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Numeracy Foundation November 2023 Unit 1 Q1

WJECFoundationCurrent spec7 marks2D Area & PerimeterAngles (Including Parallel Lines)Constructions

1. The scale drawing below shows a plan of Amir’s garden.
It shows the position of the shed, flower bed, play area and the back of the house.

Scale drawing on a 1 cm square grid, 12 squares wide and 7 squares deep, with the scale box Scale: 1 cm represents 1 m. Along the top edge: the shed (4 squares wide, 4 deep) at the left, the flower bed (5 wide, 1 deep) in the middle and the play area (3 wide, 3 deep) at the right. The bottom edge is a thick line labelled BACK OF THE HOUSE
(a)

Amir wants to put a hot tub in his garden.

The base of Amir’s hot tub is rectangular.
It is 3 m long and 2 m wide.

(i)

Amir wants the rectangular hot tub to be:

  • at least 2 m from the back of the house
  • at least 1 m from everything else.

Draw a possible position for the hot tub on the scale drawing above. [2]

(ii)

What is the area of the base of the hot tub?
Circle your answer. [1]

6 m2    6 m    5 m2    10 m    10 m2

(b)

Amir is building a swing for the play area.

The 2 long posts that meet at the top at each end of the swing need to be at an angle of 42°.

Sketch of an A-frame swing; the angle between the two posts at the top of one end is marked 42°
(i)

What type of angle is 42°?
Circle your answer. [1]

an acute angle    a right angle    a straight line    an obtuse angle    a reflex angle

(ii)

Amir is joining 2 long posts together.
One post is lying on horizontal ground.
Draw an angle of 42° at point T. [1]

A horizontal line segment with point T at its left-hand end
(iii)

Each long post makes an angle of 69° with the horizontal ground.
The diagram below shows one of these posts.
Calculate the size of angle \(x\). [2]

A post leaning to the right meets a horizontal line. The angle between the post and the ground on the right is 69°; the angle on the left is x

Diagram not drawn to scale

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