Project 2 - Math 99 Final Practice – Fall 2017
Project 2 - Math 99 - Practice Final
Due Tuesday 5th December (100 points)
Section 1: Multiple Choice Questions
Students Name :_______________________________
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) B. 100(y + 2x)(y – 2x)
C. (2y + 20x)(2y – 20x) D. Some other answer
3. The expression 4a2b3 – 8a3b3 when factored fully is:-
A. 4a2b3(1 – 2a) B. 4a2b3(– 2a) C. a2b3(4 – 8a)
D. 4ab(ab2 – 2a2b2) E some other answer
4. The expression 3x2 + 10x – 8 when factored fully is:-
A. (3x + 8)(x + 2) B. (3x – 2)(x + 4) C. (3x – 4)(x – 2)
D. (3x + 2)(x + 4) E some other answer
5. Simplify 72
3
8
4
yx
xy
A 42
1
xy B
4
4xy C 2xy4 D 32x3y10 E some other answer
Project 2 - Math 99 Final Practice – Fall 2017
6. Simplify the following expression. 4𝑥3𝑝2
2𝑧4 ∙8𝑧
𝑥𝑝2
A. 3
216
z
x
B. 2
3
16x
z
C. 3
28
z
x
D. 5
44
4z
px
7. Simplify
16
42
2
x
xx
A 4x
x B
4x
x C
4
1 D
4
x E some other answer
8. Add and simplify the following expression 4
4
4
xx
x
A – 1 B 1 C x
x
4
4 D
x
x
4
4 E some other answer
9. When you subtract the fractions 12
1
12
23
x
x
x
x and simplify the result you get:-
A. 12
32
x
x B. 1 C.
12
34
x
x D. – 1
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 )
Project 2 - Math 99 Final Practice – Fall 2017
13. Determine which of the following points, if any, satisfy the system of equations. y = 4x – 7 3x – 2y = 4
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. For the pair of equations x + 2y = 5
2x + 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 )
15. Simplify the following radical expression 48
A. 242 B. 316 C. 122 D. 34 E some other answer
16. Simplify the following radical expression 6734 zyx
A. xyzyx 6622 B. xyzxy 332 C. 332 zxy
D. xyzxy 334 E some other answer
17. When you simplify the expression zyxzyx 32533 28 into its simplest form you get.-
A. 66516 zyx B. 4x2y3z3 x C. yzzyx 2434 D. Some other answer
18. When you simplify the expression x
yx
3
3 32
by rationalizing the denominator and simplifying the result you get:-
A. x
yx
3
9 33
B. x
xyx
3
9 33
C. xxy 33 3 D. Some other answer
Project 2 - Math 99 Final Practice – Fall 2017
19. The solution to the radical equation 2√2𝑥 + 1 = 6
A. x = √3−1
2 B. x = 4 C. x =
17
2 D. Some other answer
20. 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
21. Express as a complex number a + bi 16 + 9
A 7 B 4 – 3i C 4 + 3i D 0 + 5i E some other answer
22. 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
23. 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
24. The solution to the quadratic equation (x – 5)2 = – 36 is
A x = 1301 B. x = 5 ± 6𝑖 C. x = 11i D. some other answer
Project 2 - Math 99 Final Practice – Fall 2017
Section 2 1. Factor each of the following expressions, if an expression cannot be factored then say so.
(a) 7203
72
2
xx
xx
(b) 22
2
2
121
baba
aa
ba
a
2. Complete the calculation then simplify the following expressions.
(a) 3
1
3
5
p
p
p
p (b)
4
2.
2
16 3
24
2
x
x
xx
x
Project 2 - Math 99 Final Practice – Fall 2017
3. Solve the following equations.
(a) 2
5
3
7
xx (b)
23
5
4
xx
4. Vecca can paddle her kayak 4 mph in still water. It takes her as long to paddle 6 miles upstream as it
takes her to paddle 18 miles downstream. Find the speed of the water current.
Project 2 - Math 99 Final Practice – Fall 2017
5. (a) Draw on the grid the line with equation y = 2x – 1 .
(b) Draw on the grid the line with Equation x + 2y = 8
(c) Use your diagram to find the solution
to the system of equations. y = 2x – 1 x + 2y = 8
x
y
Project 2 - Math 99 Final Practice – Fall 2017
6.(a) Solve the pair of equations 2x + y = 10 by the substitution method. 3x – 2y = 1 6.(b) Solve the system of equations x – 3y = – 10 by using the addition method.
3x + 2y = 25
Project 2 - Math 99 Final Practice – Fall 2017
7. If 2 hamburgers and 3 fries cost $4.20 and 4 hamburgers and 2 fries cost $6.80. What are the cost of a single hamburger and a single portion of fries?
8. A pet store owner wants to make 600 pounds of mixed bird seed, the sunflower seeds cost $2.30 per
pound and the peanut seeds cost $1.40 per pound. The total cost of all the seed used in the mixture
was $1200. How much of each seed was used?
Project 2 - Math 99 Final Practice – Fall 2017
9. Solve the following Radical Equations.
(a) x = 4
(b) 172 x = 9
10. Solve the quadratic equation 5x2 + 2x – 7 = 0 by using the quadratic formula x = a
acbb
2
42
Project 2 - Math 99 Final Practice – Fall 2017
11. Solve the quadratic equation. x2 + 10x + 16 = 0 by using the quadratic formula x = a
acbb
2
42
12. For the quadratic y = x2 – 2x – 6 (a) What is the shape of the quadratic? (b) What is the y-intercept? (c) What are the x-intercepts? (d) What are the coordinates of the vertex?
(e) Sketch the quadratic – use appropriate scales.
x
y
Project 2 - Math 99 Final Practice – Fall 2017
13. 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 16 feet?
(c) How long does it take the ball to reach its maximum height?
(d) What is the maximum height the ball reaches?
Project 2 - Math 99 Final Practice – Fall 2017
Answers
Section 1: Multiple Choice Questions
1. A 2. B 3.A 4.B 5.A
6.A 7.B 8.B 9.B 10.A
11.E 12.D 13. A 14.B 15.D
16.B 17.B 18.D 19.B 20.D
21.C 22.A 23. A 24.B
Section 2 1. Factor each of the following expressions, if an expression cannot be factored then say so.
(a) 7203
72
2
xx
xx =
𝑥(𝑥−7)
(3𝑥+1)(𝑥−7) =
𝑥
3𝑥+1
(b) 22
2
2
121
baba
aa
ba
a
=
(𝑎−1)
(𝑎−𝑏).
𝑎2−2𝑎+1
𝑎2−2𝑎𝑏+𝑏2 = 𝑎−1
𝑎−𝑏.
(𝑎−𝑏)(𝑎−𝑏)
(𝑎−1)(𝑎−1) =
𝑎−𝑏
𝑎−1
2. Complete the calculation then simplify the following expressions.
(a) 3
1
3
5
p
p
p
p =
𝑝+5+𝑝+1
𝑝+3 =
2𝑝+6
𝑝+3 =
2(𝑝+3)
𝑝+3 = 2
(b) 4
2.
2
16 3
24
2
x
x
xx
x =
(𝑥−4)(𝑥+4)
𝑥2(𝑥+2)∙
2𝑥3
(𝑥−4) =
2𝑥(𝑥+4)
𝑥+2
3. Solve the following equations. 2
5
3
7
xx
(a) 𝑥+7
3 =
𝑥−5
2 (b)
𝑥
4+
5
3 =
𝑥
2
2(x + 7) = 3(x – 5) 12.𝑥
4+ 12.
5
3 = 12.
𝑥
2
2x + 14 = 3x – 15 3x + 20 = 6x
2x + 29 = 3x 20 = 3x
29 = x 20
3 = x
Project 2 - Math 99 Final Practice – Fall 2017
4. Vecca can paddle her kayak 4 mph in still water. It takes her as long to paddle 8 miles upstream as it
takes her to paddle 12 miles downstream. Find the speed of the water current.
If you let x = speed of current, then upstream speed is 4 – x , while downstream will be 4 + x.
Since the times are equal
x4
8 =
x4
18
8(4 + x) = 18(4 – x)
32 + 8x = 72 – 18x
8x = 40 – 12x
20x = 40
x = 20
40
x = 2 mph
5. (a) Draw on the grid the line with equation y = 2x – 1 .
(b) Draw on the grid the line with Equation x + 2y = 8
(c) Use your diagram to find the solution
to the system of equations. y = 2x – 1 x + 2y = 8 Solution is the point (2,3) x = 2 and y = 3
Distance Speed Time
Upstream 8 4 – x x4
8
Downstream 18 4 + x x4
18
x
x y
0 – 1
1 1
2 3
x y
– 2 5
0 4
2 3
Project 2 - Math 99 Final Practice – Fall 2017
6.(a) Solve the pair of equations 2x + y = 10 by the substitution method. 3x – 2y = 1 Use 2x + y = 10 to get y = – 2x +10
Substitute y = – 2x +10 into the equation 3x – 2y = 1 3x – 2(– 2x +10) = 1 3x + 4x – 20 = 1 7x – 20 = 1 7x = 21
x = 21
7
x = 3 Substitute x = 3 into the equation y = – 2x +10 = – 2(3) +10 = – 6 + 10 = 4 So the Solution is (3, 4) 6.(b) Solve the system of equations x – 3y = – 10 by using the addition method.
3x + 2y = 25
x – 3y = – 10 multiply by 2 2x – 6y = – 20
3x + y = 25 multiply by 3 9x + 6y = 75
Add the equations 11x = 55
x = 55
11
x = 5
Put x = 5 into 3x + 2y = 25
3(5) + 2y = 25
15 + 2y = 25
2y = 10
y = 10
2
y = 5 So the Solution is (5, 5 )
Project 2 - Math 99 Final Practice – Fall 2017
7. If 2 hamburgers and 3 fries cost $4.20 and 4 hamburgers and 2 fries cost $6.80. What are the cost of a single hamburger and a single portion of fries?
Let x = cost of Hamburgers
Let y = cost of fries 2 hamburgers and 3 fries cost $4.20 gives us the equation 2x + 3y = 4.20
4 hamburgers and 2 fries cost $6.80 gives us the equation 4x + 2y = 6.80 2x + 3y = 4.20 multiply by – 2 – 4x – 6y = – 8.40 4x + 2y = 6.80 leave equation alone 4x + 2y = 6.80 add the equations – 4y = – 1.60
y = −1.60
−4
y = $0.40 = 40 cents Put y = $0.40 into 2x + 3y = 4.20 2x + 3(0.40) = 4.20 2x + 1.20 = 4.20 2x = 3.00
x = 3.00
2
x = $1.50 Hamburger cost = $1.50 each and fries cost = $0.40 = 40 cents per portion.
8. A pet store owner wants to make 600 pounds of mixed bird seed, the sunflower seeds cost $2.30 per
pound and the peanut seeds cost $1.40 per pound. The total cost of all the seed used in the mixture
was $1200. How much of each seed was used?
x = amount of sunflower seed
y = amount of peanut seed
600 pounds of mixed bird seed gives us the equation x + y = 600
Total cost was $1200 gives us the equation 2.3x + 1.4y = 1200
Solve by the substitution method, let x + y = 600 be rewritten as y = – x + 600
Put y = – x + 600 into the equation 2.3x + 1.4y = 1200
2.3x + 1.4(– x + 600) = 1200
2.3x – 1.4x + 840 = 1200
0.9x = 360
x = 400 pounds
Put x = 400 into y = – x + 600 = y = – 400 + 600 = 200 pounds.
So x = amount of sunflower seed = 400 pounds
y = amount of peanut seed = 200 pounds
Project 2 - Math 99 Final Practice – Fall 2017
9. Solve the following Radical Equations.
(a) x = 4 x = 42 = 16
(b) 172 x = 9
2x + 17 = 81 Square both sides
2x = 64
x = 64
2
x = 32
10. Solve the quadratic equation 5x2 + 2x – 7 = 0 by using the quadratic formula x = a
acbb
2
42
a = 5 b = 2 and c = – 7 b2 – 4ac = (2)2 – 4(5)( – 7) = 4 + 140 = 144
x = a
acbb
2
42
= 10
1442
= 10
122
x = −2+12
10=
10
10 = 1 and x =
−2−12
10=
−14
10 = −1.4 or −
7
5
11. Solve the quadratic equation. x2 + 10x + 16 = 0 by using the quadratic formula x = a
acbb
2
42
x2 + 10x + 16 = 0 a = 1 b = 10 c = 16
x = a
acbb
2
42
= 2
3610
= 2
610
x = −10+6
2=
−4
2 = −2 and x =
−10−6
2=
16
2 = −8
Project 2 - Math 99 Final Practice – Fall 2017
12. For the quadratic y = x2 – 2x – 8 (a) What is the shape of the quadratic? Concave up (b) What is the y-intercept? y-intercept at y = – 8 coordinates(0, – 8) (c) What are the x-intercepts? Solve x2 – 2x – 8 = 0 (x – 4)(x + 2) = 0 At x = 4 and at x = – 2 coordinates(4,0) and (– 2,0)
(d) What are the coordinates of the vertex? x = −𝑏
2𝑎 =
2
2 = 1
y = (1)2 – 2(1) – 8 = 1 – 2 – 8 = – 9 Coordinates of Vertex (1, – 9)
(e) Sketch the quadratic – use appropriate scales.
x
y
Project 2 - Math 99 Final Practice – Fall 2017
13. 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?
h = 12t – 2t2 = 12(5) – 2(5)2 = 60 – 50 = 10 feet
(b) How long does it take the ball to reach a height of 16 feet?
h = 12t – 2t2 = 16
0 = 2t2 – 12t + 16
0 = 2(t2 – 6t + 8)
0 = 2(t – 4)(t – 2)
Solution are at t = 2 and t = 4 seconds
(c) How long does it take the ball to reach its maximum height?
Use t = −𝑏
2𝑎 =
−12
−4 = 3 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
(d) What is the maximum height the ball reaches?
h = 12t – 2t2
= 12(3) – 2(3)2
= 36 – 18
h = 18 feet