Geometry: Shapes & Angles,polygons) GL ASSESSMENT QUESTIONS 11 plus exam part -6
Comprehensive GL Assessment 11+ Geometry Question Bank
SECTION 1: Angles & Types of Angles (10 Questions)
What type of angle is formed between the hands of a clock at 9:15?
A) Acute B) Right C) Obtuse D) ReflexAn angle measures 179°. What type of angle is it?
A) Acute B) Obtuse C) Reflex D) RightHow many acute angles does a right-angled isosceles triangle have?
Two angles are complementary. One measures 27°. What is the other?
A) 27° B) 63° C) 153° D) 333°Which of these is a reflex angle?
A) 89° B) 91° C) 179° D) 181°In a triangle, two angles are 45° and 45°. The third angle is:
A) Acute B) Obtuse C) Right D) ReflexA full circle is divided into 8 equal sectors. What type of angle is in each sector?
A) Acute B) Obtuse C) Right D) ReflexThe supplement of 105° is:
A) 75° B) 85° C) 95° D) 105°True or False: All angles in an equilateral triangle are acute.
Which of these cannot be the angles of a triangle?
A) 60°, 60°, 60° B) 30°, 60°, 90° C) 45°, 55°, 80° D) 70°, 80°, 90°
SECTION 2: Polygons (10 Questions)
A regular polygon has interior angles of 144°. How many sides does it have?
A) 8 B) 9 C) 10 D) 12The sum of interior angles of a heptagon is:
A) 720° B) 900° C) 1080° D) 1260°Each exterior angle of a regular 15-sided polygon measures:
A) 12° B) 24° C) 36° D) 48°How many diagonals can be drawn from one vertex of a nonagon?
True or False: A decagon has 10 sides.
The interior angles of a pentagon are 100°, 110°, 120°, 130° and x. Find x.
A) 80° B) 90° C) 100° D) 110°A regular polygon has 20 sides. What is the sum of its interior angles?
A) 2880° B) 3060° C) 3240° D) 3420°Which polygon has an interior angle sum of 1800°?
A) 10-sided B) 11-sided C) 12-sided D) 13-sidedThe exterior angle of a regular polygon is 18°. How many sides does it have?
A) 18 B) 20 C) 22 D) 24True or False: All regular polygons are convex.
SECTION 3: Properties of 2D Shapes (50 Questions)
Which triangle has no lines of symmetry?
A) Equilateral B) Isosceles C) Scalene D) Right-angledA quadrilateral with all sides equal but angles not 90° is:
A) Square B) Rhombus C) Rectangle D) TrapeziumHow many lines of symmetry does a regular hexagon have?
Which quadrilateral always has diagonals that bisect each other at 90°?
A) Rectangle B) Square C) Parallelogram D) TrapeziumAn isosceles triangle has a base of 8cm and equal sides of 6cm. What is its perimeter?
True or False: Every square is a rectangle.
What is the order of rotational symmetry of a parallelogram?
A rhombus has one angle of 70°. What is the opposite angle?
A) 70° B) 110° C) 140° D) 290°Which shape has exactly one pair of parallel sides?
A) Parallelogram B) Rhombus C) Trapezium D) KiteAll angles in a rectangle are:
A) Acute B) Right C) Obtuse D) EqualA triangle with sides 5cm, 12cm, 13cm is:
A) Acute B) Right-angled C) Obtuse D) EquilateralHow many equal sides does an isosceles triangle have?
True or False: A square is a special type of rhombus.
What is the specific name for a quadrilateral with both pairs of opposite sides parallel?
A) Trapezium B) Kite C) Parallelogram D) RhombusIn an equilateral triangle, each angle measures:
A) 45° B) 60° C) 90° D) 120°Which quadrilateral can have exactly one right angle?
A) Square B) Rectangle C) Trapezium D) RhombusA kite has two pairs of adjacent equal sides. How many lines of symmetry does it usually have?
True or False: All rectangles are parallelograms.
What type of triangle has angles 30°, 60°, and 90°?
A) Equilateral B) Isosceles C) Scalene D) Right-angledWhich statement is always true for a rhombus?
A) All angles are 90° B) All sides are equal C) Diagonals are equal D) No lines of symmetryHow many vertices does a pentagon have?
A trapezium has one pair of parallel sides. What is the sum of angles on the same side of the transversal?
True or False: A scalene triangle can be right-angled.
Which quadrilateral has diagonals that are always perpendicular?
A) Rectangle B) Square C) Parallelogram D) TrapeziumWhat is the perimeter of a square with area 64cm²?
An isosceles triangle has a vertex angle of 100°. What are the base angles?
True or False: Every rhombus is a kite.
How many degrees are there in each angle of a regular octagon?
Which triangle has all sides different lengths?
A) Equilateral B) Isosceles C) Scalene D) Right-angledA quadrilateral has rotational symmetry of order 2. What could it be?
A) Square only B) Rectangle only C) Parallelogram D) KiteWhat is the sum of angles in any quadrilateral?
True or False: A parallelogram can have exactly one right angle.
How many lines of symmetry does an equilateral triangle have?
Which quadrilateral has exactly one line of symmetry?
A) Square B) Rectangle C) Kite D) ParallelogramA triangle has sides measuring 7cm, 8cm, and 9cm. What type of triangle is it?
True or False: All squares are rhombuses.
What is the order of rotational symmetry of a regular pentagon?
Which quadrilateral has all properties of a rectangle and a rhombus?
How many pairs of parallel sides does a trapezium have?
An isosceles right-angled triangle has angles:
A) 45°, 45°, 90° B) 30°, 60°, 90° C) 60°, 60°, 60° D) 50°, 50°, 80°True or False: A rectangle has diagonals that are always perpendicular.
What type of triangle has exactly two equal sides?
How many right angles can a parallelogram have at most?
Which quadrilateral has diagonals that always bisect each other?
A) Kite B) Trapezium C) Parallelogram D) All quadrilateralsA triangle with angles 40°, 60°, 80° is:
A) Acute B) Right-angled C) Obtuse D) EquilateralTrue or False: A rhombus is always a square.
What is the perimeter of an equilateral triangle with side 12cm?
How many lines of symmetry does a regular decagon have?
Which triangle has all angles less than 90°?
A) Acute B) Obtuse C) Right-angled D) EquilateralA quadrilateral has exactly two lines of symmetry. It is not a rectangle. What is it?
SECTION 4: Angle Rules (30 Questions)
Angles on a straight line add up to:
A) 90° B) 180° C) 270° D) 360°Three angles around a point are 110°, 95°, and 75°. What is the fourth angle?
A) 70° B) 80° C) 90° D) 100°Vertically opposite angles are:
A) Supplementary B) Complementary C) Equal D) Right anglesIn triangle ABC, angle A = 50°, angle B = 60°. What is angle C?
Two angles are supplementary. One is 115°. What is the other?
Angles in a quadrilateral add up to:
A) 180° B) 270° C) 360° D) 450°Find the missing angle: In a triangle, angles are 35° and 45°. Third angle = ?
A) 80° B) 90° C) 100° D) 110°Two lines cross making angles of 40°, 140°, 40°, and x. What is x?
Angles a and b are on a straight line. a = 2b. Find b.
A) 30° B) 45° C) 60° D) 90°In parallelogram PQRS, angle P = 70°. What is angle R?
Three angles are 2x, 3x, and 4x. They are angles of a triangle. Find x.
A) 10° B) 20° C) 30° D) 40°Angles around a point: 85°, 95°, 110°, and y. Find y.
A) 60° B) 70° C) 80° D) 90°Two angles are complementary. Their difference is 30°. Find the larger angle.
A) 30° B) 45° C) 60° D) 75°In an isosceles triangle, the vertex angle is 40°. Find each base angle.
Angles on a straight line: 3x, 4x, and 5x. Find the smallest angle.
A) 30° B) 45° C) 60° D) 90°Four angles around a point are equal. What is each angle?
In a right-angled triangle, one acute angle is 28°. What is the other acute angle?
Angles of a quadrilateral are 80°, 90°, 100°, and z. Find z.
A) 80° B) 90° C) 100° D) 110°Two vertically opposite angles are (2x+10)° and (3x-20)°. Find x.
A) 10 B) 20 C) 30 D) 40In a pentagon, four angles are 100°, 110°, 120°, 130°. Find the fifth angle.
A) 80° B) 90° C) 100° D) 110°Angles a and b are supplementary. a is three times b. Find a.
A) 45° B) 60° C) 90° D) 135°Triangle angles: x, x+10, x+20. Find the largest angle.
A) 50° B) 60° C) 70° D) 80°Angles around a point: x, 2x, 3x, 4x, 5x. Find x.
A) 12° B) 18° C) 24° D) 30°In a rhombus, one angle is 50°. What is the adjacent angle?
Two angles on a straight line are 5:7. Find the smaller angle.
A) 60° B) 65° C) 70° D) 75°In triangle XYZ, angle X = 55°, angle Y = angle Z. Find angle Y.
Angles of a quadrilateral are in ratio 1:2:3:4. Find the largest angle.
A) 144° B) 120° C) 108° D) 72°Co-interior angles between parallel lines add up to:
Alternate angles between parallel lines are:
Corresponding angles between parallel lines are:
SECTION 5: Symmetry, Reflections, Rotations (50 Questions)
How many lines of symmetry does a square have?
What is the order of rotational symmetry of an equilateral triangle?
Which letter has exactly one line of symmetry?
A) A B) B C) H D) OWhen a shape is reflected in a mirror line, it is:
A) Enlarged B) Rotated C) Flipped D) TranslatedHow many lines of symmetry does a regular pentagon have?
The order of rotational symmetry of a shape is 3. How many times does it match itself in a full turn?
Which shape has infinite lines of symmetry?
A) Square B) Circle C) Equilateral triangle D) Regular hexagonTrue or False: A parallelogram has no lines of symmetry.
How many lines of symmetry does an isosceles triangle have?
What is the order of rotational symmetry of a rectangle?
Which transformation changes a shape's position but not its size or shape?
A) Reflection B) Rotation C) Translation D) All of theseA shape has rotational symmetry of order 1. This means:
A) It looks the same in only one position B) It has no rotational symmetry C) Both A and B D) It has infinite rotational symmetryHow many lines of symmetry does the letter H have?
What is the order of rotational symmetry of a regular octagon?
When you rotate a shape 180° about a point, it is called:
A) Quarter turn B) Half turn C) Three-quarter turn D) Full turnWhich shape has exactly two lines of symmetry?
A) Square B) Rectangle C) Rhombus D) All of theseTrue or False: A scalene triangle has rotational symmetry.
How many lines of symmetry does a kite have?
What is the order of rotational symmetry of the letter S?
When a shape is reflected, the image is:
A) Congruent B) Similar C) Enlarged D) ReducedWhich shape has the most lines of symmetry?
A) Square B) Regular hexagon C) Circle D) Equilateral triangleHow many lines of symmetry does a regular heptagon have?
What is the order of rotational symmetry of a square?
True or False: All regular polygons have both line and rotational symmetry.
How many lines of symmetry does a parallelogram have?
Which letter has rotational symmetry of order 2?
A) A B) H C) N D) All of theseWhen you reflect point (3,4) in the x-axis, you get:
A) (3,-4) B) (-3,4) C) (-3,-4) D) (4,3)How many lines of symmetry does an equilateral triangle have?
What is the order of rotational symmetry of a regular decagon?
True or False: A trapezium can have line symmetry.
How many lines of symmetry does a rectangle have?
Which shape has rotational symmetry but no line symmetry?
A) Square B) Parallelogram C) Rhombus D) KiteWhen you rotate point (2,3) 90° clockwise about the origin, you get:
A) (3,-2) B) (-3,2) C) (-2,-3) D) (3,2)How many lines of symmetry does a regular nonagon have?
What is the order of rotational symmetry of an isosceles triangle?
True or False: A circle has rotational symmetry of infinite order.
How many lines of symmetry does a rhombus have?
Which transformation produces a mirror image?
A) Rotation B) Reflection C) Translation D) EnlargementWhen point (5,1) is reflected in the y-axis, the image is:
A) (-5,1) B) (5,-1) C) (-5,-1) D) (1,5)How many lines of symmetry does a regular dodecagon (12 sides) have?
What is the order of rotational symmetry of a parallelogram?
True or False: All quadrilaterals have at least one line of symmetry.
How many lines of symmetry does an isosceles trapezium have?
Which letter has exactly two lines of symmetry?
A) H B) I C) X D) All of theseWhen shape A is rotated 270° clockwise, it is the same as rotating it:
A) 90° clockwise B) 90° anticlockwise C) 180° D) 360°How many lines of symmetry does a scalene triangle have?
What is the order of rotational symmetry of a kite?
True or False: A square has more lines of symmetry than a regular hexagon.
How many lines of symmetry does the number 8 have?
Which shape has exactly four lines of symmetry?
A) Square B) Rectangle C) Rhombus D) Regular pentagon
SECTION 6: Coordinates (50 Questions)
In which quadrant is point (3,4)?
A) I B) II C) III D) IVThe point (0,0) is called:
A) Origin B) Axis C) Vertex D) IntersectionPoint (-2,5) is in quadrant:
A) I B) II C) III D) IVThe x-coordinate of point (7,-3) is:
A) 7 B) -3 C) 3 D) -7What are the coordinates of a point 4 units right and 3 units up from (1,2)?
A) (5,5) B) (5,3) C) (4,3) D) (4,5)Point (4,-1) is in quadrant:
A) I B) II C) III D) IVThe distance between (1,1) and (1,5) is:
A) 0 B) 4 C) 5 D) 6Midpoint of (2,4) and (6,8) is:
A) (4,6) B) (4,4) C) (6,4) D) (8,12)Point (-3,-2) is in quadrant:
A) I B) II C) III D) IVTrue or False: In quadrant II, x is positive and y is negative.
What are the coordinates of the point 3 units left of (5,7)?
A) (2,7) B) (8,7) C) (5,4) D) (5,10)The y-coordinate of point (-4,6) is:
A) -4 B) 6 C) 4 D) -6Distance between (0,0) and (3,4) is:
A) 3 B) 4 C) 5 D) 7Midpoint of (1,3) and (5,11) is:
A) (3,7) B) (3,6) C) (6,14) D) (4,8)Point (0,5) lies on:
A) x-axis B) y-axis C) origin D) quadrant ITrue or False: Point (-2,-3) is closer to the origin than point (1,1).
What are the coordinates after reflecting (4,3) in the x-axis?
A) (4,-3) B) (-4,3) C) (-4,-3) D) (3,4)Point (5,0) lies on:
A) x-axis B) y-axis C) origin D) quadrant IDistance between (2,3) and (5,7) is:
A) 3 B) 4 C) 5 D) 7Midpoint of (-2,4) and (6,10) is:
A) (2,7) B) (4,14) C) (2,14) D) (4,7)Which point is farthest from the origin?
A) (1,1) B) (2,2) C) (3,1) D) (1,3)True or False: The point (a,b) and (b,a) are always the same.
Reflect (3,-2) in the y-axis:
A) (-3,-2) B) (3,2) C) (-3,2) D) (2,3)Point (-4,0) lies on:
A) x-axis B) y-axis C) origin D) quadrant IIDistance between (-1,-1) and (2,3) is:
A) 3 B) 4 C) 5 D) 6Midpoint of (0,0) and (8,6) is:
A) (4,3) B) (8,6) C) (6,4) D) (3,4)Which quadrant contains points with negative x and positive y?
True or False: Points (2,3), (2,5), (2,7) are collinear.
Rotate (2,3) 90° clockwise about the origin:
A) (3,-2) B) (-3,2) C) (-2,-3) D) (3,2)Point (0,-3) lies on:
A) x-axis B) y-axis C) origin D) quadrant IVDistance between (4,1) and (1,5) is:
A) 3 B) 4 C) 5 D) 6Midpoint of (-3,-4) and (5,2) is:
A) (1,-1) B) (2,-2) C) (4,6) D) (8,6)Which point is closest to (0,0)?
A) (1,2) B) (2,1) C) (1,1) D) (2,2)True or False: The midpoint of (a,b) and (c,d) is ((a+c)/2, (b+d)/2).
Reflect (-2,5) in the origin:
A) (2,-5) B) (-2,-5) C) (2,5) D) (5,-2)Point (3,-3) is in quadrant:
A) I B) II C) III D) IVDistance between (-2,-3) and (1,1) is:
A) 3 B) 4 C) 5 D) 6Midpoint of (7,2) and (3,8) is:
A) (5,5) B) (4,5) C) (5,4) D) (10,10)Which point lies on the line x = 4?
A) (4,0) B) (0,4) C) (4,4) D) All of theseTrue or False: Points (1,2), (3,4), (5,6) lie on a straight line.
Rotate (4,1) 180° about the origin:
A) (-4,-1) B) (-4,1) C) (4,-1) D) (1,4)Point (-5,-1) is in quadrant:
A) I B) II C) III D) IVDistance between (6,8) and (0,0) is:
A) 6 B) 8 C) 10 D) 14Midpoint of (a,b) and (a,c) is:
A) (a, (b+c)/2) B) ((a+b)/2, c) C) (b, (a+c)/2) D) ((b+c)/2, a)Which point is on the y-axis?
A) (3,0) B) (0,3) C) (3,3) D) (0,0)True or False: The distance between (x₁,y₁) and (x₂,y₂) is √[(x₂-x₁)² + (y₂-y₁)²].
Reflect (0,4) in the x-axis:
A) (0,-4) B) (4,0) C) (-4,0) D) (0,4)Point (2.5, -3.5) is in quadrant:
A) I B) II C) III D) IVDistance between (10,0) and (0,10) is:
A) 10 B) 10√2 C) 20 D) 100Midpoint of (2.5, 3.5) and (5.5, 8.5) is:
A) (4,6) B) (3,5) C) (4,5) D) (3,6)
SECTION 7: Properties of 3D Shapes (30 Questions)
How many faces does a cube have?
A cuboid has:
A) 6 faces, 12 edges, 8 vertices
B) 8 faces, 12 edges, 6 vertices
C) 6 faces, 8 edges, 12 vertices
D) 4 faces, 12 edges, 8 verticesHow many edges does a triangular prism have?
A square-based pyramid has how many vertices?
Which shape has 2 circular faces and 1 curved surface?
A) Cone B) Cylinder C) Sphere D) HemisphereHow many faces does a tetrahedron have?
True or False: A sphere has faces, edges, and vertices.
How many edges meet at each vertex of a cube?
Which shape has exactly one vertex?
A) Cube B) Cone C) Cylinder D) SphereA hexagonal prism has how many faces?
Euler's formula for polyhedra is:
A) F + V = E + 2 B) F + E = V + 2 C) E + V = F + 2 D) F = V + E - 2How many rectangular faces does a triangular prism have?
Which shape has all faces as triangles?
A) Cube B) Tetrahedron C) Square pyramid D) Both B and CTrue or False: All prisms have two identical parallel faces.
How many edges does a square-based pyramid have?
Which shape has 6 square faces?
A cylinder has how many flat faces?
How many vertices does a pentagonal prism have?
Which shape has a circular base and a vertex?
A) Cylinder B) Cone C) Sphere D) HemisphereTrue or False: A cube is a special cuboid.
How many faces does a pentagonal pyramid have?
Which 3D shape has no edges or vertices?
A) Cube B) Sphere C) Cone D) CylinderA triangular-based pyramid has how many edges?
How many more vertices does a cube have than a tetrahedron?
Which shape has exactly 5 faces?
A) Cube B) Square pyramid C) Triangular prism D) Both B and CTrue or False: All pyramids have a polygonal base and triangular faces.
How many edges does an octagonal prism have?
Which shape has exactly 4 vertices?
A) Cube B) Tetrahedron C) Square pyramid D) Triangular prismA cuboid measuring 3cm × 4cm × 5cm has volume:
A) 12 cm³ B) 47 cm³ C) 60 cm³ D) 120 cm³True or False: All faces of a cube are squares.
SECTION 8: Fictional "Previous Year Paper" (50 Questions)
Calculate: 347 + 589
What is 3/5 of 250?
Write 0.625 as a fraction in simplest form.
Simplify: 12:18
Find the mean of 4, 7, 9, 12, 13
A shirt costs £28.50 with 20% VAT. What is the price before VAT?
Next number in sequence: 3, 8, 15, 24, 35, ?
15% of £240 = ?
Solve: 3x - 7 = 20
Area of triangle with base 12cm, height 5cm
Convert 2.5kg to grams
Time: 3 hours 45 minutes = ? minutes
Probability of rolling an even number on a fair dice
Share £120 in ratio 3:5
Estimate: 398 × 51
Round 6.857 to 2 decimal places
Reciprocal of 8
Mode of 3, 5, 7, 5, 8, 3, 5
Perimeter of rectangle 8cm by 5cm
Value of 4³
A train travels 240km in 3 hours. Average speed?
Factorise: 12x + 18
Solve: 2(x - 3) = 14
Median of 7, 3, 9, 5, 2
Recipe for 4 needs 300g flour. How much for 10?
Range of 15, 22, 18, 25, 20
Pack of 8 pens costs £4.80. Cost per pen?
Decrease £160 by 25%
Increase £80 by 15%
0.3 × 0.4
5/8 as a decimal
2/3 + 1/4
5/6 - 1/3
3/5 × 20
4/7 ÷ 2
Write 45% as a fraction
Write 3/20 as a percentage
Find x: 2:5 = x:20
If a = 3, b = 4, find 2a² - b
Simplify: 5a + 3b - 2a + b
Expand: 3(x + 4)
Factorise: 6x - 9
Solve: 5y + 7 = 32
I think of a number, double it, add 5, get 21. The number is?
Angles in triangle are 2x, 3x, 4x. Find x.
Area of circle with radius 7cm (Ο = 22/7)
Circumference of circle with diameter 14cm
Volume of cube with side 6cm
Surface area of cuboid 3×4×5 cm
Convert 3.5 litres to ml
SECTION 9: Previous Year GL Assessment Styles (50 Questions)
Which angle is acute?
A) 91° B) 179° C) 89° D) 181°Sum of angles in a quadrilateral is:
A) 180° B) 270° C) 360° D) 450°How many sides does a heptagon have?
A) 5 B) 6 C) 7 D) 8Which triangle has all sides equal?
A) Scalene B) Isosceles C) Equilateral D) Right-angledOrder of rotational symmetry of a square is:
A) 2 B) 3 C) 4 D) 5Point (3,-4) is in quadrant:
A) I B) II C) III D) IVHow many faces does a triangular prism have?
A) 4 B) 5 C) 6 D) 7Angles on a straight line sum to:
A) 90° B) 180° C) 270° D) 360°Which quadrilateral has one pair of parallel sides?
A) Parallelogram B) Rhombus C) Trapezium D) KiteRegular polygon with interior angle 135° has how many sides?
A) 6 B) 8 C) 10 D) 12Cube has how many edges?
A) 6 B) 8 C) 12 D) 24Complementary angles add to:
A) 90° B) 180° C) 270° D) 360°How many lines of symmetry does a rectangle have?
A) 1 B) 2 C) 3 D) 4Midpoint of (1,3) and (5,7) is:
A) (3,5) B) (4,4) C) (3,4) D) (4,5)Which shape has exactly 5 vertices?
A) Cube B) Square pyramid C) Triangular prism D) CuboidAngles in triangle sum to:
A) 90° B) 180° C) 270° D) 360°How many sides does a decagon have?
A) 8 B) 9 C) 10 D) 12Which quadrilateral has diagonals that bisect at right angles?
A) Rectangle B) Parallelogram C) Rhombus D) TrapeziumPoint (-2,3) reflected in y-axis gives:
A) (2,3) B) (-2,-3) C) (2,-3) D) (3,-2)How many edges does a square-based pyramid have?
A) 5 B) 6 C) 8 D) 10Supplementary angles add to:
A) 90° B) 180° C) 270° D) 360°Order of rotational symmetry of equilateral triangle is:
A) 1 B) 2 C) 3 D) 4Distance between (0,0) and (6,8) is:
A) 6 B) 8 C) 10 D) 14Which shape has 2 circular faces?
A) Cone B) Cylinder C) Sphere D) HemisphereAngles around a point sum to:
A) 90° B) 180° C) 270° D) 360°How many vertices does a cube have?
A) 6 B) 8 C) 12 D) 24Which triangle has two equal sides?
A) Scalene B) Isosceles C) Equilateral D) Right-angledPoint (4,0) lies on:
A) x-axis B) y-axis C) origin D) quadrant IHow many faces does a tetrahedron have?
A) 3 B) 4 C) 5 D) 6Vertically opposite angles are:
A) Equal B) Supplementary C) Complementary D) NoneRegular hexagon has how many lines of symmetry?
A) 3 B) 6 C) 9 D) 12Midpoint of (0,0) and (10,6) is:
A) (5,3) B) (6,5) C) (3,5) D) (5,6)Which shape has exactly one vertex?
A) Cube B) Cylinder C) Cone D) SphereAngles in right-angled triangle: one is 35°, other acute angle is:
A) 35° B) 55° C) 65° D) 145°How many diagonals from one vertex of hexagon?
A) 2 B) 3 C) 4 D) 5Which quadrilateral is also a parallelogram?
A) Trapezium B) Kite C) Rectangle D) All of thesePoint (0,-5) lies on:
A) x-axis B) y-axis C) origin D) quadrant IVHow many edges does a triangular pyramid have?
A) 4 B) 6 C) 8 D) 12Sum of exterior angles of any polygon is:
A) 180° B) 360° C) 540° D) 720°Reflection of (5,-2) in x-axis is:
A) (-5,2) B) (5,2) C) (-5,-2) D) (2,5)Which triangle has no equal sides?
A) Scalene B) Isosceles C) Equilateral D) Right-angledHow many faces does a pentagonal prism have?
A) 5 B) 6 C) 7 D) 8Angles in isosceles triangle: vertex=40°, base angles=
A) 40° each B) 50° each C) 60° each D) 70° eachPoint in quadrant III has signs:
A) (+,+) B) (-,+) C) (-,-) D) (+,-)How many vertices does a hexagonal prism have?
A) 8 B) 12 C) 16 D) 18Area of square with perimeter 20cm is:
A) 25 cm² B) 20 cm² C) 16 cm² D) 100 cm²Volume of cuboid 4×5×6 cm is:
A) 15 cm³ B) 60 cm³ C) 120 cm³ D) 240 cm³Circumference of circle radius 7cm (Ο=22/7) is:
A) 22 cm B) 44 cm C) 88 cm D) 154 cmArea of triangle base 10cm height 6cm is:
A) 16 cm² B) 30 cm² C) 60 cm² D) 120 cm²Surface area of cube side 3cm is:
A) 9 cm² B) 18 cm² C) 27 cm² D) 54 cm²
ANSWERS WITH EXPLANATIONS
SECTION 1: Angles & Types of Angles
1. C) Obtuse
At 9:15, hour hand is slightly past 9, minute hand at 3. Angle is more than 90°, less than 180°, so obtuse.
2. B) Obtuse
179° is between 90° and 180°, so obtuse.
3. 2
Right-angled isosceles triangle has angles 90°, 45°, 45°. Acute angles are those <90°, so both 45° angles are acute → 2.
4. B) 63°
Complementary angles sum to 90°, so 90° – 27° = 63°.
5. D) 181°
Reflex angle is between 180° and 360°.
6. C) Right
Third angle = 180° – (45°+45°) = 90°, so right-angled triangle.
7. B) Obtuse
Each sector angle = 360°/8 = 45°, so acute? Wait — 45° is acute, but given options: acute? No, but 45° is acute → Wait, the question says: 360°/8 = 45°, which is acute. But options include acute, obtuse, right, reflex. So A) Acute is correct. Mist in my reading? Let’s check: full circle 360°, divided into 8 sectors: each 45°, which is acute.
Given their options: A) Acute ✅
8. A) 75°
Supplementary angles sum to 180°, so 180° – 105° = 75°.
9. True
Each angle in equilateral triangle = 60°, which is <90°, so acute.
10. D) 70°, 80°, 90°
Sum of angles in triangle = 180°, but 70°+80°+90° = 240° ≠ 180°, so cannot be.
SECTION 2: Polygons
11. C) 10
Interior angle = 144°, exterior angle = 180° – 144° = 36°. Number of sides = 360°/36° = 10.
12. B) 900°
Sum = (n–2)×180°, n=7 → 5×180° = 900°.
13. B) 24°
Exterior angle = 360°/15 = 24°.
14. 6
Nonagon has 9 sides. From one vertex, diagonals = total vertices – 3 = 9–3 = 6.
15. True
Deca = 10.
16. A) 80°
Sum of interior angles of pentagon = (5–2)×180° = 540°.
Given angles sum = 100+110+120+130 = 460°, so x = 540–460 = 80°.
17. C) 3240°
Sum = (20–2)×180° = 18×180 = 3240°.
18. C) 12-sided
Sum = (n–2)×180° = 1800° → n–2 = 10 → n=12.
19. B) 20
Exterior angle = 18° → number of sides = 360°/18° = 20.
20. True
Regular polygons have equal sides and angles, and are always convex.
SECTION 3: Properties of 2D Shapes
21. C) Scalene
Scalene triangle has no equal sides, so no symmetry lines.
22. B) Rhombus
All sides equal, angles not 90° → rhombus.
23. 6
Regular hexagon has 6 lines of symmetry.
24. B) Square
Only square (and rhombus) have perpendicular bisecting diagonals, but square always has 90° bisect.
25. 20 cm
Perimeter = 8+6+6 = 20 cm.
26. True
Square is a rectangle with all sides equal.
27. 2
Parallelogram has rotational symmetry of order 2 (180° rotation).
28. A) 70°
In rhombus, opposite angles are equal.
29. C) Trapezium
Trapezium has exactly one pair of parallel sides.
30. D) Equal
All are 90°, so equal.
31. B) Right-angled
5²+12²=25+144=169=13² → Pythagoras holds, so right-angled.
32. 2
Isosceles has 2 equal sides.
33. True
Square is a rhombus with right angles.
34. C) Parallelogram
Both pairs of opposite sides parallel = parallelogram.
35. B) 60°
Equilateral triangle angles = 60° each.
36. C) Trapezium
Trapezium can have exactly one right angle.
37. 1
A kite usually has one line of symmetry.
38. True
Rectangle has both pairs of opposite sides parallel.
39. D) Right-angled
Angles include 90°, so right-angled triangle.
40. B) All sides are equal
Definition of rhombus.
41. 5
Pentagon has 5 vertices.
42. 180°
Angles on same side of transversal between parallel lines sum to 180°.
43. True
Scalene triangle can have a right angle.
44. B) Square
Square’s diagonals are perpendicular (also rhombus, but not always perpendicular unless square).
45. 32 cm
Area = 64 cm² → side = √64 = 8 cm → perimeter = 32 cm.
46. 40° each
Base angles = (180°–100°)/2 = 40°.
47. True
Rhombus has adjacent sides equal, so fits kite definition.
48. 135°
Octagon interior each = (8–2)×180°/8 = 1080°/8 = 135°.
49. C) Scalene
All sides different.
50. C) Parallelogram
Order 2 rotational symmetry → parallelogram.
51. 360°
Sum of angles in quadrilateral.
52. False
Parallelogram having one right angle forces all to be right angles.
53. 3
Equilateral triangle has 3 lines of symmetry.
54. C) Kite
Kite has exactly one line of symmetry.
55. Acute triangle
All sides different, all angles <90° because 7²+8² > 9²? Check: 49+64=113 > 81 → all angles acute.
56. True
Square is a rhombus (all sides equal) with right angles.
57. 5
Regular pentagon has rotational symmetry order 5.
58. Square
Has properties of both rectangle and rhombus.
59. 1 pair
Trapezium has exactly one pair of parallel sides.
60. A) 45°, 45°, 90°
Isosceles right triangle angles.
61. False
Rectangle diagonals are equal but not perpendicular (except square).
62. Isosceles triangle
Exactly two equal sides.
63. 4
Parallelogram can be rectangle → 4 right angles.
64. C) Parallelogram
Parallelogram diagonals bisect each other.
65. A) Acute
All angles <90°.
66. False
Rhombus need not have right angles, so not always square.
67. 36 cm
Perimeter = 3×12 = 36 cm.
68. 10
Regular decagon has 10 lines of symmetry.
69. A) Acute
All angles <90°.
70. Rhombus
Two lines of symmetry, not rectangle → rhombus.
SECTION 4: Angle Rules
71. B) 180°
Angles on a straight line sum to 180°.
72. B) 80°
Sum around point = 360°, so 360° – (110°+95°+75°) = 360° – 280° = 80°.
73. C) Equal
Vertically opposite angles are equal.
74. 70°
Angle C = 180° – (50°+60°) = 70°.
75. 65°
Supplementary: 180° – 115° = 65°.
76. C) 360°
Sum of angles in quadrilateral.
77. C) 100°
Third angle = 180° – (35°+45°) = 100°.
78. 140°
Vertically opposite angles: x is opposite 140°, so x = 140°.
79. C) 60°
a + b = 180°, a = 2b → 2b + b = 180° → 3b = 180° → b = 60°.
80. 110°
In parallelogram, opposite angles equal, adjacent supplementary. Angle P = 70°, angle R opposite = 70°? Wait, adjacent? No: angle R is opposite angle P? Actually, in parallelogram PQRS, angle P opposite is R, so equal 70°? But that’s not an option in original question? In this standalone: if P=70°, angle R opposite = 70°, but if they mean adjacent angle to P = 180°–70°=110°, which is angle Q or S. Since not options, likely they mean angle R = 70° or 110°? Let’s check typical question: P and R are opposite, so equal = 70°; but if P=70°, angle S = 110°. Possibly question says: In parallelogram PQRS, angle P=70°, find angle R? R is opposite P = 70°. But maybe intended: angle Q or S? Usually supplementary. If they ask “adjacent angle” = 110°. Since here it’s just “What is angle R?” — opposite, so 70°. But in this set without options, maybe they imply supplementary? Let's proceed: If P=70°, adjacent to R? Actually R is opposite P. Possibly misprint. Common supplementary = 110°.
Given typical style: In parallelogram, consecutive angles supplementary. So if P=70°, then Q=110°, R=70°, S=110°. So angle R = 70°. But they write 110° in answer? Let’s assume supplementary: 180°–70°=110° if R is adjacent? No, R is opposite. So 70°.
Given this is section 4, Q80 likely 70°. But wait, earlier similar in Q81 etc. Let’s keep as per common: If they ask “angle R” and P=70°, and PQRS in order, P opposite R, so 70°.
But for consistency, I'll note: in the question list, they gave no options here but in original list it’s part of set with options: In parallelogram PQRS, angle P = 70°, what is angle R? Answer: 70° (opposite equal).
Given possible misprint, but per property: Opposite angles equal.
But in my answer key I'll put: 70°.
Actually, checking original: Q80: “In parallelogram PQRS, angle P = 70°. What is angle R?” → 70°.
81. B) 20°
Angles of triangle: 2x+3x+4x=9x=180° → x=20°.
82. B) 70°
Sum around point = 360°, so y=360°–(85°+95°+110°)=360°–290°=70°.
83. C) 60°
Let angles be a and b, a+b=90°, a–b=30° → adding: 2a=120° → a=60°, b=30°. Larger = 60°.
84. 70° each
Base angles = (180°–40°)/2 = 70°.
85. B) 45°
3x+4x+5x=12x=180° → x=15°, smallest = 3x = 45°.
86. 90°
Four equal angles around point: 4x=360° → x=90°.
87. 62°
Other acute = 90°–28°=62°.
88. B) 90°
z = 360°–(80°+90°+100°)=360°–270°=90°.
89. C) 30
Vertically opposite: 2x+10=3x–20 → 10+20=3x–2x → x=30.
90. A) 80°
Sum of interior pentagon = (5–2)×180°=540°, given angles sum=100+110+120+130=460°, so fifth = 540–460=80°.
91. D) 135°
a+b=180°, a=3b → 3b+b=180° → 4b=45° → b=45°, a=135°.
92. C) 70°
x + (x+10) + (x+20) = 3x+30=180° → 3x=150° → x=50°, largest = x+20=70°.
93. C) 24°
x+2x+3x+4x+5x=15x=360° → x=24°.
94. 130°
Adjacent angles in rhombus are supplementary: 180°–50°=130°.
95. D) 75°
Angles ratio 5:7, sum=180° → 5k+7k=12k=180° → k=15°, smaller=5k=75°.
96. 62.5°
Angle Y = angle Z, so 55° + 2Y = 180° → 2Y=125° → Y=62.5°.
97. A) 144°
Angles ratio 1:2:3:4, total parts=10, sum=360° → each part=36°, largest=4×36°=144°.
98. 180°
Co-interior angles between parallel lines sum to 180°.
99. Equal
Alternate angles are equal.
100. Equal
Corresponding angles are equal.
SECTION 5: Symmetry, Reflections, Rotations
101. 4
Square has 4 lines of symmetry.
102. 3
Equilateral triangle rotational symmetry order 3.
103. A) A
Letter A has one vertical line of symmetry.
104. C) Flipped
Reflection flips shape over mirror line.
105. 5
Regular pentagon has 5 lines of symmetry.
106. 3 times
Order 3 means matches itself 3 times in 360°.
107. B) Circle
Circle has infinite lines of symmetry.
108. False
A parallelogram has no lines of symmetry unless it’s a rhombus or rectangle? Actually general parallelogram: no lines of symmetry. So True? Wait: parallelogram (general) has no lines of symmetry. So "True" is correct for "no lines of symmetry" but they say "True or False: A parallelogram has no lines of symmetry" → True.
109. 1
Isosceles triangle has 1 line of symmetry.
110. 2
Rectangle rotational symmetry order 2.
111. D) All of these
All are transformations preserving size and shape (congruence).
112. C) Both A and B
Order 1 means only matches in original position → no rotational symmetry.
113. 2
Letter H has 2 lines of symmetry (vertical and horizontal).
114. 8
Regular octagon rotational symmetry order 8.
115. B) Half turn
180° rotation = half turn.
116. B) Rectangle
Rectangle has 2 lines of symmetry. Square has 4, rhombus has 2 only if square? Actually rhombus has 2 if not square. But "All of these" is false because square has 4. So only rectangle fits exactly 2 lines of symmetry? But square is also rectangle but special. They likely mean shape with exactly 2 lines = rectangle.
But answer given: B) Rectangle only.
117. False
Scalene triangle has no rotational symmetry.
118. 1
Kite has 1 line of symmetry.
119. 2
Letter S has rotational symmetry order 2 (180°).
120. A) Congruent
Reflection produces congruent image.
121. C) Circle
Circle has infinite lines of symmetry.
122. 7
Regular heptagon has 7 lines of symmetry.
123. 4
Square rotational symmetry order 4.
124. True
All regular polygons have both.
125. 0
General parallelogram has no lines of symmetry.
126. B) H
H has rotational symmetry order 2.
127. A) (3,-4)
Reflection in x-axis changes sign of y.
128. 3
Equilateral triangle has 3 lines of symmetry.
129. 10
Regular decagon rotational symmetry order 10.
130. True
Isosceles trapezium has 1 line of symmetry.
131. 2
Rectangle has 2 lines of symmetry.
132. B) Parallelogram
Parallelogram has rotational symmetry order 2, no line symmetry unless special.
133. A) (3,-2)
90° clockwise: (x,y) → (y,-x) = (3,-2).
134. 9
Regular nonagon has 9 lines of symmetry.
135. 1
Isosceles triangle rotational symmetry order 1 (none essentially).
136. True
Circle matches itself at any rotation.
137. 2
Rhombus has 2 lines of symmetry.
138. B) Reflection
Mirror image = reflection.
139. A) (-5,1)
Reflection in y-axis changes sign of x.
140. 12
Regular dodecagon has 12 lines of symmetry.
141. 2
Parallelogram rotational symmetry order 2.
142. False
E.g., scalene quadrilateral has none.
143. 1
Isosceles trapezium has 1 line of symmetry.
144. C) X
X has 2 lines of symmetry (and H, I also? H has 2, I has 2? Actually I has 2 lines if with serifs? Usually capital I has 2 lines: vertical and horizontal? Wait, I has 1 horizontal? Actually I with top/bottom bars: 2 lines (horizontal, vertical). They likely mean X has 2 lines. Option D says All of these: H, I, X all have 2 lines. So D).
145. B) 90° anticlockwise
270° clockwise = 90° anticlockwise.
146. 0
Scalene triangle no lines of symmetry.
147. 1
Kite rotational symmetry order 1.
148. False
Square: 4 lines, regular hexagon: 6 lines, so hexagon more.
149. 2
Number 8 has 2 lines of symmetry (vertical, horizontal).
150. A) Square
Square has 4 lines of symmetry.
SECTION 6: Coordinates
151. A) I
(+,+) → Quadrant I.
152. A) Origin
(0,0) is origin.
153. B) II
(-,+) → Quadrant II.
154. A) 7
x-coordinate is 7.
155. A) (5,5)
(1+4, 2+3) = (5,5).
156. D) IV
(+,-) → Quadrant IV.
157. B) 4
Same x, distance = |5–1| = 4.
158. A) (4,6)
Midpoint = ((2+6)/2, (4+8)/2) = (4,6).
159. C) III
(-,-) → Quadrant III.
160. False
Quadrant II: x negative, y positive.
161. A) (2,7)
3 left: subtract from x: (5–3,7) = (2,7).
162. B) 6
y-coordinate is 6.
163. C) 5
Distance = √(3²+4²) = 5.
164. A) (3,7)
Midpoint = ((1+5)/2, (3+11)/2) = (3,7).
165. B) y-axis
x=0, y≠0 → on y-axis.
166. False
Distance from origin: (-2,-3) = √(4+9)=√13≈3.6; (1,1)=√2≈1.4 → (1,1) closer.
167. A) (4,-3)
Reflect in x-axis: (x,-y).
168. A) x-axis
y=0, x≠0 → on x-axis.
169. C) 5
Distance = √[(5–2)²+(7–3)²] = √(9+16)=5.
170. A) (2,7)
Midpoint = ((-2+6)/2, (4+10)/2) = (2,7).
171. C) (3,1)
Distance from origin: (1,1)=√2, (2,2)=√8, (3,1)=√10, (1,3)=√10 → farthest: √10 largest among them? Wait: (3,1) and (1,3) both √10, (2,2)=√8≈2.83, (1,1)=1.41. So farthest: (3,1) or (1,3). Options: C) (3,1) listed.
172. False
(a,b) and (b,a) are symmetric over y=x, not always same unless a=b.
173. A) (-3,-2)
Reflect in y-axis: (-x,y) → (-3,-2).
174. A) x-axis
y=0 → on x-axis.
175. C) 5
Distance = √[(2+1)²+(3+1)²] = √(9+16)=5.
176. A) (4,3)
Midpoint = ((0+8)/2, (0+6)/2) = (4,3).
177. Quadrant II
Negative x, positive y.
178. True
All have x=2 → vertical line → collinear.
179. A) (3,-2)
90° clockwise: (x,y)→(y,-x) → (3,-2).
180. B) y-axis
x=0, y=-3 → on y-axis.
181. C) 5
Distance = √[(1–4)²+(5–1)²] = √(9+16)=5.
182. A) (1,-1)
Midpoint = ((-3+5)/2, (-4+2)/2) = (1,-1).
183. C) (1,1)
Distance from origin: √2≈1.41 smallest.
184. True
Midpoint formula.
185. A) (2,-5)
Reflection in origin: (-x,-y) → (2,-5).
186. D) IV
(+,-) → Quadrant IV.
187. C) 5
Distance = √[(1+2)²+(1+3)²] = √(9+16)=5.
188. A) (5,5)
Midpoint = ((7+3)/2, (2+8)/2) = (5,5).
189. D) All of these
x=4 includes (4,0), (4,4), etc.
190. True
They lie on line y=x+1.
191. A) (-4,-1)
180° rotation: (-x,-y) → (-4,-1).
192. C) III
(-,-) → Quadrant III.
193. C) 10
Distance = √(6²+8²) = 10.
194. A) (a, (b+c)/2)
Same x, so midpoint y averaged.
195. B) (0,3)
On y-axis: x=0.
196. True
Distance formula.
197. A) (0,-4)
Reflect in x-axis: (0,-4).
198. D) IV
(+,-) → Quadrant IV.
199. B) 10√2
Distance = √(10²+10²) = √200 = 10√2.
200. A) (4,6)
Midpoint = ((2.5+5.5)/2, (3.5+8.5)/2) = (8/2, 12/2) = (4,6).
SECTION 7: Properties of 3D Shapes
201. 6
Cube has 6 faces.
202. A) 6 faces, 12 edges, 8 vertices
Cuboid properties.
203. 9
Triangular prism: 5 faces, 9 edges, 6 vertices. Edges = 3×3 = 9.
204. 5
Square-based pyramid: 5 vertices.
205. B) Cylinder
Cylinder has 2 circular faces, 1 curved.
206. 4
Tetrahedron = triangular pyramid: 4 faces.
207. False
Sphere has no flat faces/edges/vertices.
208. 3
In cube, 3 edges meet at each vertex.
209. B) Cone
Cone has 1 vertex.
210. 8
Hexagonal prism: 8 faces.
211. A) F + V = E + 2
Euler’s formula: Faces + Vertices = Edges + 2.
212. 3
Triangular prism has 3 rectangular faces.
213. D) Both B and C
Tetrahedron: 4 triangular faces; square pyramid: 4 triangular + 1 square.
214. True
Prisms have two parallel congruent bases.
215. 8
Square-based pyramid edges: 4 base edges + 4 slant edges = 8.
216. Cube
6 square faces.
217. 2
Cylinder has 2 flat circular faces.
218. 10
Pentagonal prism: 10 vertices.
219. B) Cone
Circular base, 1 vertex.
220. True
Cube is cuboid with all edges equal.
221. 6
Pentagonal pyramid: 5 triangular + 1 pentagon = 6 faces.
222. B) Sphere
Sphere no edges/vertices.
223. 6
Triangular-based pyramid (tetrahedron) edges = 6.
224. 4
Cube: 8 vertices, tetrahedron: 4 vertices → difference 4.
225. D) Both B and C
Square pyramid: 5 faces; triangular prism: 5 faces.
226. True
Pyramid has polygonal base and triangular side faces.
227. 24
Octagonal prism edges: 8×3 = 24.
228. B) Tetrahedron
Tetrahedron: 4 vertices.
229. C) 60 cm³
Volume = 3×4×5 = 60 cm³.
230. True
Cube: all faces squares.
SECTION 8: Fictional "Previous Year Paper"
231. 936
347+589=936.
232. 150
(3/5)×250 = 150.
233. 5/8
0.625 = 625/1000 = 5/8.
234. 2:3
12:18 = 2:3.
235. 9
Mean = (4+7+9+12+13)/5 = 45/5 = 9.
236. £23.75
Price before VAT = £28.50 ÷ 1.20 = £23.75.
237. 48
Sequence differences: 5,7,9,11,13 → next difference 13 → 35+13=48.
238. £36
15% of 240 = 0.15×240 = 36.
239. x = 9
3x–7=20 → 3x=27 → x=9.
240. 30 cm²
Area = ½×12×5 = 30.
241. 2500 g
2.5 kg = 2500 g.
242. 225 minutes
3×60 + 45 = 225.
243. 1/2
Even numbers 2,4,6 → 3/6 = 1/2.
244. £45 and £75
3+5=8 parts, each part=120/8=15 → 3×15=45, 5×15=75.
245. 20000
398 ≈ 400, 51 ≈ 50 → 400×50=20000.
246. 6.86
6.857 → 6.86 (2 d.p.).
247. 1/8
Reciprocal of 8 is 1/8.
248. 5
Mode = most frequent = 5.
249. 26 cm
Perimeter = 2×(8+5) = 26.
250. 64
4³ = 64.
251. 80 km/h
Speed = 240/3 = 80 km/h.
252. 6(2x+3)
12x+18 = 6(2x+3).
253. x = 10
2(x–3)=14 → x–3=7 → x=10.
254. 5
Ordered: 2,3,5,7,9 → median = 5.
255. 750 g
For 4 → 300g, for 10 → (300/4)×10 = 750g.
256. 10
Range = 25–15 = 10.
257. £0.60
£4.80 ÷ 8 = £0.60.
258. £120
Decrease 25% = 160×0.75 = 120.
259. £92
Increase 15% = 80×1.15 = 92.
260. 0.12
0.3×0.4 = 0.12.
261. 0.625
5/8 = 0.625.
262. 11/12
2/3+1/4 = 8/12+3/12 = 11/12.
263. 1/2
5/6–1/3 = 5/6–2/6 = 3/6 = 1/2.
264. 12
(3/5)×20 = 12.
265. 2/7
(4/7) ÷ 2 = 4/14 = 2/7.
266. 9/20
45% = 45/100 = 9/20.
267. 15%
3/20 = 0.15 = 15%.
268. 8
2:5 = x:20 → x = (2×20)/5 = 8.
269. 14
2a²–b = 2×9 – 4 = 18–4=14.
270. 3a + 4b
5a–2a=3a, 3b+b=4b → 3a+4b.
271. 3x+12
3(x+4)=3x+12.
272. 3(2x–3)
6x–9 = 3(2x–3).
273. y=5
5y+7=32 → 5y=25 → y=5.
274. 8
Let n be number: 2n+5=21 → 2n=16 → n=8.
275. 20°
2x+3x+4x=9x=180° → x=20°.
276. 154 cm²
Area = Οr² = (22/7)×7×7 = 154.
277. 44 cm
Circumference = Οd = (22/7)×14 = 44.
278. 216 cm³
Volume = 6³ = 216.
279. 94 cm²
Surface area = 2(3×4 + 4×5 + 3×5) = 2(12+20+15)=2×47=94.
280. 3500 ml
3.5 litres = 3500 ml.
SECTION 9: Previous Year GL Assessment Styles
281. C) 89°
Acute < 90°.
282. C) 360°
Quadrilateral sum.
283. C) 7
Heptagon sides = 7.
284. C) Equilateral
All sides equal.
285. C) 4
Square rotational symmetry order 4.
286. D) IV
(+,-) → Quadrant IV.
287. B) 5
Triangular prism faces = 5.
288. B) 180°
Straight line.
289. C) Trapezium
One pair parallel.
290. B) 8
Interior 135° → exterior 45° → sides = 360/45=8.
291. C) 12
Cube edges = 12.
292. A) 90°
Complementary sum.
293. B) 2
Rectangle lines of symmetry = 2.
294. A) (3,5)
Midpoint = ((1+5)/2, (3+7)/2) = (3,5).
295. B) Square pyramid
Square pyramid vertices = 5.
296. B) 180°
Triangle sum.
297. C) 10
Decagon sides = 10.
298. C) Rhombus
Diagonals bisect at right angles in rhombus.
299. A) (2,3)
Reflect in y-axis: (-x,y) → (2,3).
300. C) 8
Square pyramid edges = 8.
301. B) 180°
Supplementary sum.
302. C) 3
Equilateral triangle rotational symmetry order 3.
303. C) 10
Distance = √(6²+8²)=10.
304. B) Cylinder
Two circular faces.
305. D) 360°
Around a point.
306. B) 8
Cube vertices = 8.
307. B) Isosceles
Two equal sides.
308. A) x-axis
y=0 → on x-axis.
309. B) 4
Tetrahedron faces = 4.
310. A) Equal
Vertically opposite equal.
311. B) 6
Regular hexagon lines = 6.
312. A) (5,3)
Midpoint = ((0+10)/2, (0+6)/2) = (5,3).
313. C) Cone
One vertex.
314. B) 55°
Other acute = 90°–35°=55°.
315. B) 3
Hexagon: from one vertex diagonals = 6–3=3.
316. C) Rectangle
Rectangle is a parallelogram.
317. B) y-axis
x=0 → on y-axis.
318. B) 6
Triangular pyramid (tetrahedron) edges = 6.
319. B) 360°
Sum exterior angles always 360°.
320. B) (5,2)
Reflect in x-axis: (x,-y) → (5,2).
321. A) Scalene
No equal sides.
322. C) 7
Pentagonal prism faces = 7.
323. D) 70° each
Base angles = (180°–40°)/2 = 70°.
324. C) (-,-)
Quadrant III.
325. B) 12
Hexagonal prism vertices = 12.
326. A) 25 cm²
Perimeter 20 → side=5 → area=25.
327. C) 120 cm³
Volume = 4×5×6=120.
328. B) 44 cm
Circumference = 2Οr = 2×(22/7)×7 = 44.
329. B) 30 cm²
Area = ½×10×6 = 30.
330. D) 54 cm²
Surface area = 6×(3²) = 54.
Critical Formulas to Remember:
Polygons: Sum of interior angles = (n-2) × 180°
Regular polygons: Each interior angle = (n-2) × 180° ÷ n
Exterior angles: Sum always = 360°, each = 360° ÷ n
3D shapes: Euler's Formula: F + V = E + 2
Coordinates: Distance = √[(x₂-x₁)² + (y₂-y₁)²]
Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)
Angle rules: Straight line=180°, Point=360°, Triangle=180°, Quadrilateral=360°
Exam Tips:
Draw diagrams for angle problems
Label all known angles
Check your work using angle sums
Memorize properties of common shapes
Practice visualizing 3D shapes from nets
Be careful with coordinate signs in different quadrants
Remember: Vertically opposite angles are ALWAYS equal
Corresponding/alternate angles are equal ONLY with parallel lines
This comprehensive question bank covers every aspect of geometry tested in the GL Assessment 11+ exam. Regular practice with these questions will ensure mastery of all required concepts.
