Mathematics for Construction - Desklib

Higher National Certificate/Diploma in Construction and the Built Environment
Unit Number and Title 8 Mathematics for Construction
Academic Year 2018/19

Contents
TASK 1............................................................................................................................................3
Scenario 1....................................................................................................................................3
Scenario 2....................................................................................................................................4
Scenario 3....................................................................................................................................5
TASK 2............................................................................................................................................9
Scenario 1....................................................................................................................................9
Scenario 2..................................................................................................................................11
TASK 3..........................................................................................................................................13
Scenario 1..................................................................................................................................13
Scenario 2..................................................................................................................................16
TASK 4..........................................................................................................................................18
Scenario 1..................................................................................................................................18
Scenario 2..................................................................................................................................20
Scenario 3..................................................................................................................................21

TASK 1
Scenario 1
1. Given area of a rectangular water tank is 26.5 m2: A=lw ( i )
w=3.2 m shorter ⟹ w=l−3.2 (ii)
Replace w in equation (i) with equation (ii) ∴ A=l ( l−3.2 )=26.5l2−3.2 l−26.5=0(ii)
Solving quadratic equation (III): x=−b ± √b2−4 ac
2 a , gives the length of the rectangular
tank l= 3.2 ± √ 3.22− ( 4 ×−26.5 )
2× 1 ¿ 6.990732789∨−3.790733∴l=6.99 m
w=6.99−3.2=3.79 m
The length and width of the rectangular tank is 6.99 m and 3.79 m respectively.
2. Let x represent the total amount the money contactor will forfeit each day for late
completion
For 5 days, amount forfeited is 5x
For 12 days, amount forfeited is12x: If the initial amount is y, then
y−5 x=4250(1) y−12 x=2120(2)
Solving the system of equation, gives: Equation (1) minus (2)
7 x=2130 ⟹ x=2130
7 =304.2857 y=4250+5 ( 2130
7 )= 40400
7 =5771.4285
Thus, the daily forfeit is £ 304.29
And the original contract is £ 5, 771.43

Scenario 2
a) A car driving at an average speed 65 miles/hour:
 Speed in Meter per second (from the given table)
sm
s
=
65 miles × (1.61 km ×1000 m
1 km )
1mile × (1 hour
1 hour ×3600 s )¿ 29.0694 m
s
 Time taken to drive 100 miles
Time= distance
speed
t= 100 miles
65 mile
hour
=100
65 hours ¿ 1.5385 hours
 fuel consumption averages 30miles/gallon converting this to liters/kilometer
C l
km
= 1 gal ×3.78 l
1 gal × 1 mi
30 mi ×1.61 km = 9
115
l
km¿ 0.07826 l
km
 fuel required in liters for the journey
Distance =100 mi =161 km
C=161 km× 0.07826 l
km =12.6 l
b) given the lift produced by an aircraft wing is:
lift=k × ρ× V 2 × A
The units of lift is then:
[ lift ] =
[ kg
m2 ] × [ ( m
s )
2
] × [ m2 ]¿ kg . m2
s2
Scenario 3
1. An arithmetic sequence is given by: b , 2b
3 , b
3 , 0 , ...