Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Higher

Maths · GCSE Higher · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?
(a)Not enough information
(b)Cuboid — not necessarily a cube
(c)Triangular prism
(d)Cube — only a cube fits this
2.A drinks company sells a novelty giant bottle that is geometrically similar to its standard 500 ml bottle, scaled up by a length factor of 1.5. Work out the capacity of the giant bottle, in ml.
(a)750 ml
(b)2250 ml
(c)1125 ml
(d)1687.5 ml
3.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).
(a)(5, 2)
(b)(3, 10)
(c)(0, 11)
(d)(1, 7)
4.ABCD is an isosceles trapezium. The sides AB and DC are parallel, and the two sloping sides AD and BC are equal in length. Angle D is 112°. Work out the size of angle B.
(a)112°
(b)68°
(c)248°
(d)90°
5.In pentagon PQRST, which of the following correctly names the interior angle at vertex R, using standard three-letter angle notation?
(a)∠QRS
(b)∠PQR
(c)∠TRP
(d)∠RST
6.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15
7.A rotation of 200° clockwise about the origin is applied, and the image is then rotated 250° anticlockwise about the origin. Work out the single angle of rotation, measured clockwise and between 0° and 360°, that has the same overall effect as the two rotations combined.
(a)310°
(b)130°
(c)50°
(d)90°
8.A point is translated twice by the vector $(5 - 3)$ . Write down the single column vector that describes the overall translation.
(a) $(5 - 3)$
(b) $(10 - 6)$
(c) $(5 - 6)$
(d) $(15 - 9)$
9.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.
(a)A square's diagonals are equal in length
(b)A square has only one pair of parallel sides
(c)A square's diagonals do not cross at right angles
(d)A square's sides are not all equal in length
10.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?
(a)335°
(b)025°
(c)155°
(d)065°
11.A vertical line passes through the point (5, 2). Write down the equation of this line.
(a)x = 2
(b)x = 5
(c)y = 2
(d)y = 5
12.Work out the gradient of the line segment joining A(2, 3) and B(6, 11).
(a)2
(b)−2
(c)8
(d)0.5
13.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
(a)vertically opposite angles are equal
(b)corresponding angles are equal
(c)base angles of an isosceles triangle are equal
(d)angles in a triangle add up to 180°
14.The perimeter of a square is 20 cm. Work out the area of the square.
(a)5 cm
(b)25 cm²
(c)100 cm²
(d)400 cm²
15.A, B and C are points on a circle with centre O, and AC is a diameter of the circle. Work out the size of angle ABC.
(a)90°
(b)45°
(c)It cannot be worked out without knowing the radius
(d)180°

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