## Diplomas in Construction and the Built Environment

CONSTRUCTION MANAGEMENT
Qualification Level 3 BTEC QCF Diplomas in Construction and the Built Environment
Unit number and title Unit 3 Mathematics in construction and the built environment
Assignment no. and title 1 of 4 Simplify expressions and solve problems and formula
Student name Assessor
Issue date Hand In Deadline Date Submitted
Lead Iv Authorisation
for Re-submission
Signed: Re-submission
Deadline Re-submission
date

Learning outcome 1

Be able to use basic underpinning mathematical techniques and methods to manipulate and/or solve formulae, equations and algebraic expressions.

Criteria reference Assessment criteria 1st Submission Final Submission
P1 Use the main functions of a scientific calculator to perform calculations, applying manual checks to results. Yes/No Yes/No
P2 Use standard mathematical techniques to simplify expressions and solve problems using linear formulae. Yes/No Yes/No
M1 Use algebraic methods to solve linear, quadratic, simultaneous linear and quadratic equations. Yes/No Yes/No
D1 Independently carry out checks on calculations using relevant
alternative mathematical methods and make appropriate
judgements on the outcome. Yes/No Yes/No
Student declaration I certify that the evidence submitted for this assignment is my own. I have clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice.

Student signature Date

Assessor declaration I certify that the evidence submitted for this assignment is the student’s own. The student has clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice.

Assessor signature Date

Grade accepted by student Yes/No Student signature Date

Assignment 1 brief

Assignment written by Steve Atherton Date 26/08/2014
Assignment IV’d by Giles Dawes Date 1/09/2014

P1 Use a scientific calculator to perform calculations and apply manual checks to
results (where asked to).
Give answers to the stated levels of accuracy and in the correct units.

1 Calculate your answer to a, b and c without a calculator.
Show your working out. If you only write the answer you will fail.

a) 2 + 3 x 15 – 4 b) 33 – (18 – 23 ÷ 2) c) 105 ÷ 103

2 Work out the following using a calculator.

a) 40 – p 3.52 b) 2¼ x 3½ c) 13 + 122 – v121 d) 6! – 4!

3 The volume of a cone is given by V = 1/3 p r2 h
Calculate the volume if the radius, r is 100mm and the height h, is 150mm.
Give your answer to the nearest mm3

4 A rectangular piece of land has sides length 32.15m by 16.45m

a) Calculate an estimated answer for the area, show your working out.
b) Calculate an exact answer to the area.
c) Give your answer to the nearest square metre.
P2 Use standard mathematical techniques to simplify expressions and
solve problems using linear formulae

1 Simplify the following expressions

a) 3ab + 4bc + 2ab – bc b) 4x + 19 – 5x – 8 + 7x

c) 9 – 3(1 + 7c) d) 7(2f – 1) – 1(6f + 3)
2 Solve the following equations showing your working out. Check your answers by
substituting them in the original equation. Show your checking out for a) and b).

a) 8x + 12 = 54 b) 40 – 4y = y

c) 3x + 5 = 10 d) 5(x + 2) – 3(x – 5) = 29
2
M1 Use algebraic methods to solve linear, quadratic, simultaneous linear and quadratic
equations.

1 Solve these simultaneous equation using a recognised algebraic method.

a) 3x + 2y = 13 and 6x + y = 20
b) y = 2x + 5 and x² + 4y = 5

2 Produce simultaneous linear equations from the information below then solve them.

3 kilos of nails and 2 kilos of screws cost £25.60
4 kilos of nails and 1 kilo of screws cost £23.30

What is the cost of a) 1kg of screws and b) 1kg of nails?

3 Solve the following quadratic equations using a recognised method.

a) x2 + 6x + 5 = 0 b) x² – 13x + 22 = 0 c) m² = 6m + 27

D1 Independently carry out checks on calculations using relevant alternative mathematical methods and make appropriate judgments on the outcome.

Solve M1 questions number 1a and 3 using an alternative method and make
appropriate judgments on your answers.

Feedback sheet
P1 Use the main functions of a scientific calculator to perform calculations, applying manual checks to results
Assessor feedback

P2 Use standard mathematical techniques to simplify expressions and solve problems using linear formulae
Assessor feedback

M1 Use algebraic methods to solve linear, quadratic, simultaneous linear and quadratic equations
Assessor feedback

D1 Independently carry out checks on calculations using relevant alternative mathematical
methods and make appropriate judgments on the outcome.
Assessor feedback

Additional Comments for Re-submission.
Re-submission Date
(10 days after the feedback date given below)

Student Feedback
Assessor Signature Feedback
Date
Student Signature Date

CONSTRUCTION MANAGEMENT
Qualification Level 3 BTEC QCF Diplomas in Construction and the Built Environment
Unit number and title Unit 3 Mathematics in Construction and the Built Environment
Assignment no. and title 2 of 4 Solve problems associated with perimeters, areas and volumes
Student name Assessor
Issue date Hand In Deadline Date Submitted
Lead Iv Authorisation
for Re-submission
Signed: Re-submission
Deadline Re-submission
date

Learning outcome 2

Be able to select and apply mathematical techniques correctly to solve practical construction
problems involving perimeters, areas and volumes.

Criteria reference Assessment criteria 1st Submission Final Submission
P4 Use mathematical techniques to solve construction problems
associated with simple perimeters, areas and volumes. Yes/No Yes/No
M2 Use appropriate algebraic methods to find angles, areas and
volumes for one 2D and one 3D complex problem. Yes/No Yes/No

Student declaration I certify that the evidence submitted for this assignment is my own. I have clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice.

Student signature Date

Assessor declaration I certify that the evidence submitted for this assignment is the student’s own. The student has clearly referenced any sources used in the work. I understand that false declaration is a form of malpractice.

Assessor signature Date

Grade accepted by student Yes/No Student signature Date
Assignment 2 brief

Assignment written by Steve Atherton Date 27/8/2014
Assignment IV’d by Giles Dawes Date 1/09/2014

P4
1 A conical roof has a base of 5 m diameter and is 5 m high. Calculate:
a) the length of the sloping side b) the area of the roof (excluding the base)
c) the volume of the roof

2 The diagram below shows a cross section through a concrete component 2m long containing a
30mm diameter hole. Calculate:
a) the cross sectional area of the component (excluding the hole)
b) the volume of concrete in the component
50mm
130 mm
80mm

3 The cross-sectional area of flow of a river which is to be carried in a culvert is 1.5 m2.
Calculate the dimensions of the possible culvert sections shown below.

a) b)

D D

2D D
M2
Apply appropriate algebraic methods to find areas and volumes for one 2D and one 3D
complex problem.

1 A swimming pool is to be built on the plot of land shown below.
The pool is to be 1.5m deep and is a rectangle 20 m by 10 m with a semi-circular end. Around the pool is a paved area 1.5 m wide. The remaining area is to be lawn.
The pool is to be tiled with light blue tiles, with an oval shape on the bottom tiled in dark blue, measuring 15 m x 8 m

Calculate:
a) The perimeter of the pool.
b) The surface area of the pool.
c) The area of dark blue tiles.
d) The area of light blue tiles (remember the walls need tiling too).
e) The volume of the pool.
Feedback sheet

P4 Use mathematical techniques to solve construction problems associated with simple
perimeters, areas and volumes.

Assessor feedback
M2 Use appropriate algebraic methods to find, areas and volumes for one 2D and one 3D
complex problem.

Assessor feedback

Additional Comments for Re-submission.
Re-submission Date
(10 days after the feedback date given below)

Student Feedback
Assessor Signature Feedback
Date
Student Signature Date