represents condition (iii).

[1 分]

(b)

y = x

[2 分]

(c)

A

[1 分]

(d)

A

[2 分]

此为作答题,交卷后显示参考答案供自我核对。

15

(a) A study was conducted on 100 farms in a district to study the types of crops grown in the district. The finding of the study is shown in Diagram 16. Given that universal set, $\xi = \{G \cup N \cup S\}$ , set $G = \{\text{rubber plantation}\}$ , set $N = \{\text{pineapple plantation}\}$ and set $S = \{\text{oil palm plantation}\}$ .

(图 16:文氏图。 $S$ 与 $N$ 两大圆相交; $G$ 为完全包含在 $S$ 内的小圆。区域: $S$ 内 $G$ 外 = $2x$ ; $G$ 内(不与 $N$ 交)= $48$ ; $G \cap N$ = $3x$ ; $N \cap S$ 但在 $G$ 外 = $16$ ; $N$ 内其余 = $x + 12$ 。)

(a(i))

Given that plantation that are only grown with pineapples will be given vouchers to buy fertilizer for free on Farmers' Day. On the Venn diagram in the answer space, shade the area that represents the field.

[1 分]

(a(ii))

x

[1 分]

(a(iii))

x

[4 分]

(b(i))

X

[3 分]

(b(ii))

Z

[2 分]

此为作答题,交卷后显示参考答案供自我核对。

16

【Bahagian C:第 16 题与第 17 题择一作答 / Answer either Question 16 or Question 17】

Answer this question. (Bahagian C — jawab satu soalan sahaja / Section C — answer one question only.)

(a(i))

Encik Azrul is the Photography Club advisor teacher at SMK Murni Indah. Table 6 shows the information of the Photography Club members. | Form | Boys' student | Girls' student | |---|---|---| | Three | 10 | 10 | | Four | 12 | 8 | | Five | 5 | 15 | State the ratio of the number of boys to the number of girls.

[1 分]

(a(ii))

A student is randomly selected from boys' group to be the photographer for a school event. Find the probability that the selected student is a boy from Form 5.

[1 分]

(b(i))

m

[2 分]

(b(ii))

Hence, calculate the variance and standard deviation of the distribution.

[3 分]

(c)

x

[5 分]

(d)

Q

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

17

【Bahagian C:第 16 题与第 17 题择一作答 / Answer either Question 16 or Question 17】

Encik Aiman works as a manager at Syarikat Maju Bersama Sdn Bhd with a monthly income of RM 4 100. Encik Aiman saves 10% of his monthly income and RM 200 as savings for his emergency fund. Table 9 shows Encik Aiman's fixed and variable monthly expenses.

Item	Amount
Housing loan	RM 1 200
Car loan	RM 650
Utility bills	RM 400
Insurance	RM 300
Groceries	RM 700

(Bahagian C — jawab satu soalan sahaja / Section C — answer one question only.)

(a)

Encik Aiman has a goal to achieve a positive cash flow of RM 300 per month. Has he achieved his goal? Give your own justification. Suggest a suitable recommendation if Encik Aiman's goal is not achieved.

[2 分]

(b(i))

Table 10 shows the annual income statement for the year 2023 of Encik Aiman. He received a tax relief of RM 9 000 for individual expenses and RM 3 600 for his child. At the end of each year the company grants a bonus of RM 500. He also donated RM 200 to the Penang State Public Library Corporation. Income: Basic pay RM 49 200.00, Attendance allowance RM 1 200.00, Medical fee RM 3 000.00, Petrol RM 1 800.00 (Total income RM 55 200.00). Deduction: KWSP RM 672.00, Insurance RM 4 200.00, Zakat RM 360.00 (Total deduction RM 5 232.00). Nett income RM 49 968.00. By referring to the Table of Individual Income Tax Rates of Assessment 2023, calculate Encik Aiman's chargeable income for the assessment year 2023.

[2 分]

(b(ii))

Is Encik Aiman eligible to receive a rebate? Give justification.

[1 分]

(b(iii))

Calculate Encik Aiman's income tax for the assessment year 2023. (Tax rates: first RM 20 000 = RM 150; next RM 15 000 at 3%.)

[3 分]

(c)

Solving using matrix method is not allowed for this question. Encik Aiman has cultivated a farm to plant corn and sugarcane. The total number of corn and sugarcane plants grown on his farm is 2 080, while the ratio of the number of corn plants to sugarcane plants is 3 : 5. Calculate the number of corn plants and sugarcane plants.

[4 分]

(d)

Encik Aiman wants to buy a Perodua Axia for his daughter, Kamilia. Diagram 19 (Bank Berjaya): Financing offer up to 90%, Interest rate 4.25% per annum. The price of a Perodua Axia is RM 39 900. Calculate the monthly instalment payment if the selected loan repayment period is seven years.

[3 分]

此为作答题,交卷后显示参考答案供自我核对。

SPM Mathematics · 2025 · Pulau Pinang · Percubaan Kertas 2 (Pulau Pinang)