SPM Mathematics · 2025 · Pulau Pinang · Percubaan Kertas 1 (Pulau Pinang)

All of the following relations are functions except

Simplify $\dfrac{16 - 9h^2}{m} \div \dfrac{4 - 3h}{m^3}$

Round off the answer of the difference between $0.0368$ and $12.1 \times 10^{-3}$ correct to two significant figures.

Diagram 1 shows a solid lies on a horizontal plane. The line $VW$ lies 7 cm vertically above the base $ABCD$. 图1:一个三角柱屋顶置于长方体上,底 $ABCD$ 中 $AD=4$ cm、侧棱高 5 cm,屋脊 $VW$ 在底面上方 7 cm。图N。Which of the following is the orthogonal projection of the solid on the vertical plane parallel to $BC$ as viewed from $X$?

Simplify $\dfrac{9p^2 q^6 \times 3p^2}{27 q^2}$

Diagram 2 shows straight lines $TR$ and $RS$ on a Cartesian plane, with $R(0, 8)$, $S(6, 0)$, and $T$ lying on the horizontal line through $R$. Given $TR = \dfrac{1}{2}RS$, find the coordinates of point $T$.

Express $\dfrac{2}{m - 3n} - \dfrac{m + 3n}{m^2 - 9n^2}$ as a single fraction in its simplest form.

Diagram 3 shows hexagon $PRSTUV$ is the image of hexagon $PQABCW$ under an enlargement with vertex $P$ as the centre of enlargement. It is given that $Q$ is the midpoint of side $PR$ and the area of $PQABCW$ is 17 cm². Calculate the area, in cm², of the shaded region.

Rodi earns overtime when he works at least 9 hours a day. If $t$ is the number of hours worked per day, describe an inequality based on the given situation.

Table 1 shows values of $L$, $M$ and $N$.

It is given that $L$ varies directly as $M$ and varies inversely as $N$. Find the value of $w$.

Diagram 4 shows a ladder $AB$ leaning against the wall of a building. The length of the ladder is 4.0 m and the distance of its base from the wall is 1.2 m. When the top of the ladder slides down by $x$ m, the base of the ladder moves outward to 2.0 m. Find the value of $x$.

Given $S = \dfrac{n}{2}(a + t)$, express $t$ in terms of $a$, $n$ and $S$.

Diagram 5 shows a speed-time graph of the movement of two vehicles. Graph $OPQR$ shows the movement of a car and graph $AB$ shows the movement of a van. If the difference in distance of the car and the van for the last $\dfrac{1}{4}$ hour is 12.5 km, calculate the value of $v$.

Diagram 6 shows a set of dot plot for 20 students in a school that participate in a History quiz. Calculate the median.

Kamal has 3 red balls, 5 blue balls and 8 yellow balls. If he chooses one ball at random, what is the probability that he does not choose a blue or yellow ball?

Suraya is a teacher with monthly income RM 3 500. She also does a part time job as a tuition teacher with monthly payment of RM 600. If the total fixed expenses are RM 1 250 and she found that her cash flow worth RM 100, calculate the variable expenses.

The following information is about a situation. [Rihana wants to buy a handbag. The price of the handbag at shop $A$ is more expensive than the price at shop $B$. However, shop $B$ is located further away from Rihana's house than shop $A$.] Which of the following is a problem for the situation above?

Siti bought a washing machine costing RM 2 400. She paid a deposit of 10% of the price and paid the balance in monthly installments over 18 months. The simple interest rate charged is 8% per annum. What is the monthly installment?

Diagram 8 shows a straight line that passes through points $A(-2, 6)$ and $B(3, -4)$. Find the gradient of the straight line.

Given $\xi = \{x : x \text{ is an integer}, 5 \leq x \leq 25\}$, set $A = \{x : x \text{ is a factor of } 20\}$ and set $B = \{x : x \text{ is a factor of } 25\}$. Which of the following statements is true?

In Diagram 9, $EFG$ is a tangent to the circle $FHJK$ at $F$. Given $\angle JKF = 110^{\circ}$ and $\angle GFH = 50^{\circ}$ (the angle $y^{\circ}$ is $\angle JFH$ at $F$). Find the value of $y$.

Encik Arjun plans to purchase a motor insurance policy for his car. The details of the car are: Car model: Honda City; Location: Kedah; Sum insured: RM 50 000; NCD: 25%; Basic premium for comprehensive policy: RM 1 613.10. Calculate the gross premium for the car under the third party, fire and theft policy.

The solution for $2x - 5 < 7$ and $6 - \dfrac{1}{2}x \leq 4$ is $h \leq x < k$. Find the value of $h$ and of $k$.

The pie chart in Diagram 10 shows the favourite fruits of a group of students (Oranges $54^{\circ}$, Bananas $108^{\circ}$, and a right angle marked at the centre for the Grapes sector). Given that 12 students like bananas and 10% of the total students like apples, calculate the total number of students who like apples and grapes.

The first terms of a sequence are $9, x, -5, -12, y, \ldots$ Calculate the value of $x - y$.

Puan Alia wants to buy a laptop with cash in six months' time. Her total monthly income is RM 5 100 and her total monthly expenses is RM 4 300. The laptop is priced at RM 4 999. Will she be able to achieve her financial goal?

Diagram 11 shows part of the graph $y = \cos x^{\circ}$. The point $P$ is the lowest point where $y = -1$. Find the coordinates of the point $P$.

In Diagram 12, $NPQRW$ is a regular pentagon and $RSTUVW$ is a regular hexagon. $PNM$ and $TUL$ are straight lines. Find the value of $x + y$.

The length of base and height of a triangle are given as 0.9 m and 0.62 m, respectively. Find the area of the triangle, in mm².

Diagram 13 is a pie chart showing the types of transportation used by a group of workers to get to their workplace (Bus $125^{\circ}$, Taxi $70^{\circ}$, and sectors for Car and LRT). The number of workers who drive cars is twice the number of workers who take the LRT. Find the ratio of the number of workers who take the car to the number of workers who take the bus.

The relation between $H$, $g$ and $j$ is $H$ varies directly as the square root of $g$ and varies inversely with $j$. It is given that $H = 10$ when $g = 4$ and $j = 2$. Calculate the value of $H$ when $g = 9$ and $j = 6$.

Diagram 13 shows a top view of a park drawn to a scale of $1 : 20$. $PQR$ and $STU$ are fish ponds with area 1.257 cm² each. Given the area of the park is 30 cm × 13 cm (a rectangular flower bed and two semicircular ponds are inside). Find the actual area that will be planted with grass.

$\begin{pmatrix} -1 \\ 2 \end{pmatrix}\begin{pmatrix} 1 & 3 \end{pmatrix} =$

Diagram 15 shows four numbered cards arranged in ascending order: $10010110_2$, $2231_4$, $M$, $310_8$. Which of the following represents the value of $M$?

Aliani's hobby is collecting stamps. She has a collection of 75 pieces of stamps from Southeast Asia countries consisting of Indonesia, Singapore, Thailand, the Philippines and Malaysia. A stamp is selected at random. The probability of getting a stamp from Singapore and Indonesia is $\dfrac{3}{5}$. If the number of stamps from Thailand and the Philippines equals the number of stamps from Malaysia, calculate the probability of selecting stamps from Malaysia.

The stem-and-leaf plot represents the distance running of a group of participants of the Penang state level charity run event. Key: $2\,|\,3$ refers to 23 km.

What is the percentage of participants who ran a distance of 32 km or more?

In Diagram 17, the right-angled triangle $N$ is the image of an object under a combined transformation. It is given that transformation $P =$ Translation $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$ and $Q =$ Reflection in the line $x + y = 6$. Among the objects $A$, $B$, $C$ and $D$, which is the object of triangle $N$ under the combined transformation $PQ$?

The directed weighted graph in Diagram 18 shows the prices of tickets and travel times for some choices of flights. Vertex $S$ is the destination from vertex $P$. Vertices $Q$ and $R$ are transit airports; the transit time at each airport is 45 minutes. If you need to go to the destination at optimum cost, state the best route that you will choose.

Diagram 19 shows a set of data: $2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9$. Find the interquartile range of the set of data.

Khairul owns a house with an area of 200 m². Given that the tax rate is RM 0.45 per square meter. What type of tax does Khairul have to pay each year?