OCR GCSE Maths · OCR 8

Basic Geometry

50 maths questions with worked answers with answers for OCR 8 Basic Geometry in OCR GCSE Maths (spec J560). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official OCR material.

All 50 questions and answers

Question 1 · 3D shapes · OCR 8.01d
How many faces, edges and vertices does a triangular prism have?
Answer:
Two triangles and three rectangles.
5 faces, 9 edges, 6 vertices.
Question 2 · Solids · OCR 8.01d
How many faces does a cube have?
Answer:
A cube has a top, a bottom and four side faces.
2 + 4 = 6 faces.
Question 3 · Solids · OCR 8.01d
How many vertices does a square-based pyramid have?
Answer:
The square base has 4 vertices; the apex adds 1.
4 + 1 = 5 vertices.
Question 4 · Constructions · OCR 8.01f
Which compass construction gives a triangle when three side lengths are given?
Answer:
Draw one side, then arcs of the other two lengths from each end.
Join the ends to where the arcs cross.
Question 5 · Coordinate geometry · OCR 8.01g · Higher only
A(1, 2), B(5, 2) and C(5, 5) form a triangle. Show it is right-angled and find AC.
Answer:
AB is horizontal and BC is vertical, so angle B = 90°.
AC² = 4² + 3² = 25, so AC = 5.
Question 6 · Transformations · OCR 8.01g
Translate (2, −1) by the vector 34. Give the image.
Answer:
Add 3 to the x-coordinate: 2 + 3 = 5.
Add 4 to the y-coordinate: −1 + 4 = 3.
The image is (5, 3).
Question 7 · Transformations · OCR 8.01g
Reflect the point (4, −2) in the x-axis.
Answer:
Reflection in the x-axis keeps x and changes the sign of y.
(4, −2) becomes (4, 2).
Question 8 · Transformations · OCR 8.01g
Reflect the point (3, 5) in the y-axis.
Answer:
Reflection in the y-axis changes the sign of x and keeps y.
(3, 5) becomes (−3, 5).
Question 9 · Transformations · OCR 8.01g
Reflect (2, −3) in the line y = x.
Answer:
Reflection in y = x swaps the coordinates.
(2, −3) becomes (−3, 2).
Question 10 · Constructions · OCR 8.02a
How do you construct the perpendicular bisector of a line AB?
Answer:
With compasses set more than half of AB, draw arcs from A and from B on both sides.
Join the two crossing points.
Question 11 · Constructions · OCR 8.02b
How do you bisect an angle with compasses?
Answer:
Draw an arc from the vertex cutting both arms. From each cut, draw arcs that cross.
Join the vertex to the crossing point.
Question 12 · Loci · OCR 8.02c
Describe the locus of points 3 cm from a fixed point P.
Answer:
All points at the same distance from P.
A circle with centre P and radius 3 cm.
Question 13 · Loci · OCR 8.02c
Describe the locus of points equidistant from two points A and B.
Answer:
Points the same distance from A and B.
The perpendicular bisector of AB.
Question 14 · Angle facts · OCR 8.03a
Angles around a point are 110°, 95° and x. Find x.
Answer:
Angles at a point sum to 360°.
x = 360 − 205 = 155°.
Question 15 · Triangles · OCR 8.03a
Two angles of a triangle are 48° and 67°. Find the third.
Answer:
Angles in a triangle sum to 180°.
180 − 115 = 65°.
Question 16 · Quadrilaterals · OCR 8.03a
Three angles of a quadrilateral are 85°, 100° and 70°. Find the fourth.
Answer:
Angles in a quadrilateral sum to 360°.
360 − 255 = 105°.
Question 17 · Proof · OCR 8.03a · Higher only
Prove that the angles in a triangle add up to 180°.
Answer:
Draw a line through one vertex parallel to the opposite side.
The two alternate angles and the vertex angle lie on a straight line, so they sum to 180°.
Question 18 · Angle facts · OCR 8.03b
Angles on a straight line are 3x and 2x. Find x.
Answer:
3x + 2x = 180.
x = 36°.
Question 19 · Parallel lines · OCR 8.03c
What is the relationship between alternate angles on parallel lines?
Answer:
They form a Z shape.
Alternate angles are equal.
Question 20 · Isosceles triangles · OCR 8.03c
An isosceles triangle has one angle of 40° between its two equal sides. Find the other two angles.
Answer:
180 − 40 = 140.
Each is 70°.
Question 21 · Angles · OCR 8.03c
Two parallel lines are crossed by a transversal. One angle is 63°. Find its corresponding angle.
Answer:
Corresponding angles formed by parallel lines are equal.
The corresponding angle is 63°.
Question 22 · Angles · OCR 8.03c
Co-interior angles between parallel lines are x and 72°. Find x.
Answer:
Co-interior angles add to 180°.
x = 180° − 72° = 108°.
Question 23 · Polygons · OCR 8.03d
Find the sum of the interior angles of a hexagon.
Answer:
(n − 2) × 180 with n = 6.
4 × 180 = 720°.
Question 24 · Polygons · OCR 8.03d
Find the size of each exterior angle of a regular octagon.
Answer:
Exterior angles sum to 360°.
360 ÷ 8 = 45°.
Question 25 · Polygons · OCR 8.03d
Each interior angle of a regular polygon is 150°. How many sides does it have?
Answer:
Exterior angle = 180 − 150 = 30°.
360 ÷ 30 = 12 sides.
Question 26 · Polygons · OCR 8.03d
Find each interior angle of a regular hexagon.
Answer:
Interior angle sum = (6 − 2) × 180° = 720°.
Each angle = 720° ÷ 6 = 120°.
Question 27 · Triangles · OCR 8.04a
An isosceles triangle has a vertex angle of 40°. Find each equal base angle.
Answer:
The two equal angles total 180° − 40° = 140°.
Each equal angle = 140° ÷ 2 = 70°.
Question 28 · Triangles · OCR 8.04a
An equilateral triangle has one angle marked x. Find x.
Answer:
All three angles of an equilateral triangle are equal.
180° ÷ 3 = 60°, so x = 60°.
Question 29 · Quadrilaterals · OCR 8.04b
State two properties of a rhombus.
Answer:
Any two from:
All four sides are equal. Opposite angles are equal. Diagonals bisect each other at right angles.
Question 30 · Quadrilaterals · OCR 8.04b
What is the difference between a kite and a parallelogram?
Answer:
A kite has two pairs of equal adjacent sides and one line of symmetry.
A parallelogram has two pairs of parallel, equal opposite sides.
Question 31 · Quadrilaterals · OCR 8.04b
Which quadrilateral has exactly one pair of parallel sides in UK terminology?
Answer:
Identify the quadrilateral with one pair of parallel sides.
In UK terminology it is a trapezium.
Question 32 · Quadrilaterals · OCR 8.04b
What is the sum of adjacent interior angles of a parallelogram?
Answer:
Adjacent sides meet across parallel lines, making co-interior angles.
Co-interior angles add to 180°.
Question 33 · Symmetry · OCR 8.04c
How many lines of symmetry does a regular pentagon have?
Answer:
A regular polygon has as many lines of symmetry as sides.
5.
Question 34 · Symmetry · OCR 8.04c
What is the order of rotational symmetry of a square?
Answer:
A square matches itself after turns of 90°, 180°, 270° and 360°.
Its rotational symmetry has order 4.
Question 35 · Symmetry · OCR 8.04c
How many lines of symmetry does an equilateral triangle have?
Answer:
Each vertex and the midpoint of its opposite side define one symmetry line.
There are 3 such lines.
Question 36 · Circle vocabulary · OCR 8.05a
Name the line segment that joins two points on a circle and passes through the centre.
Answer:
It is twice the radius.
The diameter.
Question 37 · Circle vocabulary · OCR 8.05a
What is a chord?
Answer:
A straight line joining two points on the circumference.
The diameter is the longest chord.
Question 38 · Circle theorems · OCR 8.05b · Higher only
The angle at the centre is 140°. Find the angle at the circumference subtended by the same arc.
Answer:
The angle at the centre is twice the angle at the circumference.
70°.
Question 39 · Circle theorems · OCR 8.05b · Higher only
Opposite angles of a cyclic quadrilateral: one is 105°. Find the other.
Answer:
Opposite angles in a cyclic quadrilateral add to 180°.
75°.
Question 40 · Circle theorems · OCR 8.05b · Higher only
An angle at the centre and an angle at the circumference stand on the same arc. The centre angle is 110°. Find the circumference angle.
Answer:
The angle at the centre is twice the angle at the circumference on the same arc.
110° ÷ 2 = 55°.
Question 41 · Circle theorems · OCR 8.05b · Higher only
Opposite angles of a cyclic quadrilateral are 72° and x. Find x.
Answer:
Opposite angles of a cyclic quadrilateral add to 180°.
x = 180° − 72° = 108°.
Question 42 · Circle theorems · OCR 8.05c · Higher only
What is the angle in a semicircle?
Answer:
An angle subtended by a diameter at the circumference.
90°.
Question 43 · Circle theorems · OCR 8.05d · Higher only
What can you say about two tangents drawn from the same external point?
Answer:
They are equal in length.
The line to the centre bisects the angle between them.
Question 44 · Circle theorems · OCR 8.05d · Higher only
Angles in the same segment: one is 38°. What is another angle in the same segment, subtended by the same chord?
Answer:
Angles in the same segment are equal.
38°.
Question 45 · Circle theorems · OCR 8.05d · Higher only
Two tangents from the same external point touch a circle. How do their lengths compare?
Answer:
Tangents drawn from the same external point have equal lengths.
Therefore the two tangent segments are equal.
Question 46 · Circle theorems · OCR 8.05d · Higher only
Two angles in the same segment of a circle stand on the same chord. One is 43°. Find the other.
Answer:
Angles in the same segment standing on the same chord are equal.
The other angle is 43°.
Question 47 · Circle theorems · OCR 8.05f · Higher only
What is the angle between a tangent and a radius at the point of contact?
Answer:
The tangent meets the radius at a right angle.
90°.
Question 48 · Circle theorems · OCR 8.05f · Higher only
A tangent touches a circle at T. What angle does the tangent make with radius OT?
Answer:
A tangent is perpendicular to the radius at the point of contact.
The angle is 90°.
Question 49 · Circle theorems · OCR 8.05g · Higher only
What does the alternate segment theorem state?
Answer:
The angle between a tangent and a chord is equal to the angle in the alternate segment.
That angle is at the circumference on the other side of the chord.
Question 50 · Plans and elevations · OCR 8.06b
What is the plan view of a cylinder standing upright?
Answer:
The view from above.
A circle.

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