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

MathsUKwww.geekhero.co.uk

1.A drone flies from its base in three stages, each stage measured in metres east and north as a column vector. Stage 1 is the column vector with top number 30 and bottom number 40. Stage 2 is the column vector with top number −10 and bottom number 20. Stage 3 is the column vector with top number 15 and bottom number −5. Work out the column vector that would take the drone in a single straight flight back to its base from where it ends up.
(a)(−35, 55)
(b)(35, −55)
(c)(−35, −55)
(d)(35, 55)
2.A water tank holds 2.5 m³. Work out this volume in cm³.
(a)2500 cm³
(b)2 500 000 cm³
(c)25 000 cm³
(d)250 cm³
3.Which of these correctly compares a 'line' with a 'line segment'?
(a)A line has two endpoints; a segment has none
(b)A line segment is always curved
(c)A line has no endpoints; a segment has two
(d)A line segment is a closed shape
4.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.
y = x
(a)(−7, −3)
(b)(7, 3)
(c)(−3, 7)
(d)(3, −7)
5.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?
(a)A perpendicular of AB
(b)A plane of AB
(c)The midpoint of AB
(d)The vertex of AB
6.A sector of a circle has radius 9 cm and angle 60°. Using π = 3.14, work out the area of the sector, to 1 decimal place.
(a)9.4 cm²
(b)4.7 cm²
(c)254.3 cm²
(d)42.4 cm²
7.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.
(a)40 cm
(b)12 cm
(c)88 cm
(d)768 cm
8.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
(a)£4.20
(b)£0.34
(c)£3.60
(d)£420.00
9.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.
(a)180°
(b)59°
(c)62°
(d)118°
10.A right-angled triangle has a hypotenuse of 29 cm and one shorter side of 20 cm. Work out the length of the other shorter side.
(a)441 cm
(b)21 cm
(c)35 cm
(d)9 cm
11.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.
(a)(2, 6)
(b)(9, −1)
(c)(2, −2)
(d)(8, 6)
12.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.
(a)Parallel, since both gradients are 2
(b)Not parallel, since the gradients are 2 and 4
(c)Parallel, since both lines pass through positive coordinates
(d)Not parallel, since the two lines cross the y-axis at different points
13.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.
(a)2.5 cm
(b)10 cm
(c)5 cm
(d)15.7 cm
14.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.
(a)94.2 cm
(b)56.52 cm
(c)28.26 cm
(d)113.04 cm
15.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?
(a)a cone
(b)a cylinder
(c)a sphere
(d)a square-based pyramid

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