Geometry and MeasuresEdexcel GCSE Maths: Topic test

20 questions, 52 marks

Edexcel GCSE Maths

Geometry and Measures topic test

Total 52 marks

Name

Class

Date

1
A design team is checking three facts before finalising a garden layout: the interior angle of a regular polygon used for a paved area, the area of a triangular flower bed, and a bearing used for a path.
(a)
A regular polygon has 9 sides. What is the size of each interior angle?
[1 mark]
A140°
B160°
C120°
D100°
(b)
A triangular flower bed has a base of 8 m and a perpendicular height of 5 m. What is its area?
[1 mark]
A40 m²
B13 m²
C20 m²
D6.5 m²
(c)
A path runs on a bearing of 072° from point P to point Q. What is the bearing of P from Q (the back bearing)?
[1 mark]
A108°
B252°
C072°
D288°
Total for question 1: 3 marks
2
Shape $P$ has vertices $A(1, 2)$ , $B(4, 2)$ and $C(1, 5)$ . It is translated by the vector $\binom{3}{-2}$ to form shape $Q$ . Two sensor posts, S and T, are placed 6 m apart.
(a)
State the coordinates of the image of vertex $C$ under the translation by $\binom{3}{-2}$ .
[2 marks]
(b)
Describe fully the locus of points that are equidistant from S and T.
[2 marks]
Total for question 2: 4 marks
3
Triangle $XYZ$ is right-angled at $Y$ , with $XY = 9$ cm and $YZ = 12$ cm. In a separate problem, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$ , and $M$ is the midpoint of $AB$ .
(a)
Find the length of the hypotenuse $XZ$ .
[3 marks]
(b)
Show that $\overrightarrow{OM} = \frac{1}{2}(\mathbf{a} + \mathbf{b})$ .
[3 marks]
Total for question 3: 6 marks
4
A landscaper is building a patio and a decorative path. The patio is a composite shape made from a rectangle measuring 10 m by 6 m, with a semicircular section of diameter 6 m removed from one of the 6 m sides. Separately, a ladder of length 7.5 m leans against a vertical wall with its foot 2.4 m from the base of the wall. The path runs on a bearing of 048° for 120 m from point R to point S, then turns and runs on a bearing of 138° for 90 m from S to point T.
(a)
Work out the area of the patio, giving your answer correct to 1 decimal place.
[4 marks]
(b)
Find the height up the wall that the ladder reaches, correct to 1 decimal place, and hence find the angle the ladder makes with the ground, correct to 1 decimal place.
[4 marks]
(c)
Work out the distance $RT$ , giving your answer to the nearest metre.
[5 marks]
Total for question 4: 13 marks
5
A design team is checking three facts before finalising a courtyard layout: the interior angle of a regular polygon used for a paved area, the area of a triangular herb bed, and a bearing used for a path.
(a)
A regular polygon has 12 sides. What is the size of each interior angle?
[1 mark]
A144°
B160°
C140°
D150°
(b)
A triangular herb bed has a base of 10 m and a perpendicular height of 7 m. What is its area?
[1 mark]
A35 m²
B70 m²
C17.5 m²
D24.5 m²
(c)
A path runs on a bearing of 115° from point P to point Q. What is the bearing of P from Q (the back bearing)?
[1 mark]
A065°
B115°
C295°
D245°
Total for question 5: 3 marks
6
Shape $P$ has vertices $A(2, 1)$ , $B(5, 1)$ and $C(2, 4)$ . It is translated by the vector $\binom{-4}{3}$ to form shape $Q$ . Two transmitter masts, F and G, are placed 10 m apart.
(a)
State the coordinates of the image of vertex $B$ under the translation by $\binom{-4}{3}$ .
[2 marks]
(b)
Describe fully the locus of points that are equidistant from F and G.
[2 marks]
Total for question 6: 4 marks
7
Triangle $DEF$ is right-angled at $E$ , with $DE = 8$ cm and $EF = 15$ cm. In a separate problem, $\overrightarrow{OC} = \mathbf{c}$ and $\overrightarrow{OD} = \mathbf{d}$ , and $N$ is the midpoint of $CD$ .
(a)
Find the length of the hypotenuse $DF$ .
[3 marks]
(b)
Show that $\overrightarrow{ON} = \frac{1}{2}(\mathbf{c} + \mathbf{d})$ .
[3 marks]
Total for question 7: 6 marks
8
A landscaper is building a courtyard and a decorative path. The courtyard is a composite shape made from a rectangle measuring 12 m by 8 m, with a semicircular section of diameter 8 m removed from one of the 8 m sides. Separately, a ladder of length 8.5 m leans against a vertical wall with its foot 3.0 m from the base of the wall. The path runs on a bearing of 065° for 140 m from point R to point S, then turns and runs on a bearing of 155° for 105 m from S to point T.
(a)
Work out the area of the courtyard, giving your answer correct to 1 decimal place.
[4 marks]
(b)
Find the height up the wall that the ladder reaches, correct to 1 decimal place, and hence find the angle the ladder makes with the ground, correct to 1 decimal place.
[4 marks]
(c)
Work out the distance $RT$ , giving your answer to the nearest metre.
[5 marks]
Total for question 8: 13 marks

End of questions