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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


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 )


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


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


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


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.


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


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


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?


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


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


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?


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


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


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 )


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


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


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


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

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