BTEC Level 1Level 2 First Award in Construction

BTEC Level 1/Level 2 First Award in Construction and the Built Environment Unit 2: Learning Aim B Scientific and Mathematical Applications for Construction The Use of Mathematics in Construction

Question A

The site is to be cleared before construction work starts. The contractor requires the area calculations before a price is quoted. Calculate the area of land shown in Figure 1.

Answer: Copy and complete the following • Step 1: Record the data • a = 20 m • b = 14 m • h = 12 m

Answer: Copy and complete the following • Step two: • Split the area into a rectangle and two triangles. • Combine the triangles into one larger triangle

Answer: Copy and complete the following •

Question B

If the topsoil removed is 200 mm thick all over the site, what is the volume of this topsoil?

Answer: Copy and complete the following •

Question C

• The plot of land is to be fenced using 50 mm diameter hollow posts and safety fencing. The pipes will be painted to protect against the weathering agents. The posts are to be placed on concrete pad foundations of 300 mm × 500 mm.

C) i • Calculate the surface area required to paint a post of 2. 5 m length.

Answer: Copy and complete the following •

Answer: Copy and complete the following • Step one: Record the data and look for the unknown • Diameter (d) = 50 mm • Height (h) = 2. 5 m • Area (a) = ?

Answer: Copy and complete the following •

C) ii • Calculate quantity of concrete required for foundation of one post.

Answer: Copy and complete the following •

Question D • Earthworks are to be carried out before construction work could start. • You have received quotations from two plant companies A and B. • Company A uses a plant that will require 12 hours to complete the job while company B’s plant could do it in 7 hours. • Applying your knowledge of mathematics, calculate the time required to complete earthworks if your manager decides to employ both companies.

Answer: Copy and complete the following •

Question E) i

Using details in Figure 2, calculate: area of the roof required for tiling

Answer: Copy and complete the following • Step one: Examine the diagram and record the data • Height (a) = 3 m • Width (b) = 8 m • We need to find out the length of the sloping side (c)

Answer: Copy and complete the following •

Question E) ii

Using details in Figure 2, calculate: the pitch of the roof (the angle the slope makes).

Answer: Copy and complete the following • Trigonometric functions describe the relationship between angle and the length of the sides of a triangle • Step one: Calculate the pitch • Identify the appropriate trigonometric identity

Answer: Copy and complete the following •

Question F • You have asked the materials’ suppliers to test the materials and provide the data so that you could check their suitability. One of the suppliers has provided you with the following data: Stress (MN/m 2) 110 101 80 75 55 43 31 Strain x 10 -4 5. 5 5. 13 4. 59 3. 75 3. 6 2. 61 1. 58

• Plot a graph of this data by taking Strain along the X-axis and Stress along the Y-axis. • Work out the gradient of this graph (E) and check whether the data and result obey Hooke’s law = E

Answer: Copy and complete the following • Step one: Plot the graph • Choose an appropriate scale so that the graph fits on the paper • Plot the strain along the x-axis and stress along the y-axis • Draw a line of best fit

Answer: Copy and complete the following • Step two: Choose two points on the graph • The points chosen in this case are A (2, 35) and B (5, 95)

Answer: Copy and complete the following •

Question G

Another supplier has sent you the following test results. Using the given graph, estimate the compressive strength when water ratio is 0. 35, 0. 45 and 0. 8.

Answer: Copy and complete the following Water ratio 0. 35 0. 45 0. 8 Compressive 22. 5 strength 20. 0 12. 0