Download Math 99 Test 1

Math 99 Test 1 –Spring 2013
Math 99 Test 1
Students Name:_____________________________________________
1.(a)
Evaluate the following using the function f(x) = 2x2 – 3x + 4
(i)
1.(b)
(ii)
f(– 2)
(ii)
3(x – 2) + 5
Solve the following equations.
(i)
1.(c)
f(4)
12x – 7 =
8x – 23
=
2(2x – 7) + 1
Solve the following in equation
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Math 99 Test 1 –Spring 2013
2.(a)
On the grid below graph 2x + 4y = 8 by plotting 3 points.
2.(b)
On the grid below graph y = 2x – 3 by plotting 3 points.
2.(c)
Use the graphs below to solve the system of equations
y
0
x
y
x
y
2x + 4y = 8
y = 2x – 3
x
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Math 99 Test 1 –Spring 2013
3.
Solve the following system of equations using the Substitution method.
(a)
y
=
2x + 7y =
(b) 2x + 6y
5x – 4y
=
=
2x – 7
–1
12
11
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Math 99 Test 1 –Spring 2013
4.
Solve the following system of equations using the Addition (Elimination) method.
(a)
2x – 3y = 13
4x + 3y = 17
(b)
x + 8y =
x– y =
–9
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Math 99 Test 1 –Spring 2013
5.
Use system of equations to solve the following two problems.
(a)
The total wages earned by two friends in one day was $250 if one made $38 more than
the other – how much wages did each friend make on that day?
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Math 99 Test 1 –Spring 2013
5.(b)
A person has $10,000 to invest , he puts his money into two banks one gives 2% interest rate
and the other gives 4% interest. The total interest he got in a year was $320, how much money
did he place in each bank?
6. Bonus Question (Extra 5 points). Change the formula L = (2b – 3a) to be in the form a = …….
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Math 99 Test 1 –Spring 2013
Solutions:
1.(a)
1.(b)
1.(c)
Evaluate the following using the function f(x) = 2x2 – 3x + 4
(i)
f(4)
=
=
=
=
2(4)2 – 3(4) + 4
2(16) – 12 + 4
32 – 12 + 4
24
(ii)
f(– 2)
=
=
=
=
2(– 2)2 – 3(– 2) + 4
2(4) + 6 + 4
8+6+4
18
Solve the following equations.
(i)
12x – 7
12x
4x
x
=
=
=
=
(ii)
3(x – 2) + 5
3x – 6 + 5
3x – 1
–x
x
8x – 23
8x – 16
– 16
–4
=
=
=
=
=
2(2x – 7) + 1
4x – 14 + 1
4x – 13
– 12
12
Solve the following in equation
multiply by both sides by4
Subtract 3 from both sides
Subtract 6x from both sides
Divide both sides by – 2
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Math 99 Test 1 –Spring 2013
2.(a)
2.(c)
On the grid below graph 2x + 4y = 8
by plotting 3 points.
2.(b)
On the grid below graph y = 2x – 3
by plotting 3 points.
x
y
x
y
0
2
0
–3
2
1
1
–1
4
0
2
1
Use the graphs below to solve the system of equations
y
0
x
2x + 4y = 8
y = 2x – 3
Scale x-axis
1 = 1 box
Scale y-axis
1 = 2 boxes
Solution is the point (2,1)
3.
Solve the following system of equations using the Substitution method.
(a)
y
=
2x + 7y =
2x – 7
–1
Substitute y = 2x – 7 into the equation
2x + 7y
2x + 7(2x – 7)
2x + 14x – 49
16x – 49
16x
x
=
=
=
=
=
=
–1
–1
–1
–1
48
3
Put x = 3 into the equation y = 2x – 7 = 2(3) – 7 = – 1
So the solution is (3, – 1)
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Math 99 Test 1 –Spring 2013
3.(b)
2x + 6y =
5x – 4y =
12
11
Take the equation
2x + 6y = 12
2x
= – 6y + 12
x
= – 3y + 6
Substitute x = – 3y + 6 into the equation
and rewrite it in the form x = …………..
5x – 4y =
5(– 3y + 6) – 4y =
– 15y + 30 – 4y =
– 19y + 30
=
– 19y
=
y
=
11
11
11
11
– 19
1
Put y = 1 into the equation x = – 3y + 6 = – 3(1) + 6 = 3
So the solution is (3, 1)
4.
Solve the following system of equations using the Addition (Elimination) method.
(a)
2x – 3y
4x + 3y
6x
x
=
=
=
=
13
17
30
5
add the two equations
Put x = 5 into the equation
4x + 3y
4(5) + 3y
20 + 3y
3y
y
=
=
=
=
=
17
17
17
–3
–1
So the solution is (5, – 1)
4.(b)
x + 8y =
x– y =
x + 8y
3x – 4y
x + 8y
6x – 8y
7x
x
Put x =
–9
multiply equation by 6 3x – 4y =
=
=
–9
1
multiply equation by 2 6x – 8y =
=
=
=
=
–9
2
–7
–1
Add the Equations
Divide both sides by 7
into the equation
So the solution is(
,
x + 8y
+ 8y
8y
y
=
=
=
=
1
2
–9
–9
–8
)
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Math 99 Test 1 –Spring 2013
5.
Use system of equations to solve the following two problems.
(a)
The total wages earned by two friends in one day was $250 if one made $38 more than
the other – how much wages did each friend make on that day?
x
y
=
=
wage of first friend
wage of second friend
The total wages earned by two friends in one day was $250 gives equation x + y = 250
one made $38 more than the other gives the equation y = x + 38
Solve the system of equations x + y
y
Substitute y
= x + 38
= 250
= x + 38
into the equation
Put x = 1 into the equation y
by using the substitution method
x+y
x + x + 38
2x + 38
2x
x
=
=
=
=
=
250
250
250
212
106
= x + 38 = 106 + 38 = 144
Solution is that one friend made $106 while the other made $144
5.(b)
A person has $10,000 to invest , he puts his money into two banks one gives 2% interest rate
and the other gives 4% interest. The total interest he got in a year was $320, how much money
did he place in each bank?
Let
x = money invested in the 2% Bank
y = money invested in the 4% Bank
Total amount of money was $10,000 becomes
x+y
Total Interest of $320 becomes
0.02x + 0.04y
=
=
x+y
0.02x + 0.04y
x+y =
2x + 4y =
x+y =
2x + 4y =
10,000
320
Put x = 4,000 into
=
=
10,000
320
multiply by 100
multiply by – 4
– 4x– 4y
2x + 4y
Add the two equations – 2x
x
x+y
=
4,000 + y =
y =
=
=
=
=
10,000
320
10,000
32,000
– 40,000
32,000
– 8,000
4,000
10,000
10,000
6,000
Solution: So he invested x = $4,000 in the 2% bank and $6,000 in the 4% bank.
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Math 99 Test 1 –Spring 2013
6. Bonus Question (Extra 5 points). Change the formula L = (2b-3a) to be in the form a = …….
L
=
2L
=
(2b – 3a)
2b – 3a
Multiply both sides by 2
– 3a
Subtract 2b form both sides
=
a
Divide both sides by – 3
=
a
2L – 2b =
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