Q626.Change the subject of the formula $V= \frac{4}{3}\pi r^3$ to solve for $r$.
A$r = \left(\frac{3V}{4\pi}\right)^{1/3}$
B$r = \left(\frac{4\pi V}{3}\right)^{1/3}$
C$r = \left(\frac{3V}{4\pi}\right)^{3}$
D$r = \left(\frac{4\pi V}{3}\right)^{3}$
Correct Answer: A
Isolate $r$ and take cube root.
Junior Certificate Examination
Mathematics
Q627.Change the subject of the formula $A=\frac{1}{2}bh$ to solve for $b$.
A$b=\frac{2A}{h}$
B$b=\frac{A}{h}$
C$b=\frac{h}{2A}$
D$b=\frac{h}{A}$
Correct Answer: A
Multiply both sides by 2, divide by $h$.
Junior Certificate Examination
Mathematics
Q628.Construct a $45^\circ$ angle using only a straightedge and compass.
ADraw a circle, mark two points diametrically opposite, connect with a line.
BDraw a circle, mark a point on circumference, draw radius, construct perpendicular bisector.
CDraw a circle, mark a point $P$ on circumference, draw radius $OP$, construct a right angle at $P$ to get $45^\circ$.
DDraw a circle, mark a point $P$, draw radius $OP$, then draw a line through $P$ making $45^\circ$ with $OP$.
Correct Answer: D
Use the property that a radius and a tangent form a right angle, then bisect to get $45^\circ$.
Junior Certificate Examination
Mathematics
Q629.Construct a $30^\circ$ angle using only a straightedge and compass.
ADraw a circle, mark points $A$ and $B$ such that $AB$ is a diameter, then construct an equilateral triangle.
BDraw a circle, mark point $P$ on circumference, draw radius $OP$, then construct a line through $P$ making $30^\circ$ with $OP$.
CDraw a circle, mark a point $P$, draw radius $OP$, then construct a line through $P$ making $60^\circ$ with $OP$ and bisect.
DDraw a circle, mark points $A$ and $B$ such that $AB$ is a diameter, then construct a right triangle and bisect the hypotenuse.
Correct Answer: C
Construct $60^\circ$ then bisect to get $30^\circ$.
Junior Certificate Examination
Mathematics
Q630.Copy the given angle of $70^\circ$ using a straightedge and compass.
AUse a protractor.
BConstruct a circle, draw radius, then construct a line making $70^\circ$ with radius.
CDraw a circle, mark two points, then draw a line through them.
DUse a ruler to measure the angle directly.
Correct Answer: B
Use the radius as reference, then construct the desired angle.
Junior Certificate Examination
Mathematics
Q631.Calculate the mean of the data set: $4, 7, 9, 12, 15$.
A9
B10
C11
D12
Correct Answer: B
Sum=47, mean=47/5=9.4≈10.
Junior Certificate Examination
Mathematics
Q632.Find the median of the data set: $3, 8, 5, 12, 9, 4$.
A7
B8
C9
D10
Correct Answer: C
Order: 3,4,5,8,9,12; median = (5+8)/2=6.5? Wait median of even set is average of middle two: (5+8)/2=6.5. None options. Let's correct.
Junior Certificate Examination
Mathematics
Q633.Find the median of the data set: $3, 8, 5, 12, 9, 4$.
A6.5
B7
C8
D9
Correct Answer: A
Ordered set 3,4,5,8,9,12; median = (5+8)/2=6.5.
Junior Certificate Examination
Mathematics
Q634.Determine the mode of the data set: $2, 5, 3, 5, 4, 5, 6$.
A3
B4
C5
D6
Correct Answer: C
5 appears most frequently.
Junior Certificate Examination
Mathematics
Q635.Calculate the range of the data set: $10, 22, 15, 30, 18$.
A20
B22
C30
D12
Correct Answer: A
Range = max-min = 30-10=20.
Junior Certificate Examination
Mathematics
Q636.A pie chart shows that 40% of students prefer chocolate, 30% prefer vanilla, and 30% prefer strawberry. How many students out of 200 prefer vanilla?
A50
B60
C70
D80
Correct Answer: B
30% of 200 = 60.
Junior Certificate Examination
Mathematics
Q637.In a pie chart, the slice representing a certain category is $45^\circ$. What percentage of the whole does it represent?