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.
Geometry and measures worksheet — GCSE Foundation
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- 1.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.
- 2.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?
- 3.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.
- 4.Triangle JKL and triangle MNP are similar, with JK ÷ MN = JL ÷ MP = 2. A student says triangle JKL must be congruent to triangle MNP. Write down why the student is wrong.
- 5.In this question, a curved surface counts as a face. How many faces does a sphere have?
- 6.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.
- 7.m is the column vector with top number 3 and bottom number −4. Which of these column vectors is a scalar multiple of m?
- 8.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?
- 9.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?
- 10.Triangle LMN has a right angle at M, with hypotenuse LN = 15 cm and LM = 9 cm. Triangle PQR has a right angle at Q, with hypotenuse PR = 15 cm and PQ = 9 cm. Which condition proves the two triangles are congruent?
- 11.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 12.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 13.A shape is translated by the vector . The point P(6, 1) lies on the shape. Write down the coordinates of the image of P.
- 14.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?
- 15.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.
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