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 straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.
(a)242
(b)62
(c)118
(d)28
2.In kite WXYZ, WX = WZ and XY = ZY (so at each of X and Z, one side from each of the two unequal pairs meets). Angle X = 100°. Work out angle Z.
(a)100°
(b)260°
(c)80°
(d)50°
3.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.
(a)10.4 cm
(b)4.0625 cm
(c)9.5 cm
(d)13 cm
4.A circular plate has a diameter of 20 cm. Work out the area of the plate. Use π = 3.14.
(a)314 cm²
(b)1256 cm²
(c)62.8 cm²
(d)628 cm²
5.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
6.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?
(a)320
(b)180
(c)295
(d)310
7.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.
(a)1.5
(b)−10
(c)−1.5
(d)−24
8.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
9.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.
(a)Parallelogram
(b)Rhombus
(c)Square
(d)Kite
10.A path goes from A(1, 1) to B(1, 5), then from B to C(6, 5). Work out the total length of the path from A to C.
(a)9
(b)5
(c)20
(d)4
11.Points A, B, C and D lie on a circle with centre O, in that order around the circle, and AC is a diameter. Which of the following circle facts does NOT apply to this diagram?
(a)Angle at the centre = twice angle at circumference.
(b)Opposite angles of a cyclic quadrilateral sum to 180°.
(c)Tangent-chord angle = angle in the alternate segment.
(d)Angle in a semicircle = 90°.
12.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?
(a)arc
(b)tangent
(c)chord
(d)radius
13.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.
(a)The same as the cylinder's volume
(b)Two thirds of the cylinder's volume
(c)One third of the cylinder's volume
(d)Half the cylinder's volume
14.Each of these has an exact value. Write down the one whose value is the greatest.
(a)cos 60°
(b)sin 45°
(c)tan 45°
(d)cos 30°
15.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate

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