Calculate the perimeter of a rectangle with length $15 \text{ cm}$ and width $4 \text{ cm}$.

Correct Answer: Option B - 38 cm. Perimeter $= 2(l + w) = 2(15 + 4) = 2(19) = 38 \text{ cm}$.

A parallelogram has an area of $96 \text{ cm}^2$ and a base of $12 \text{ cm}$. Find its height.

Correct Answer: Option B - 8 cm. Area $= \text{base} \times \text{height} \Rightarrow 96 = 12 \times h \Rightarrow h = 96 / 12 = 8 \text{ cm}$.

The length of the boundary around a circle is known as the:

Correct Answer: Option D - Circumference. The perimeter of a circle is specifically called the circumference.

If the side of a square is doubled, the area increases by a factor of:

Correct Answer: Option B - 4. Let side $= s$. Area $= s^2$. If new side $= 2s$, new Area $= (2s)^2 = 4s^2$. The area increases by a factor of 4.

Which of the following is NOT a property of a rectangle?

Correct Answer: Option C - Diagonals intersect at 90 degrees. For a standard rectangle, diagonals bisect each other but not necessarily at $90^\circ$ (unless it is a square).

Find the length of a side of a square whose area is $81 \text{ cm}^2$.

Correct Answer: Option A - 9 cm. Area $= s^2 = 81$. Side $s = \sqrt{81} = 9 \text{ cm}$.

A Kite has diagonals of length $10 \text{ cm}$ and $24 \text{ cm}$. What is its area?

Correct Answer: Option B - 120 cm². Area of a kite $= \frac{p \times q}{2}$ where $p$ and $q$ are diagonals. Area $= \frac{10 \times 24}{2} = 120 \text{ cm}^2$.

How many lines of symmetry does an equilateral triangle have?

Correct Answer: Option C - 3. An equilateral triangle has 3 lines of symmetry, each passing from a vertex to the midpoint of the opposite side.

Calculate the area of a sector of a circle with radius $7 \text{ cm}$ and angle $90^\circ$. (Take $\pi = \frac{22}{7}$)

Correct Answer: Option A - 38.5 cm². Area $= \frac{\theta}{360} \times \pi r^2 = \frac{90}{360} \times \frac{22}{7} \times 7^2 = \frac{1}{4} \times 154 = 38.5 \text{ cm}^2$.

What is the name of a polygon with 8 sides?

Correct Answer: Option C - Octagon. An 8-sided polygon is called an Octagon.

How many faces does a cube have?

Correct Answer: Option B - 6. A cube has 6 square faces.

Calculate the volume of a cuboid with length $5 \text{ cm}$, breadth $3 \text{ cm}$, and height $4 \text{ cm}$.

Correct Answer: Option D - 60 cm³. Volume of cuboid $= L \times B \times H = 5 \times 3 \times 4 = 60 \text{ cm}^3$.

Which of the following solids has a circular base and a single vertex?

Correct Answer: Option B - Cone. A cone has a circular base and tapers to a single vertex at the top.

The volume of a cube is $27 \text{ cm}^3$. What is the length of one side?

Correct Answer: Option A - 3 cm. Volume $= s^3$. If $s^3 = 27$, then $s = \sqrt[3]{27} = 3 \text{ cm}$.

A cylinder has a base radius of $7 \text{ cm}$ and a height of $10 \text{ cm}$. Calculate its volume. (Take $\pi = \frac{22}{7}$)

Correct Answer: Option B - 1540 cm³. Volume of cylinder $= \pi r^2 h = \frac{22}{7} \times 7^2 \times 10 = 154 \times 10 = 1540 \text{ cm}^3$.

How many edges does a cuboid have?

Correct Answer: Option D - 12. A cuboid has 12 edges (4 length, 4 breadth, 4 height).

Which solid shape is formed by a net of two circles and one rectangle?

Correct Answer: Option B - Cylinder. A cylinder's net consists of two circles (bases) and a rectangular sheet (curved surface).

Calculate the Total Surface Area (TSA) of a cube with side $2 \text{ cm}$.

Correct Answer: Option D - 24 cm². TSA of a cube $= 6s^2 = 6 \times (2^2) = 6 \times 4 = 24 \text{ cm}^2$.

A triangular prism has a length of $10 \text{ cm}$ and the area of the triangular cross-section is $12 \text{ cm}^2$. What is its volume?

Correct Answer: Option B - 120 cm³. Volume of a prism $= \text{Area of cross-section} \times \text{length} = 12 \times 10 = 120 \text{ cm}^3$.

Which of the following solids does NOT have flat faces?

Correct Answer: Option B - Sphere. A sphere is a curved surface with no flat faces.

Angles on a straight line add up to:

Correct Answer: Option B - 180 degrees. The sum of angles on a straight line is $180^\circ$.

In the diagram of parallel lines intersected by a transversal, alternate angles are:

Correct Answer: Option C - Equal. Alternate angles (often forming a 'Z' shape) between parallel lines are equal.

What is the sum of angles at a point?

Correct Answer: Option C - 360 degrees. Angles at a full circle (a point) sum to $360^\circ$.

Two angles are vertically opposite. If one is $40^\circ$, the other is:

Correct Answer: Option A - 40 degrees. Vertically opposite angles are equal. Thus, the other is $40^\circ$.

If a bearing is written as $045^\circ$, which direction does it correspond to?

Correct Answer: Option C - North-East. $045^\circ$ is halfway between North ($000^\circ$) and East ($090^\circ$), which is North-East.

What is the bearing of South?

Correct Answer: Option B - 180 degrees. South is directly opposite North. $000^\circ + 180^\circ = 180^\circ$.

In a triangle, if two angles are $50^\circ$ and $60^\circ$, what is the third angle?

Correct Answer: Option B - 70 degrees. Sum of angles in a triangle is $180^\circ$. Third angle $= 180 - (50 + 60) = 180 - 110 = 70^\circ$.

Calculate the exterior angle of a regular hexagon.

Correct Answer: Option B - 60 degrees. Exterior angle of a regular polygon $= \frac{360}{n}$. For a hexagon ($n=6$), exterior angle $= \frac{360}{6} = 60^\circ$.

Point A is due North of Point B. What is the bearing of A from B?

Correct Answer: Option A - 000 degrees. Bearing is measured clockwise from North. Since A is due North of B, the bearing from B to A is $000^\circ$ (or $360^\circ$).

The bearing of X from Y is $120^\circ$. What is the bearing of Y from X (the back bearing)?

Correct Answer: Option C - 300 degrees. Back bearing $= \text{Forward bearing} + 180^\circ$ (if $<180$). $120 + 180 = 300^\circ$.

If two lines intersect and one angle is $90^\circ$, then the lines are:

Correct Answer: Option B - Perpendicular. Perpendicular lines intersect at $90^\circ$.

Complementary angles sum up to:

Correct Answer: Option A - 90 degrees. Complementary angles add up to $90^\circ$.

Which instrument is primarily used to draw arcs and circles in geometry?

Correct Answer: Option B - Pair of compasses. A pair of compasses is the standard tool for drawing circles and arcs.

To construct an angle of $60^\circ$, which shape is effectively being constructed first?

Correct Answer: Option B - Equilateral Triangle. Drawing a $60^\circ$ angle involves creating the geometry of an equilateral triangle where all angles are $60^\circ$.

When bisecting a line segment AB, the arcs drawn from A and B must have a radius:

Correct Answer: Option C - Greater than half the length of AB. To ensure the arcs intersect, the radius must be greater than half the distance between the centers (points A and B).

Which angle is obtained by bisecting a $90^\circ$ angle?

Correct Answer: Option B - 45 degrees. Bisecting divides an angle into two equal parts. $90 / 2 = 45^\circ$.

The locus of points equidistant from two fixed points A and B is:

Correct Answer: Option B - The perpendicular bisector of AB. The set of all points equidistant from two endpoints of a segment is the perpendicular bisector of that segment.

Which of these angles cannot be constructed using only a pair of compasses and a ruler?

Correct Answer: Option C - 50 degrees. $50^\circ$ is not a standard constructible angle (unlike $90$, $60$, $45$, $30$, $15$, etc.). It requires a protractor.

To construct a $30^\circ$ angle, one would typically bisect which angle?

Correct Answer: Option B - 60 degrees. $60^\circ$ is easily constructed, and bisecting it gives $30^\circ$.

In constructing a perpendicular to a line from a point P on the line, the first step is to:

Correct Answer: Option A - Draw a circle with P as center cutting the line at two points. Using compasses, one places the point on P and marks arcs on either side of P on the line to create equidistant reference points.

What is the instrument used to measure angles?

Correct Answer: Option C - Protractor. A protractor is used to measure angles in degrees.

BECENational Examinations Council (NECO), NigeriaCertificationJunior Secondary Exit ExaminationPaper-Based

BECE Mathematics Geometry & Measurement Practice Questions & Answers

72 Questions·Free Practice·MCQ with Explanations

Module: Geometry & Measurement

Focus: Shapes & Dimensions | Level: Junior Secondary (JSS3)

Comprehensive review of geometric properties and measurement calculations for JSS3 students.

Key Topics:

Plane Shapes: Properties of triangles, quadrilaterals, and circles.
Solid Shapes: Volumes and surface areas of prisms, cylinders, and pyramids.
Measurement: Length, perimeter, area, and weight conversions.
Trigonometry: Basic ratios and angle properties.

Ready to test yourself?

Take this exam in our timed interactive simulator to track your performance and get detailed analytics.

Which of the following properties is true for all squares but not necessarily for all rhombuses?

All sides are equal in length.
Diagonals bisect each other at 90 degrees.
All interior angles are 90 degrees.
Opposite sides are parallel.

View Answer & Explanation

Correct Answer: Option C -

All interior angles are 90 degrees.

Explanation:

Both squares and rhombuses have equal sides and diagonals that bisect at right angles. However, a square must have all interior angles equal to $90^\circ$ , whereas a rhombus does not necessarily have $90^\circ$ angles.

Calculate the perimeter of a regular hexagon with a side length of $8 \text{ cm}$ .

32 cm
40 cm
48 cm
64 cm

View Answer & Explanation

Correct Answer: Option C -

48 cm

Explanation:

A regular hexagon has 6 equal sides. Perimeter $= 6 \times \text{side length} = 6 \times 8 = 48 \text{ cm}$ .

What is the area of a triangle with a base of $10 \text{ cm}$ and a height of $6 \text{ cm}$ ?

16 cm²
30 cm²
60 cm²
300 cm²

View Answer & Explanation

Correct Answer: Option B -

30 cm²

Explanation:

Area of a triangle $= \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 6 = 30 \text{ cm}^2$ .

The area of a circle is calculated using the formula $A = \pi r^2$ . Calculate the area of a circle with radius $7 \text{ cm}$ . (Take $\pi = \frac{22}{7}$ )

44 cm²
154 cm²
144 cm²
100 cm²

View Answer & Explanation

Correct Answer: Option B -

154 cm²

Explanation:

Area $= \frac{22}{7} \times 7^2 = \frac{22}{7} \times 49 = 22 \times 7 = 154 \text{ cm}^2$ .

Which quadrilateral has only one pair of parallel sides?

Parallelogram
Rectangle
Trapezium
Rhombus

View Answer & Explanation

Correct Answer: Option C -

Trapezium

Explanation:

A trapezium (or trapezoid) is defined as having exactly one pair of parallel sides. Parallelograms, rectangles, and rhombuses have two pairs.

Calculate the area of a parallelogram with a base of $12 \text{ m}$ and a perpendicular height of $5 \text{ m}$ .

30 m²
60 m²
17 m²
34 m²

View Answer & Explanation

Correct Answer: Option B -

60 m²

Explanation:

Area of a parallelogram $= \text{base} \times \text{height} = 12 \times 5 = 60 \text{ m}^2$ .

The sum of the interior angles of a quadrilateral is:

180 degrees
270 degrees
360 degrees
540 degrees

View Answer & Explanation

Correct Answer: Option C -

360 degrees

Explanation:

The sum of interior angles of a polygon is $(n-2) \times 180$ . For a quadrilateral ( $n=4$ ), sum $= (4-2) \times 180 = 360^\circ$ .

Find the area of a trapezium where the parallel sides are $8 \text{ cm}$ and $12 \text{ cm}$ , and the height is $5 \text{ cm}$ .

50 cm²
100 cm²
60 cm²
48 cm²

View Answer & Explanation

Correct Answer: Option A -

50 cm²

Explanation:

Area $= \frac{1}{2}(a+b)h = \frac{1}{2}(8+12) \times 5 = \frac{1}{2}(20) \times 5 = 10 \times 5 = 50 \text{ cm}^2$ .

If the diameter of a circle is $14 \text{ cm}$ , what is its circumference? (Take $\pi = \frac{22}{7}$ )

22 cm
44 cm
88 cm
154 cm

View Answer & Explanation

Correct Answer: Option B -

44 cm

Explanation:

Circumference $C = \pi d = \frac{22}{7} \times 14 = 22 \times 2 = 44 \text{ cm}$ .

A triangle with all three sides equal is called:

Isosceles
Scalene
Equilateral
Right-angled

View Answer & Explanation

Correct Answer: Option C -

Equilateral

Explanation:

An equilateral triangle has all three sides equal and all three angles equal to $60^\circ$ .

BECE Mathematics Geometry & Measurement Practice Questions & Answers

Module: Geometry & Measurement

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