Printable · GCSE Foundation · ages 14-16

Geometry and measures worksheet — GCSE Foundation

Fifteen questions across the geometry and measures statements at Foundation 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 Foundation

Maths · GCSE Foundation · Geometry and measures · 15 questions

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1.A triangular sail for a small boat has a base of 2.4 m and a height of 1.75 m. Sailcloth costs £12.50 per m². Work out the total cost of the sailcloth needed for the sail.
(a)£30.00
(b)£26.25
(c)£25.00
(d)£52.50
2.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
3.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(2, 3)
(c)(5, 4)
(d)(6, 3)
4.Which of the following correctly describes what it means for two lines to be perpendicular?
(a)Two lines equal in length
(b)Two lines crossing at any angle
(c)Two lines that never meet
(d)Two lines that cross at right angles
5.Point B is at (1, 6). It is reflected in the x-axis. Work out the coordinates of the image of point B.
(a)(1, 6)
(b)(−1, 6)
(c)(−1, −6)
(d)(1, −6)
6.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.
(a)TU
(b)PQ
(c)VW
(d)RS
7.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.
(a)18
(b)36
(c)13
(d)26
8.The vector $(- 2 5)$ describes a translation. A student writes it as $(5 - 2)$ by mistake. Write down what error the student has made.
(a)Doubled the x component
(b)Reversed both signs
(c)Swapped the x and y components
(d)Reversed only the y sign
9.Work out the y-coordinate of the midpoint of the line segment joining (2, 4) and (8, 10).
(a)3
(b)7
(c)14
(d)5
10.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
11.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
12.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.
(a)25.0 m
(b)30.0 m
(c)15.0 m
(d)21.2 m
13.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?
(a)AB, CD and EF are all parallel
(b)None of the lines are parallel
(c)AB ∥ CD only; EF not confirmed
(d)EF is parallel to AB
14.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
(a)10.5 cm²
(b)21 cm²
(c)27 cm²
(d)30 cm²
15.Point A is at (2, 3). It is translated by the vector (4, −1) to give point A′. Work out the coordinates of A′.
(a)(1, 7)
(b)(6, 4)
(c)(6, 2)
(d)(−2, 4)

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