Topic 1: Substitution into expressions, equations and
formulae
The term ‘substitution’ means that the value of the variable is known and the variable will be
replaced by the value given for each variable.
Examples
a 5,=
b 2 and
=
c
4a + 5b − c when=
4a + 5b − c
= 4× 5 + 5× 2 − −3
( − − → +)
= 20 + 10 + 3
= 33
Evaluate (find the value of) the expression
Evaluate
b 2 − 4ac
when
−
3
a = 1, b = 8 and c = −7
b 2 − 4ac
= 82 − 4 × 1 × − 7
= 64 + 28
= 92
Centre for Teaching and Learning | Academic Practice | Academic Skills
T +61 2 6626 9262 E [email protected] W www.scu.edu.au/teachinglearning
Page 1
[last edited on] CRICOS Provider: 01241G
Centre for Teaching and Learning
Numeracy
Evaluate
Evaluate
a 1
=
a 4=
and b − 5
− when
b 2
a 1
−
b 2
 4 −4 
4 1
=
−
− =

−
5 2
 5 5 
−
4 1
=
−
5 2
−
8 5
=
−
10 10
−
13
3
=
or −1
10
10
p3 + q 2 − r
=
p
when
3.1,
=
q 1.9 and
=
r 5.5
p3 + q 2 − r
=
=
(3.1)3 + (1.9) 2 − 5.5
29.791 + 3.61 − 5.5
= 27.901
. 5.282 ( to 3 d.p.)
y
In the equation =
3 x + 4 , find the value of y when x = 5
y 3x + 4
=
y = 3× 5 + 4
y 15 + 4
=
y = 19
Centre for Teaching and Learning | Academic Practice | Academic Skills
T +61 2 6626 9262 E [email protected] W www.scu.edu.au/teachinglearning
Page 2
[last edited on] CRICOS Provider: 01241G
Centre for Teaching and Learning
Numeracy
In the formula
V=
2d1
, find the value of
V when d1 4500
=
=
and d 2 1250
d1 − d 2
2d1
V=
d1 − d 2
2 × 4500
V=
4500 − 1250
9000
V=
3250
V = 2.77 (to 2 d.p.)
Video ‘Substitution’
Centre for Teaching and Learning | Academic Practice | Academic Skills
T +61 2 6626 9262 E [email protected] W www.scu.edu.au/teachinglearning
Page 3
[last edited on] CRICOS Provider: 01241G
Centre for Teaching and Learning
Numeracy
Activity
1.
Evaluate the following expressions when
m+n
(a)
(b)
2m − n
(c)
(d)
Evaluate the following expressions when
(d)
3.
and
n = 12
m 2 − 5m + 6
( n − m) 2 + 2n − m
2.
(a)
(b)
(c)
m=5
a = 2 , b = − 3 and c =
2a − 3b + 4c
a ÷c
ab 2 − a 2c
b
+c
a
The speed (s) of a car is given by the equation
s=
d
t
1
4
, where d is the distance
covered by the car in kilometres and t is the time taken to cover that distance in hours.
Calculate the speed of the car if it covers 250km in 3 hours.
4.
The Potential Energy (P)of a moving object is given by the formula
P = mgh
where
m is the mass of the object in kilograms, g is the acceleration due to gravity in
m / sec2 and h is the height above the ground in metres.
Find the potential energy of 550kg object when it is 10m above the ground, given the
g=9.8 m / sec 2
Centre for Teaching and Learning | Academic Practice | Academic Skills
T +61 2 6626 9262 E [email protected] W www.scu.edu.au/teachinglearning
Page 4
[last edited on] CRICOS Provider: 01241G