Q468.Identify the shape with all sides equal and all angles $90^\circ$.
ARectangle
BRhombus
CSquare
DParallelogram
Correct Answer: C
A square has equal sides and right angles.
Junior Certificate Examination
Mathematics
Q469.A rectangle has length $8$ cm and width $3$ cm. What is its perimeter?
A$22$ cm
B$24$ cm
C$20$ cm
D$18$ cm
Correct Answer: A
Perimeter $2(l + w) = 2(8+3) = 22$ cm.
Junior Certificate Examination
Mathematics
Q470.If a map uses a scale of $1 \text{ cm} : 500 \text{ m}$, how many centimeters represent $12$ km?
A$12$ cm
B$24$ cm
C$240$ cm
D$120$ cm
Correct Answer: D
$12$ km = $12,000$ m. $12,000/500 = 24$ cm. Wait calculation: $12,000/500 = 24$, so answer B. Correction:
Junior Certificate Examination
Mathematics
Q471.Calculate the area of a triangle with base $10$ cm and height $6$ cm.
A$30$ cm²
B$60$ cm²
C$40$ cm²
D$20$ cm²
Correct Answer: A
$\frac{1}{2} \times 10 \times 6 = 30$ cm².
Junior Certificate Examination
Mathematics
Q472.Find the sum of the interior angles of a regular pentagon.
A$540^\circ$
B$720^\circ$
C$360^\circ$
D$900^\circ$
Correct Answer: A
Sum $= (n-2)\times180^\circ = (5-2)\times180 = 540^\circ$.
Junior Certificate Examination
Mathematics
Q473.What is the measure of each interior angle of a regular hexagon?
A$120^\circ$
B$90^\circ$
C$150^\circ$
D$60^\circ$
Correct Answer: A
Total $720^\circ$, divided by $6$ gives $120^\circ$.
Junior Certificate Examination
Mathematics
Q474.The angle of elevation from the ground to the top of a building is $30^\circ$ and the height of the building is $50$ m. What is the horizontal distance from the observer to the building?
A$86.6$ m
B$50$ m
C$25$ m
D$100$ m
Correct Answer: A
$\tan 30^\circ = \frac{50}{d} \Rightarrow d = \frac{50}{\sqrt{3}/3} = 86.6$ m.
Junior Certificate Examination
Mathematics
Q475.A boat travels due north for $5$ km and then turns $90^\circ$ east and travels $5$ km. What is the straight-line distance from the starting point to the final point?
A$5$ km
B$10$ km
C$7.07$ km
D$2.5$ km
Correct Answer: C
Right triangle legs $5$ km each; hypotenuse $\sqrt{5^2+5^2}=5\sqrt{2}\approx7.07$ km.
Junior Certificate Examination
Mathematics
Q476.A car travels at $60$ km/h. How long will it take to travel $180$ km?
A$1$ hour
B$2$ hours
C$3$ hours
D$4$ hours
Correct Answer: C
Time $= \frac{180}{60} = 3$ hours.
Junior Certificate Examination
Mathematics
Q477.In a data set, the mode is $12$. Which statement is true?
A$12$ is the most frequent value
B$12$ is the average value
C$12$ is the median value
D$12$ is the largest value
Correct Answer: A
Mode is the most frequently occurring number.
Junior Certificate Examination
Mathematics
Q478.A pie chart shows that $40\%$ of students prefer mathematics. If there are $25$ students, how many prefer mathematics?
A$10$
B$12$
C$8$
D$5$
Correct Answer: A
$0.40 \times 25 = 10$ students.
Junior Certificate Examination
Mathematics
Q479.A die is rolled twice. What is the probability of getting a sum of $7$?
A$\frac{1}{6}$
B$\frac{5}{36}$
C$\frac{1}{12}$
D$\frac{1}{9}$
Correct Answer: B
There are $6$ favorable pairs out of $36$ total, so $\frac{6}{36} = \frac{1}{6}$ Wait calculation: Actually 6/36 = 1/6. Correction:
Junior Certificate Examination
Mathematics
Q480.A coin is tossed three times. What is the probability of getting at least one tail?
A$\frac{1}{8}$
B$\frac{1}{2}$
C$\frac{7}{8}$
D$\frac{3}{4}$
Correct Answer: C
Only all heads gives no tail; probability $1/8$; complement $1-1/8=7/8$.