GS 291 - Review Test 31
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School
Centennial College *
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Course
291
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by ChancellorNeutronFlamingo39
GS 291 Pre-Test 3 Section A (Quadratic Equation) 1) Solve the quadratic equation 0
2
9
4
2
=
−
−
x
x
Solution
From the quadratic equation above 2
9
,
4
−
=
−
=
=
c
and
b
a
. Substitute these values in the quadratic formula Quadratic formula a
ac
b
b
x
2
4
2
−
−
=
Please memorize this formula for your test
On substituting the values in the quadratic formula you will get (
)
(
)
( )(
)
( )
4
2
2
4
4
9
9
2
−
−
−
−
−
=
x
8
32
81
9
+
=
x
This implies 8
113
9
=
x
8
6301
.
10
9
=
x
This implies 8
6301
.
10
9
+
=
x
or 8
6301
.
10
9
−
=
x
4538
.
2
=
x
or 2038
.
0
−
=
x
2) Solve 0
4
3
2
=
+
+
−
n
n
Note for the above 4
3
,
1
=
=
−
=
c
and
b
a
Using the quadratic formula a
ac
b
b
n
2
4
2
−
−
=
( )
(
)( )
(
)
1
2
4
1
4
3
3
2
−
−
−
−
=
n
2
16
9
3
−
+
−
=
n
This implies 2
5
3
−
+
−
=
n
2
5
3
−
−
−
=
n
4
=
n
or 1
−
=
x
3) Solve 0
3
5
2
2
=
−
+
p
p
Answer: 3
5
.
0
−
=
=
p
or
p
4) Solve 0
2
5
3
2
=
+
−
k
k
Answer: 3
2
1
=
=
k
or
k
5) Solve 0
16
32
12
2
=
+
−
y
y
Answer: 3
2
2
=
=
y
or
y
GS 291 Pre-Test 3 Section B
Solve the following systems of linear equations algebraically using Substitution Method and show your work.
1) 7
2
7
33
5
2
=
−
=
−
y
x
y
x
(Remember to test your solution) Answer 7
1
−
=
−
=
y
and
x
2) 34
9
4
15
5
3
−
=
−
=
+
−
y
x
y
x
(Remember to test your solution) Answer 6
5
=
=
y
and
x
3) 8
3
7
4
7
9
−
=
+
−
−
=
+
−
y
x
y
x
(Remember to test your solution) Answer 2
2
=
=
y
and
x
4) 28
7
3
36
9
7
=
−
=
−
y
x
y
x
(Remember to test your solution) Answer 4
0
−
=
=
y
and
x
Section C
Solve the following systems of linear equations algebraically using Elimination Method and show your work.
1) 7
2
7
33
5
2
=
−
=
−
y
x
y
x
(Remember to test your solution) Answer 7
1
−
=
−
=
y
and
x
2) 34
9
4
15
5
3
−
=
−
=
+
−
y
x
y
x
(Remember to test your solution) Answer 6
5
=
=
y
and
x
3) 8
3
7
4
7
9
−
=
+
−
−
=
+
−
y
x
y
x
(Remember to test your solution) Answer 2
2
=
=
y
and
x
4) 28
7
3
36
9
7
=
−
=
−
y
x
y
x
(Remember to test your solution) Answer 4
0
−
=
=
y
and
x
Section D
(Remember that in the questions below, you must use the closest interval) 1)
The following table gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area A (in m
2
). f 0.22 0.30 0.37 0.44 0.50 0.56 0.61 A (m
2
) 20 30 40 50 60 70 80 a)
Using linear interpolation and the table above find A for when f=0.54 (Answer A=66.7m
2
) b)
Using linear interpolation and the table above find A for when f=0.33 (Answer A=34.3m
2
) c)
Using linear interpolation and the table above find f for when A=49m
2
(Answer f = 0.43)
GS 291 Pre-Test 3 2)
A steam boiler was heated to 150
C
0
and allowed to cool down. The cooling is tabulated as follows:- Time (min) 0.0 1.0 2.0 3.0 4.0 5.0 Temperature
C
0
150.0 142.8 138.5 135.2 132.7 130.8 a)
Using linear interpolation determine the temperature after 2.9 min (Answer is 135.5
C
0
) b)
Using linear interpolation determine the temperature after 1.8 min (Answer is 139.4
C
0
) c)
Using linear interpolation what time will it take to cool down to 139.4
C
0
(Answer is 1.79 or 1.8min) Section E
Mixture Problems 3) How many litres of a solution containing 9% sulphuric acid by volume, and how many litres of another solution containing 17% sulphuric acid must be combined to make 615 ℓ of solution containing 15% sulphuric acid? State your answers correct to the nearest litre. (Learn how to solve the resulting simultaneous equation using both Elimination and Substitution Method) (Asnwer 154 litres of 9% solution and 461 litres of the 17% solution are required) 4) A manufacturer has a 8% and 19% acid solution in stock. How much of each solution must be used to fill an order of 230L of a 12% solution? State your answers correct to the nearest litre
. (Learn how to solve the resulting simultaneous equation using both Elimination and Substitution Method)
(Asnwer 146 litres of 8% solution and 84 litres of the 19% solution are required) 5) A distributor receives an order for 800L of a 13% sulphuric acid solution. He has 27% and 5% solutions on hand which he has to mix to fill the order. How much of each must he use? State your answers correct to the nearest litre. (Learn how to solve the resulting simultaneous equation using both Elimination and Substitution Method)
(Asnwer 291 litres of the 27% solution and 509 litres of the 3% solution are required) 6) How many litres of a solution containing 32% sulphuric acid by volume must be combined with 1
95 ℓ of a solution containing 23% sulphuric acid in order to produce a solution that is 30% sulphuric acid? State your answers correct to the nearest litre. (Asnwer 683 litres of the 32% solution is required)
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GS 291 Pre-Test 3 Section F 1) Write one of the functions listed below on top of the appropriate graph: x
y
5
.
0
log
=
, 3
x
y
=
, 2
x
e
y
−
=
, x
e
y
3
=
, 8
3
2
2
−
+
−
=
x
x
y
, x
y
3
log
2
=
, 13
5
2
−
+
=
x
x
y
3
3
x
y
−
=
-250
-200
-150
-100
-50
0
50
100
150
200
250
-6
-4
-2
0
2
4
6
_____________
-4
-3
-2
-1
0
1
2
3
0
0.5
1
1.5
2
____________________
-20
-10
0
10
20
30
40
-4
-2
0
2
4
____________________
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-4
-2
0
2
4
6
___________
GS 291 Pre-Test 3 2) Write one of the functions listed below on top of the appropriate graph: x
y
5
.
0
log
=
, 3
x
y
=
, 2
x
e
y
−
=
, x
e
y
3
=
, 8
3
2
2
−
+
−
=
x
x
y
, x
y
3
log
2
=
, 13
5
2
−
+
=
x
x
y
3
3
x
y
−
=
-80
-60
-40
-20
0
20
40
60
80
-5
0
5
____________
-3
-2
-1
0
1
2
3
4
5
0
1
2
3
4
__________________
0
1
2
3
4
5
6
7
8
-3
-2
-1
0
1
2
3
__________________
-30
-25
-20
-15
-10
-5
0
-4
-2
0
2
4
6
___________________________