SPM Add Math · 2025 · Pahang · Percubaan Kertas 2 (Pahang)

It is given that quadratic equation $x(x-5)=4$. (i) Express the equation in the form $ax^{2}+bx+c=0$. (ii) State the sum of roots and the product of roots of the equation.

Express $h(x)=-x^{2}-8x+9$ in the form $h(x)=-(x+p)^{2}+q$. Hence state the maximum value of $h(x)$ and the corresponding value of $x$.

Find (i) $\vec{OM}$, (ii) $\vec{PR}$.

If $\vec{PN}=-\mathbf{a}+\lambda\mathbf{b}$ and $\vec{PR}=k\,\vec{PN}$, find $\vec{ON}:\vec{NQ}$.

If $\theta=1\text{ rad}$, state the relationship between the arc length of $PQ$ and its radius.

(i) If $\theta=60^{\circ}$, calculate the minor arc length of $PQ$ in terms of $\pi$ and $x$. (ii) Hence, find the radius, in cm, if the minor arc length of $PQ$ is $12\text{ cm}$.

(i) $49^{3x}\cdot\sqrt{3^{12x}}=21$ (ii) $y\sqrt{12}=6-\sqrt{3}$

Given $\log_{3}r=m$ and $\log_{9}s=n$. Express $\log_{3}(r^{2}s^{3})$ in terms of $m$ and/or $n$.

Solve the equation $\dfrac{{}^{2n}P_{n}}{(2n-2)!}=\dfrac{10n}{n!}$.

Find the number of ways Balqis arranges 8 beads to form a bracelet.

Yusof owns 5 shirts, 7 pairs of long pants and 4 pairs of shoes. In how many ways can Yusof choose two from each item to pack for a vacation?

(i) Calculate the volume of production of soy sauce on the fourth day. (ii) Hence, find the total volume of production of soy sauce in the first week of operation.

It is given that $x,6,10,14,\ldots,54$ is an arithmetic progression. (i) State the value of $x$. (ii) Find the number of terms of the sequence.

Calculate (i) the probability that Awang will get exactly 3 fishes in 7 throws, (ii) the number of throws made by Awang so that the probability of getting at least a fish is greater than 0.95.

Diagram 3 shows the probability distribution of $X$ where $X$ is a discrete random variable. Find the standard deviation. (图3:直方图,$P(X=x)$ 对 $x=0,1,2,3$ 分别为 $\dfrac{1}{27},\dfrac{2}{9},\dfrac{4}{9},\dfrac{8}{27}$)

(i) State the value of $b$ and $c$. (ii) By marking the solution in Diagram 4, state the number of solutions for $2\sin bx=\dfrac{1}{2}$.

Prove that $\tan x(1+\cos 2x)=\sin 2x$.

Solve the equation $3\cos 2x-\sin x=2$ for $0^{\circ}\le x\le 360^{\circ}$.

Based on Table 1.1, complete Table 1.2 (values of $\log_{10}y$).

Plot $\log_{10}y$ against $x$, using a scale of 2 cm to 2 units on the $x$-axis and 2 cm to 0.1 unit on the $\log_{10}y$-axis. Hence, draw the line of best fit.

Using the graph in (b), find the value of (i) $y$ when $x=2$, (ii) $p$ and $q$.

Find the equation of the straight line $CE$.

(i) Find the area of triangle $ABC$, hence find the ratio of $EA$ to $AC$ if it is given that the area of triangle $ABE$ is $37\dfrac{1}{2}\text{ unit}^{2}$. (ii) Hence, find the coordinates of $E$.

Point $R$ moves such that its distance from $E$ is always $\dfrac{3}{2}$ times its distance from $C$. Find the equation of locus of $R$.

Determine the equation of the curve represented by the skateboard ramp.

Calculate the area bounded by the curve of the skateboard ramp and $y=8$.

For the long term plan, if the skateboard ramp is no longer in use, it will be modified into a covered structure and used as a water storage tank. Calculate the maximum volume of water, in terms of $\pi$, when the region bounded by the curve $y=f(x)$, the straight line $y=8$ and the $y$-axis is rotated through $360^{\circ}$ about the $y$-axis.

the initial velocity, in $\text{ms}^{-1}$, of the particle,

the value of $t$, in seconds, when the particle stops instantaneously,

the maximum velocity, in $\text{ms}^{-1}$, of the particle,

the total distance, in m, travelled by the particle in the first 8 seconds.

Find the value of $p$, $q$ and $r$.

Calculate the composite index of the ingredients price in the year 2023 based on the year 2021.

The total cost of all ingredients in the year 2021 was RM2560. Calculate the corresponding total cost in the year 2023.

The composite index is expected to decrease by $m\%$ from the year 2023 to 2025. Given that the composite index in the year 2025 based on the year 2021 is 117, find the value of $m$.

Sketch a triangle $ABC$ with side $a=BC$, $b=AC$ and angle $C=\angle ACB$. Hence, by using the concept of trigonometry and area of triangle, derive the formula: $\text{Area}=\dfrac{1}{2}ab\sin C$.

Diagram 7 shows the positions of a boat, an aircraft, an oil rig station and a shark. Given that the distance between the boat and the aircraft is 24 units and the distance between the oil rig to the shark is 12 units, while the angle between the boat, the aircraft and the oil rig is $32^{\circ}$. The distance between the oil rig and the aircraft is equal to the distance of the boat and the oil rig. The positions of the shark, the oil rig and the aircraft are aligned in a straight line. (i) Find the distance, in unit, between the aircraft and the oil rig. (ii) Find the distance, in unit, between the boat and the shark. (iii) Calculate the area bounded by the positions of the boat, the aircraft and the shark.

In one week, a participant has allocated $x$ hours for the cooking class and $y$ hours for the sewing class. Write the inequalities for constraints I and II.

Write constraint III as an inequality and explain its meaning in words.

Construct and label the region $R$ that satisfies all the constraints and $x>0$, $y>0$.

It is given that, on average, cooking burns 350 calories per hour, while sewing burns 450 calories per hour. By drawing the objective function, find the maximum number of calories that can be burned in one week.