Simplify x 4 x
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Math 99 Final Exam Practice
Math 99 Final Exam Practice
Section 1: Multiple Choice Questions
1. The expression 3x2 – 10x + 3 when factored fully is:-
A. (3x – 1)(x – 3) B. (3x – 1)(x + 3) C. (3x + 1)(x – 3) D. (3x + 1)(x + 3)
2. The expression 100y2 – 400x2 when factored fully is:-
A. 100(y2 – 4x2)
C. (2y + 20x)(2y – 20x)
B. 100(y + 2x)(y – 2x)
D. Some other answer
3. The expression 4a2b3 – 8a3b3 when factored fully is:-
C. a2b3(4 – 8a)A. 4a2b3(1 – 2a)
D. 4ab(ab2 – 2a2b2)
B. 4a2b3(– 2a)
E some other answer
4. The expression 3x2 + 10x – 8 when factored fully is:-
C. (3x – 4)(x – 2)A. (3x + 8)(x + 2)
D. (3x + 2)(x + 4)
B. (3x – 2)(x + 4)
E some other answer
4. Simplify4 xy 3
8x 2 y 7
A1
2 xy 4
Bxy 4
4C 2xy4 D 32x3y10 E some other answer
5. Simplify the following expression.
A.16 x 2
z 3B.
z 3
16 x 2C.
8 x 2
z 3D.
x 4 p 4
4 z 5
6.2
x 2 16
Ax
x 4B
x
x 4C
1
4D
x
4E some other answer
x( x 1)
x 1
2 x 1x( x 1)
Math 99 Final Exam Practice
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7. Add and simplify the following expression 4
x 4
x
x 4
A – 1 B1 C4 x
4 xD
4 x
4 xE some other answer
8. When you add the fractions
A. B.
3 2
x5 5
and simplify the result you get:-
5x 3C. D. some other answer
9. What is the slope of the line that passes through the points A(–5, 3) and B(10, – 2)
A. – 3 B. 3 C.1
3
1
3D.
10. What is the slope and y-intercept of the line with equation 4x + 2y = 20
A. Slope = – 2 and y-intercept = 10 B. Slope = – 4 and y-intercept = 20
C. Slope = 2 and y-intercept = 10 D. Slope = – ½ and y-intercept = 10
11. For the line with equation 4y + 2x = 8 what is the slope of the line.
A. 2 B. 4 C.6 D.½ E. – ½
12. For the line with equation 2x – 4y = 12 where does it cut the y – axis?
A. (0,12) B. (0,6) C. (0,3) D. (0, – 3 ) E. (0, – 4 )
13. Determine which of the following points, if any, satisfy the system of equations.
y =3x – 2y =
4x – 74
A. The point (2,1) B. The point (1, – 3)
C. The point (– 1 , 3) D. None of the points satisfy the system of equations
14. The system of equations x + 2y = 5 are:-102x + 4y =
A. Consistent and have 1 solution B. Inconsistent and have no solutions
C. Dependant and have an infinite solution D. Some other answer
Math 99 Final Exam Practice
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15. For the pair of equations x + 2y = 52x + 4y = 10
Which is the only coordinates that satisfy both equations?
A. (1,1) B. (1,2) C. (2,1) D. (– 1, – 3 ) E. (– 1, 3 )
16. Simplify the following radical expression 48
A. 2 24 B. 16 3 C. 2 12 D. 4 3 E some other answer
17. Simplify the following radical expression 4x 3 y 7 z 6
A. 2x 2 y 6 z 6 xy B. 2xy 3 z 3 xy C. 2xy 3 z 3
D. 4xy 3 z 3 xy
18. When you simplify the expression
E some other answer
8x 3 y 3 z 5 2x 2 y 3 z into its simplest form you get.-
A. 16x5 y 6 z 6 B. 4x2y3z3 x C. 4x3 y 4 z 2 yz D. Some other answer
19. When you simplify the expression3x 2 y 3
3xby rationalizing the denominator and simplifying the result you get:-
A.9 x3 y 3
3xB.9 x3 y 3 x
3xC. 3xy 3 3x D. Some other answer
20. The solution to the radical equation = 6
A. x = B. x = 4 C. x = D. Some other answer
21. When you express 16 + 9 as a complex number in the form a + bi you get :-
A. 4 – 3i B. 4 + 3i C. 0 + 5i D. Some other answer
22. Express as a complex number a + bi 16 + 9
A 7 B 4 – 3i C 4 + 3i D 0 + 5i E some other answer
V X
Math 99 Final Exam Practice
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23. The quadratic equation x2 – 4x + 9 = 0 has the following number of real number solutions
A 0 solutions B 1 solution C 2 solutions D 3 solutions
24. The solution to the quadratic equation 2x2 + 9 = 59 is:-
A x = 5 and x = – 5 B. x = 625 C. x = 25 D x = 12.5 and x = – 12.5
25. The solution to the quadratic equation (x – 5)2 = – 36 is
A x = 1301 B. x = C. x = 11i D. some other answer
26. The coordinates of the vertex of the quadratic equation y = x2 + 4x + 6 is:
A (– 2,2) B (– 2,0) C (– 2, – 6) D (2, –2) E some other answer
27. When the formula V = 2ab 2 is expressed in terms of b we get.
Ab =1
2aV 2 Bb= aV
1
2Cb=
2V
aDb=
V
2aE some other answer
28. If you take the formulaV = x 4r 2 and change the subject of the formula to r you get:-
A.
C.
r=
r=
V 2 x
4
42
B.
D.
r=
r=
V 2 x
4
x V 2
4
2
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Math 99 Final Exam Practice
Section 21. Simplify each of the following expressions, if an expression cannot be factored then say so.
(a)x 2 7 x
3x 2 20 x 7
(b)a 2 2a 1
a 2ab b 2
a 1
a b
2. Add or subtract the following and simplify the answer where possible.
(a)3
p
6
p 3(b)
2
x 2
x
x 2
Math 99 Final Exam Practice
3. Solve the following equations.
(a) x 5
2
x 7
3(b)
5
3
x
2
x
4
4. Vecca can paddle her kayak 4 mph in still water. It takes her as long to paddle 6 miles upstream as ittakes her to paddle 18 miles downstream. Find the speed of the water current.
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Math 99 Final Exam Practice
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5. (a) Draw on the grid the line with
yx + 2y
==
2x – 18
equation y = 2x – 1 .
x
(b) Draw on the grid the line withEquation x + 2y = 8
(c) Use your diagram to find the solutionto the system of equations.
y
Math 99 Final Exam Practice
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6.(a) Solve the pair of equations by the substitution method.2x + y =3x – 2y =
101
6.(b) Solve the system of equations x – 3y = – 10 by using the addition method.3x + 2y = 25
Math 99 Final Exam Practice
7.
8.
If 2 hamburgers and 3 fries cost $3.50 and 4 hamburgers and 3 fries cost $6.50.What are the cost of a single hamburger and a single portion of fries?
A pet store owner wants to make 600 pounds of mixed bird seed, the sunflower seeds cost $2.30 perpound and the peanut seeds cost $1.40 per pound. The total cost of all the seed used in the mixturewas $1200. How much of each seed was used?
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Math 99 Final Exam Practice
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9. Solve the following Radical Equations.
(a) x = 4
(b) 2x 17 = 9
10. Solve the quadratic equation x2 + 8x – 20 = 0 by using “Completing the square” method.
11. Solve the quadratic equation x2 + 3x – 10 = 0 by using “Completing the square” method.
Math 99 Final Exam Practice
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12. Solve the quadratic equation 5x2 + 2x – 7 = 0 by using the quadratic formula x = b b2 4ac
2a
13. Solve the quadraticequation. x2+ 10x + 16 = 0 by using the quadratic formula x = b b2 4ac
2a
Math 99 Final Exam Practice
14. For the quadratic y = x2 – 2x – 6
15. The height h, in feet of a ball after t seconds is given by the model h = 12t – 2t2
(a) What is the height of the ball after 5 seconds?
(b) How long does it take the ball to reach a height of 3.6 feet?
(c) How long does it take the ball to reach its maximum height?
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(a) What is the shape of the quadratic?
(b) What is the y-intercept?
x
(c) What are the x-intercepts?
(d) What are the coordinates of the vertex?
(e) Sketch the quadratic – use appropriate scales.
y
Math 99 Final Exam Practice
16. V = x y 2 change the subject of the formula to y.
17. H = r2h change the subject of the formula to r.
18. John traveled from his own home to his mother’s home 200 miles away and then he returned back home thatsame day. During these journey’s he noticed that his speed was 10 mph faster coming homethan it was when he traveled to his mothers home. The total time spent on both parts of the journey was 9hours. What were his speeds during this journey?
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(a 1) (a b)(a b) (a b)
3x 20 x 7
2
3 ( p 3)
2 x ( x 2)2 ( x 2)
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Math 99 Final Exam Practice
Math 99 Final Exam Practice – Solutions.Section I
9. D19. D
10. A20.B
1. A11. E21. D
2.B12. D22. C
3. A13. A23. A
4. A14. C24. A
5. A15. B25. B
6. B16. D26. A
7. B17. D27.D
8. C18. B28. A
Section 21. Factor each of the following expressions, if an expression cannot be factored then say so.
(a)x 2 7 x
2=
x( x 7)
(3x 1)( x 7)=
x
(3x 1)
(b)a 2 2a 1
a 2ab b 2
a 1
a b=
a 2 2ab b 2
a 2 2a 1
(a 1)
(a b)= =
(a b) (a 1)(a 1) (a 1)
2. Add or subtract the following and simplify the answer where possible.
(a)3
p
6
p 3=
p ( p 3)
p
p
6
( p 3)=
3( p 3)
p( p 3)
6 p
p( p 3)=
9 p 9
p( p 3)
(b) x
x 2
( x 2) ( x 2)=
x 2 ( x 2) ( x 2)=
2( x 2)
( x 2)( x 2)
x( x 2)
( x 2)( x 2)
=
=
x 2 2 x 2 x 4
( x 2)( x 2)
x 2 4 x 4
( x 2)( x 2)3. Solve the following equations.
(a) x 5
2
x 7
3(b)
5
3
x
2
x
4
2(x+ 7) =
2x + 14 =
3(x – 5)
3x – 15
x
2x
2
3x 20
12 123x 20
1229 = x 6x + 40 =
40 =12x
6x20
3
40
6so x
Distance Speed Time
Upstream 6 4 – x
Downstream 18 4+x
x y0 42 34 2
x y0 – 11 12 3
Math 99 Final Exam Practice
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4. Vecca can paddle her kayak 4 mph in still water. It takes her as long to paddle 6 miles upstream as ittakes her to paddle 18 miles downstream. Find the speed of the water current.
and Speed (Downstream) = 4 + xLet x = speed of current then
Since times are the same
Speed (upstream) = 4 – x
=
18(4 – x)
6(4 + x) =
72 – 18x
24 + 6x =
24x =
48
x = 2
5. (a) Draw on the grid the line withequation y = 2x – 1 .
(b) Draw on the grid the line withEquation x + 2y = 8
(c) Use your diagram to find the solution to the system of equations. yx + 2y
==
2x – 18
6.(a) Solve the pair of equations 2x + y = 10 by the substitution method.3x – 2y = 1
3x – 2y3x – 2(10 – 2x)3x – 20 + 4x
7x – 207xx
======
1111213
Rearrange equation 1 to get y = 10 – 2x and substitute it into equation 2
So y = 10 – 2x = 10 – 2(3) = 10 – 6 = 4
So solution is (3,4)
x
So the Speed of current = 2 mphy
y = 2x - 1
X + 2y = 8
Math 99 Final Exam Practice
6.(b) Solve the system of equations x – 3y = – 10 by using the addition method.3x + 2y = 25
x – 3y = – 10 Equation 1 x – 3 = – 3x +9y = 303x + 2y = 25 Equation 2 = 3x + 2y = 25
Add the equations 11yy
==
555
Put y = 5 into 3x + 2y3x + 2(5)
3x + 103x
====
25252515
x = 5 So solution is(5,5)
7. If 2 hamburgers and 3 fries cost $3.50 and 4 hamburgers and 3 fries cost $6.50.What are the cost of a single hamburger and a single portion of fries?
Let x = cost of hamburger and y = cost of fries
2 hamburgers and 3 fries cost $3.50 gives us the equation4 hamburgers and 2 fries cost $6.50. gives us the equation
2x + 3y =4x + 3y =
3.56.5
2x + 3y =4x + 3y =
3.5 Equation 1 x – 16.5 Equation 2
– 2x – 3y =4x + 3y =
– 3.56.5
2xx
==
3.1.50
Put x = 1.50 into
Add the equations
2x + 3y =
3.5
2x + 3(1.50) =
3.5
2x + 3
= 3.5
2x
= 0.5
x
= 0.25
So cost of hamburger = $1.50 and the cost of fries = $0.25
8. A pet store owner wants to make 600 pounds of mixed bird seed, the sunflower seeds cost $2.30 perpound and the peanut seeds cost $1.40 per pound. The total cost of all the seed used in the mixturewas $1200. How much of each seed was used?
Let x = amount of sunflower seed and y = amount of peanut seed
to make 600 pounds of mixed bird seed gives us the equation x+y = 600The total cost of all the seed used in the mixture was $1200 gives us the equation 2.3x + 1.4y = 1200
Rearranging x + y = 600 to y = 600 – x and substituting it into the equation 2.3x + 1.4y = 12002.3x +1.4(600 – x) = 1200
2.3x + 840 – 1.4x = 12000.9x
x= 360= 400
Put x = 400 into x + y = 600 to get y = 200, solution is 400 of sunflower and 200 pounds peanuts
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Math 99 Final Exam Practice
9. Solve the following Radical Equations.
(a) (b)x
x ==
416
2x 172x + 17
==
981
2xx
==
6432
10. Solve the quadratic equation x2 + 8x – 20 = 0 by using “Completing the square” method.
So solutions are x + 4x
==
62
x2 + 8x – 20x2 + 8x(x + 4)2
===
02020 + 16
(x + 4)2 = 36 and x + 4 = – 6x+4 = x = – 10x+4 =
11. Solve the quadratic equation x2 + 3x – 10 = 0 by using “Completing the square” method.
So solutions arex2 + 3x – 10x2 + 3x
==
010
x + 1.5x
==
3.52
10 + 1.52
12.25(x + 1.5)2
(x + 1.5)2
x + 1.5
===
and x + 1.5x==
– 3.5– 5
x + 1.5 =
12. Solve the quadratic equation 5x2 + 2x – 7 = 0 by using the quadratic formula x = b b2 4 ac
2a
a=5 b=2 c= – 7 b2 – 4ac = (2)2 – 4(5)(– 7) = 4 + 140 = 144
x = = = so x =
x=
13. Solve the quadraticequation. x2+ 10x + 16 = 0 by using the quadratic formula x = b b2 4 ac
2a
a=1 b = 10 c = 16 b2 – 4ac = (10)2 – 4(1)(16) = 100 – 64 = 36
x = = = so x =
x=
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b b2 4 ac
2a
b b2 4 ac
2a
12t – 2t = 12(3) – 2(3)2 = 36 – 18 = 18 ft
Math 99 Final Exam Practice
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14. For the quadratic y = x2 – 2x – 6
x= =
x = 3.65 and x = – 1.65
(d) What are the coordinates of the vertex?
x = = = 1
y = (1)2 – 2(1) – 6 = 1 – 2 – 6 = – 7 Coordinate of vertex is (1,– 7)
(f) Sketch the quadratic – use appropriate scales.
h = 12t – 2t215. The height h, in feet of a ball after t seconds is given by the model
(a) What is the height of the ball after 5 seconds?
h = 12t – 2t2 = 12(5) – 2(5)2 = 60 – 2(25) = 60 – 50 = 10 ft
(b) How long does it take the ball to reach a height of 3.6 feet?
h = 12t – 2t2
3.6 = 12t – 2t2
– 2t2 + 12t – 3.6 = 0 Use quadratic formula to get t = =
t = 5.7sec and t = 0.3 sec
(c) How long does it take the ball to reach its maximum height?
Maximum height will occur at vertex. t = = = 3 sec
h = 2
16. V =x y 2 change the subject of the formula to y.
V2 =
x + y2
V2 – x =
y2
=
y
y
=
(a) What is the shape of the quadratic?Concave up
(b) What is the y-intercept?y= – 6
x
(c) What are the x-intercepts?Use quadratic formula to get
y
Math 99 Final Exam Practice
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17. H = r2hchange the subject of the formula to r.
H
= r2h
=
r2
=
r
r
=
18. John traveled from his own home to his mother’s home 200 miles away and then he returned back home thatsame day .During these journey’s he noticed that his speed was 10 mph faster coming home than it was whenhe traveled to his mothers home. The total time spent on both parts of the journey was 9 hours. What were hisspeeds during this journey?
= 9
=
=
=
9(x2 + 10x)9x2 + 90x
==
400x + 2000400x + 2000
9x2 + 90x – 400x – 2000 = 0= 09x2 – 310x – 2000
Use quadratic formula to get x =
=
x = = = 40 So the speeds are x = 40 mph and a + 10 = 50 mph
x = = = – 5.55 not a usable solution
Distance Speed Time
Going to mother
Returning Home
Since total time was 12 hours
200
200
x
x + 10
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