Junior Certificate Examination
Mathematics
Q351.
What is the least common multiple (LCM) of 48, 72 and 90?
A
360
B
720
C
1080
D
1440
View Answer
Correct Answer: B
Prime factors: 48=2^4·3, 72=2^3·3^2, 90=2·3^2·5. Take the highest powers: 2^4·3^2·5=720.
Junior Certificate Examination
Mathematics
Q352.
Round 987 654 to the nearest thousand.
A
987 000
B
988 000
C
987 500
D
986 000
View Answer
Correct Answer: B
The hundreds digit is 6, so we round up to 988 000.
Junior Certificate Examination
Mathematics
Q353.
Add the binary numbers \(1011_2\) and \(1100_2\).
A
\(10111_2\)
B
\(10011_2\)
C
\(1111_2\)
D
\(11011_2\)
View Answer
Correct Answer: A
\(1011_2 = 11\) and \(1100_2 = 12\); 11+12=23, which is \(10111_2\).
Junior Certificate Examination
Mathematics
Q354.
Simplify the expression \(3x + 5 - 2x + 7\).
A
\(x + 12\)
B
\(5x + 12\)
C
\(x + 2\)
D
\(5x + 2\)
View Answer
Correct Answer: A
Combine like terms: \((3x-2x)+(5+7)=x+12\).
Junior Certificate Examination
Mathematics
Q355.
Solve the equation \(5x - 7 = 3x + 9\).
A
\(x = 8\)
B
\(x = 4\)
C
\(x = -4\)
D
\(x = 2\)
View Answer
Correct Answer: A
\(5x-3x = 9+7\) gives \(2x = 16\), so \(x = 8\).
Junior Certificate Examination
Mathematics
Q356.
Which of the following is a quadrilateral with two pairs of parallel sides?
A
Triangle
B
Rhombus
C
Trapezoid
D
Rectangle
View Answer
Correct Answer: D
A rectangle has opposite sides parallel, satisfying the definition.
Junior Certificate Examination
Mathematics
Q357.
Which of the following numbers is the greatest?
A
1,234,567
B
1,234,576
C
1,234,657
D
1,234,675
View Answer
Correct Answer: D
The thousands, hundreds, tens and units places are compared from left to right; 1,234,675 has the highest units digit.
Junior Certificate Examination
Mathematics
Q358.
Find the least common multiple of $48,\;180,\;$ and $210$.
A
840
B
1260
C
2520
D
5040
View Answer
Correct Answer: C
Prime factorisation gives $48=2^4\cdot3$, $180=2^2\cdot3^2\cdot5$, $210=2\cdot3\cdot5\cdot7$. The LCM uses the highest powers: $2^4\cdot3^2\cdot5\cdot7=2520$.
Junior Certificate Examination
Mathematics
Q359.
Find the highest common factor of $420,\;660,\;$ and $840$.
View Answer
Correct Answer: B
$420=2^2\cdot3\cdot5\cdot7$, $660=2^2\cdot3\cdot5\cdot11$, $840=2^3\cdot3\cdot5\cdot7$. Common primes: $2^2\cdot3\cdot5=60$.
Junior Certificate Examination
Mathematics
Q360.
What is the binary representation of the decimal number $18$?
A
10010
B
10011
C
10100
D
10101
View Answer
Correct Answer: A
$18 = 16 + 2 = 2^4 + 2^1$, so the binary digits are $1\,0\,0\,1\,0$.
Junior Certificate Examination
Mathematics
Q361.
Convert the binary number $1101.101_2$ to decimal.
A
$13.625$
B
$14.125$
C
$13.5$
D
$14.0$
View Answer
Correct Answer: A
$1\cdot8 + 1\cdot4 + 0\cdot2 + 1\cdot1 + 1\cdot0.5 + 0\cdot0.25 + 1\cdot0.125 = 13.625$.
Junior Certificate Examination
Mathematics
Q362.
Simplify the fraction $\frac{48}{180}$.
A
$\frac{4}{15}$
B
$\frac{8}{30}$
C
$\frac{12}{45}$
D
$\frac{16}{60}$
View Answer
Correct Answer: A
The greatest common divisor of $48$ and $180$ is $12$, so dividing numerator and denominator by $12$ gives $\frac{4}{15}$.
Junior Certificate Examination
Mathematics
Q363.
Which of the following fractions is equivalent to $\frac{7}{12}$?
A
$\frac{14}{24}$
B
$\frac{21}{30}$
C
$\frac{28}{48}$
D
$\frac{35}{60}$
View Answer
Correct Answer: A
Multiplying numerator and denominator by $2$ yields $\frac{14}{24}$, which reduces back to $\frac{7}{12}$.
Junior Certificate Examination
Mathematics
Q364.
Evaluate $5^3 - \frac{4^2}{3-1} + 7$.
A
$124$
B
$122$
C
$126$
D
$120$
View Answer
Correct Answer: A
$5^3=125$, $4^2=16$, $3-1=2$, so $\frac{16}{2}=8$. Then $125-8+7=124$.
Junior Certificate Examination
Mathematics
Q365.
Compute $\frac{5}{6} + \frac{7}{8} - \frac{3}{4}$.
A
$\frac{23}{24}$
B
$\frac{22}{24}$
C
$\frac{24}{24}$
D
$\frac{25}{24}$
View Answer
Correct Answer: A
Common denominator $24$: $5/6=20/24$, $7/8=21/24$, $3/4=18/24$. Sum: $(20+21-18)/24 = 23/24$.
Junior Certificate Examination
Mathematics
Q366.
Compute $\frac{7}{9} \div \frac{2}{3} \times \frac{4}{5}$.
A
$\frac{14}{15}$
B
$\frac{7}{15}$
C
$\frac{28}{15}$
D
$\frac{7}{5}$
View Answer
Correct Answer: A
$\frac{7}{9}\div\frac{2}{3} = \frac{7}{9}\times\frac{3}{2} = \frac{21}{18} = \frac{7}{6}$. Then $\frac{7}{6}\times\frac{4}{5} = \frac{28}{30} = \frac{14}{15}$.
Junior Certificate Examination
Mathematics
Q367.
What is the place value of 7 in the number 3,472,658?
A
Ten thousands
B
Thousands
C
Hundreds
D
Millions
View Answer
Correct Answer: A
The digit 7 is in the ten‑thousands place.
Junior Certificate Examination
Mathematics
Q368.
Which of the following is a property of whole numbers?
A
They can be negative
B
They include fractions
C
They start from zero
D
They end at 100
View Answer
Correct Answer: C
Whole numbers are non‑negative integers starting at zero.
Junior Certificate Examination
Mathematics
Q369.
Find the LCM of 12 and 18.
View Answer
Correct Answer: A
Prime factors: 12=2^2·3, 18=2·3^2; LCM=2^2·3^2=36.
Junior Certificate Examination
Mathematics
Q370.
Which method can be used to find the LCM of 8 and 20?
A
List multiples of each number
B
Subtract the numbers
C
Add the numbers
D
Divide the numbers
View Answer
Correct Answer: A
Listing multiples reveals the smallest common multiple.
Junior Certificate Examination
Mathematics
Q371.
If 6 is a multiple of 3, then 18 is a multiple of:
View Answer
Correct Answer: A
18 ÷ 3 = 6, so 18 is a multiple of 3.
Junior Certificate Examination
Mathematics
Q372.
The HCF of 48 and 60 is:
View Answer
Correct Answer: A
48=2^4·3, 60=2^2·3·5; common factors give 2^2·3=12.
Junior Certificate Examination
Mathematics
Q373.
Which of the following pairs of numbers has an HCF of 1?
A
14 and 21
B
9 and 12
C
17 and 24
D
10 and 15
View Answer
Correct Answer: C
17 is prime and shares no common factor with 24 other than 1.
Junior Certificate Examination
Mathematics
Q374.
Using factorisation, find the HCF of 27 and 45.
View Answer
Correct Answer: A
27=3^3, 45=3^2·5; common factor 3^2=9.
Junior Certificate Examination
Mathematics
Q375.
Which of the following is NOT a multiple of 4?
View Answer
Correct Answer: C
33 ÷ 4 is not an integer.
Junior Certificate Examination
Mathematics
Q376.
Convert the decimal number 13 to binary.
A
1101
B
1111
C
1011
D
1001
View Answer
Correct Answer: A
13 = 8+4+1 = 1101₂.
Junior Certificate Examination
Mathematics
Q377.
The binary number 1010₂ equals which decimal number?
View Answer
Correct Answer: A
1·8 + 0·4 + 1·2 + 0·1 = 10.
Junior Certificate Examination
Mathematics
Q378.
In base‑2, the digit 1 represents:
View Answer
Correct Answer: A
Each binary digit represents a power of 2.
Junior Certificate Examination
Mathematics
Q379.
Which of the following is a valid binary number?
A
102
B
1101
C
2110
D
10002
View Answer
Correct Answer: B
Binary digits can only be 0 or 1.
Junior Certificate Examination
Mathematics
Q380.
A proper fraction is:
A
Numerator greater than denominator
B
Numerator equal to denominator
C
Numerator less than denominator
D
Numerator and denominator are equal
View Answer
Correct Answer: C
Proper fractions have numerator < denominator.
Junior Certificate Examination
Mathematics
Q381.
Which of these is an improper fraction?
View Answer
Correct Answer: B
Improper fractions have numerator ≥ denominator.
Junior Certificate Examination
Mathematics
Q382.
Convert the mixed number 2 ⅔ to an improper fraction.
View Answer
Correct Answer: A
2 ⅔ = 2 + 2/3 = 8/3.
Junior Certificate Examination
Mathematics
Q383.
Expand the algebraic expression (x + 3)(x – 2).
A
x² + x – 6
B
x² – 2x + 3x – 6
C
x² + x + 6
D
x² – 5x + 6
View Answer
Correct Answer: A
(x+3)(x-2)=x²–2x+3x–6=x²+x–6.
Junior Certificate Examination
Mathematics
Q384.
Find the value of x in x + 4 = 12.
View Answer
Correct Answer: A
Subtract 4 from both sides: x = 8.
Junior Certificate Examination
Mathematics
Q385.
A triangle has sides 5 cm, 12 cm, and 13 cm. What type of triangle is it?
A
Equilateral
B
Isosceles
C
Right‑angled
D
Scalene
View Answer
Correct Answer: C
5²+12²=13², so it is right‑angled.
Junior Certificate Examination
Mathematics
Q386.
Which of the following is a property of a rectangle?
A
Opposite sides are equal and all angles are right angles
B
All sides are equal
C
Opposite sides are unequal
D
Only one right angle
View Answer
Correct Answer: A
Rectangles have opposite sides equal and all angles 90°.
Junior Certificate Examination
Mathematics
Q387.
The volume of a cuboid with length 4 cm, width 3 cm, and height 2 cm is:
A
24 cm³
B
12 cm³
C
8 cm³
D
6 cm³
View Answer
Correct Answer: A
Volume = l × w × h = 4×3×2 = 24 cm³.
Junior Certificate Examination
Mathematics
Q388.
What is the surface area of a cube with side 5 cm?
A
125 cm²
B
150 cm²
C
100 cm²
D
75 cm²
View Answer
Correct Answer: B
Surface area = 6a² = 6×25 = 150 cm².
Junior Certificate Examination
Mathematics
Q389.
Construct a right angle using only a ruler and compass. Which step is NOT required?
A
Draw a circle with radius AB
B
Draw a perpendicular line from a point on AB
C
Use a protractor to measure 90°
D
Mark the intersection point of the perpendicular and AB
View Answer
Correct Answer: C
A protractor is not needed; construction uses circle and perpendicular.
Junior Certificate Examination
Mathematics
Q390.
In a circle, an angle that subtends a diameter is:
View Answer
Correct Answer: A
The angle subtended by a diameter is a right angle.
Junior Certificate Examination
Mathematics
Q391.
Which of the following data sets can be represented by a pie chart?
A
Number of students in each class
B
Temperature readings over a week
C
Scores of a test
D
All of the above
View Answer
Correct Answer: A
Pie charts show parts of a whole, suitable for class sizes.
Junior Certificate Examination
Mathematics
Q392.
A data table lists the ages of five students: 12, 13, 14, 13, 12. What is the mode?
View Answer
Correct Answer: A
12 appears twice, more than others.
Junior Certificate Examination
Mathematics
Q393.
Which of the following is a correct statement about significant figures?
A
All zeros are significant
B
Only the leading zeros are significant
C
Trailing zeros after a decimal are significant
D
None of the above
View Answer
Correct Answer: C
Trailing zeros after a decimal are significant.
Junior Certificate Examination
Mathematics
Q394.
Convert the fraction 7/8 to a decimal.
A
0.875
B
0.75
C
0.8
D
0.9
View Answer
Correct Answer: A
7 ÷ 8 = 0.875.
Junior Certificate Examination
Mathematics
Q395.
Which of these fractions is in simplest form?
A
6/9
B
8/12
C
15/20
D
5/7
View Answer
Correct Answer: D
5/7 cannot be reduced further.
Junior Certificate Examination
Mathematics
Q396.
The binary number 1111₂ equals which decimal?
View Answer
Correct Answer: A
1·8+1·4+1·2+1·1=15.
Junior Certificate Examination
Mathematics
Q397.
Which of the following is a correct representation of the number 0.004 in binary?
A
100₀₂
B
10000₂
C
100₀₂
D
0.000100₀₂
View Answer
Correct Answer: D
0.004 in decimal ≈ 0.000100₀₂.
Junior Certificate Examination
Mathematics
Q398.
What is the place value of the digit 7 in the number 4 738 591?
A
Hundred thousands
B
Ten thousands
C
Thousands
D
Millions
View Answer
Correct Answer: A
The digit 7 is in the hundred‑thousands place of 4 738 591.
Junior Certificate Examination
Mathematics
Q399.
Arrange the following whole numbers in ascending order: 4 500, 4 500 000, 45 000, 450 000.
A
4 500 000, 450 000, 45 000, 4 500
B
4 500, 45 000, 450 000, 4 500 000
C
4 500, 450 000, 45 000, 4 500 000
D
45 000, 4 500, 450 000, 4 500 000
View Answer
Correct Answer: B
The numbers increase as 4 500 < 45 000 < 450 000 < 4 500 000.
Junior Certificate Examination
Mathematics
Q400.
What is the least common multiple of 12 and 18?
View Answer
Correct Answer: A
12 = 2²·3, 18 = 2·3²; LCM = 2²·3² = 36.