SPM Malaysia · Mathematics

Probability, Statistics, Coordinate Geometry, and Taxation

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A fair coin is tossed and a fair six-sided die is rolled simultaneously. What is the probability of obtaining a Head on the coin and a prime number on the die?
A single card is drawn at random from a standard deck of 52 playing cards. Find the probability of drawing a King or an Ace.
A single card is selected at random from a standard deck of 52 playing cards. What is the probability of drawing a Heart or a Queen?
A box contains 5 red marbles and 3 blue marbles. Two marbles are drawn sequentially at random without replacement. Find the probability that both marbles drawn are red.
A competitive archer has a probability of $0.8$ of hitting the target center on any individual shot. If she releases 2 independent shots, what is the probability that she hits the center at least once…
Determine the interquartile range of the data set: $4, 7, 8, 10, 12, 15, 18$ .
Calculate the standard deviation of the data set: $2, 4, 6, 8, 10$ .
The variance of a set of numerical data is 16. If every value in the data set is multiplied by 3, what is the new variance of the transformed data set?
A cohort of students achieves examination scores with a variance of $49$ . If each student is granted an additional 5 bonus marks, what will be the new standard deviation of the scores?
A delivery van travels between two logistic hubs. Its distance-time graph indicates that it traverses $180 km$ in $2.5 hours$ . Calculate the average speed of the van.
A motorcycle accelerates uniformly from rest to a velocity of $24 m/s$ in $6 seconds$ . What is the rate of change of speed (acceleration) of the motorcycle?
A car moves at a constant speed of $20 m/s$ for $10 seconds$ , and then decelerates uniformly to rest over the next $5 seconds$ . Calculate the total distance travelled by the car.
A passenger train moving at an initial velocity of $30 m/s$ applies its brakes and comes to a complete standstill in $12 seconds$ . What is the magnitude of its uniform deceleration?
Farhan has a medical insurance policy with an annual deductible of $RM 1, 500$ . During the year, he undergoes a minor medical procedure costing $RM 14, 000$ in eligible medical expenses.…
Halim owns a residential property with an insurable value of $RM 400, 000$ . His fire insurance policy has an $80%$ co-insurance clause and a deductible of $RM 2, 000$ . Halim insures his…
Azman earned a total annual income of $RM 68, 000$ in 2025. He contributed $RM 2, 000$ in tax-exempt charitable donations to an approved institution. His allowable personal tax reliefs t…
Based on Malaysian income tax brackets, a chargeable income of $RM 51, 500$ is taxed as follows:
- On the first $RM 50, 000$ , the base tax is $RM 1, 800$ .
- On the next…
If Azman's calculated basic income tax is $RM 1, 995$ and he paid $RM 600$ in Zakat during the assessment year, what is his final net income tax payable?
In Peninsular Malaysia, the road tax for a private passenger car with an engine capacity of $1, 800 cc$ is calculated with a base rate of $RM 200.00$ plus a progressive rate of…
Puan Rohana owns a terrace home with an estimated annual rental value of $RM 12, 000$ . The municipal council levies a property assessment tax (cukai pintu) rate of $5%$ per annum. What is th…
A parcel of freehold residential land has a surface area of $250 m^{2}$ . The state land registry fixes the annual quit rent (cukai tanah) rate at $RM 0.35$ per square metre. Calculate the…
A dining patron orders food and beverages totaling $RM 180.00$ at a licensed restaurant. The restaurant adds a $10%$ service charge on food items, followed by a $6%$ service tax levied on the…
The bearing of landmark $B$ from observation post $A$ is $06 5^{\circ}$ . What is the back bearing of observation post $A$ from landmark $B$ ?
The bearing of a coastal lighthouse $L$ from a cargo vessel $S$ is $21 5^{\circ}$ . Determine the bearing of vessel $S$ from lighthouse $L$ .
Points $P (4 0^{\circ} N, 2 0^{\circ} E)$ and $Q (4 0^{\circ} N, 7 0^{\circ} E)$ lie on the same parallel of latitude. What is the distance between $P$ and $Q$ , measured along the parallel…
Calculate the gradient of the straight line connecting points $P (- 2, 5)$ and $Q (4, - 7)$ .
Find the coordinates of the midpoint of the line segment joining $A (3, - 4)$ and $B (9, 8)$ .
Find the distance between the points $C (1, 2)$ and $D (7, 10)$ in a Cartesian plane.
In triangle $A B C$ , angle $A = 3 0^{\circ}$ , side opposite angle $A$ is $a = 6 cm$ , and side $b = 10 cm$ . Using the sine rule, calculate the exact value of $sin B$ .
A student stands on level horizontal ground $20 m$ away from the base of a vertical school flagpole. The angle of elevation from the student's eyes to the top of the flagpole is $4 5^{\circ}$ . If…

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Probability, Statistics, Coordinate Geometry, and Taxation

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