Project 2 - Math 99 - Practice Final Due Tuesday 5 th December (100 points) Section 1: Multiple Choice Questions

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1 Project - Math 99 Final Practice Fall 017 Project - Math 99 - Practice Final Due Tuesday 5 th December (100 points) Section 1: Multiple Choice Questions Students Name : 1. The epression 10 + when factored fully is:- A. ( 1)( ) B. ( 1)( + ) C. ( + 1)( ) D. ( + 1)( + ). The epression 100y 00 when factored fully is:- A. 100(y ) B. 100(y + )(y ) C. (y + 0)(y 0) D. Some other answer. The epression a b 8a b when factored fully is:- A. a b (1 a) B. a b ( a) C. a b ( 8a) D. ab(ab a b ) E some other answer. The epression when factored fully is:- A. ( + 8)( + ) B. ( )( + ) C. ( )( ) D. ( + )( + ) E some other answer y 5. Simplify 7 8 y 1 A y B y C y D y 10 E some other answer

2 Project - Math 99 Final Practice Fall Simplify the following epression. p z 8z p 16 A. z z B C. z p D. 5 z 7. Simplify 16 A B C 1 D E some other answer 8. Add and simplify the following epression A 1 B 1 C D E some other answer 1 9. When you subtract the fractions and simplify the result you get:- 1 1 A. B. 1 C. D What is the slope and y-intercept of the line with equation + y 0 A. Slope and y-intercept 10 B. Slope and y-intercept 0 C. Slope and y-intercept 10 D. Slope ½ and y-intercept For the line with equation y + 8 what is the slope of the line. A. B. C.6 D.½ E. ½ 1. For the line with equation y 1 where does it cut the y ais? A. (0,1) B. (0,6) C. (0,) D. (0, ) E. (0, )

3 1. Determine which of the following points, if any, satisfy the system of equations. y 7 y A. The point (,1) B. The point (1, ) Project - Math 99 Final Practice Fall 017 C. The point ( 1, ) D. None of the points satisfy the system of equations 1. For the pair of equations + y 5 + y 10 Which is the only coordinates that satisfy both equations? A. (1,1) B. (1,) C. (,1) D. ( 1, ) E. ( 1, ) 15. Simplify the following radical epression 8 A. B. 16 C. 1 D. E some other answer 16. Simplify the following radical epression 7 6 y z 6 6 A. y z y B. y z y C. y z D. y z y E some other answer When you simplify the epression 8 y z y z into its simplest form you get.- A. 16 y z B. y z C. y z yz D. Some other answer 18. When you simplify the epression y by rationalizing the denominator and simplifying the result you get:- A. 9 y B. 9 y C. y D. Some other answer

4 Project - Math 99 Final Practice Fall The solution to the radical equation A. 1 B. C. 17 D. Some other answer 0. When you epress as a comple number in the form a + bi you get :- A. i B. + i C i D. Some other answer 1. Epress as a comple number a + bi A 7 B i C + i D 0 + 5i E some other answer. The quadratic equation has the following number of real number solutions A 0 solutions B 1 solution C solutions D solutions. The solution to the quadratic equation is:- A 5 and 5 B. 65 C. 5 D 1.5 and 1.5. The solution to the quadratic equation ( 5) 6 is A 101 B. 5 ± 6i C. 11i D. some other answer

5 Project - Math 99 Final Practice Fall 017 Section 1. Factor each of the following epressions, if an epression cannot be factored then say so. (a) (b) 1 1 b ab a a a b a a. Complete the calculation then simplify the following epressions. (a) 1 5 p p p p (b). 16

6 Project - Math 99 Final Practice Fall 017. Solve the following equations. (a) 7 5 (b) 5. Vecca can paddle her kayak 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.

7 Project - Math 99 Final Practice Fall (a) Draw on the grid the line with equation y 1. y (b) Draw on the grid the line with Equation + y 8 (c) Use your diagram to find the solution to the system of equations. y 1 + y 8

8 Project - Math 99 Final Practice Fall (a) Solve the pair of equations + y 10 by the substitution method. y 1 6.(b) Solve the system of equations y 10 by using the addition method. + y 5

9 7. If hamburgers and fries cost $.0 and hamburgers and fries cost $6.80. What are the cost of a single hamburger and a single portion of fries? Project - Math 99 Final Practice Fall A pet store owner wants to make 600 pounds of mied bird seed, the sunflower seeds cost $.0 per pound and the peanut seeds cost $1.0 per pound. The total cost of all the seed used in the miture was $100. How much of each seed was used?

10 9. Solve the following Radical Equations. Project - Math 99 Final Practice Fall 017 (a) (b) 17 9 b 10. Solve the quadratic equation by using the quadratic formula b ac a

11 Project - Math 99 Final Practice Fall Solve the quadratic equation by using the quadratic formula b b ac a 1. For the quadratic y 6 y (a) What is the shape of the quadratic? (b) What is the y-intercept? (c) What are the -intercepts? (d) What are the coordinates of the verte? (e) Sketch the quadratic use appropriate scales.

12 Project - Math 99 Final Practice Fall height h, in feet of a ball after t seconds is given by the model h 1t t (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 maimum height? (d) What is the maimum height the ball reaches?

13 Answers Project - Math 99 Final Practice Fall 017 Section 1: Multiple Choice Questions 1. A. B.A.B 5.A 6.A 7.B 8.B 9.B 10.A 11.E 1.D 1. A 1.B 15.D 16.B 17.B 18.D 19.B 0.D 1.C.A. A.B Section 1. Factor each of the following epressions, if an epression cannot be factored then say so. 7 ( 7) (a) 0 7 (+1)( 7) +1 a 1 a a 1 (b) a b a ab b (a 1). a a+1 (a b) a ab+b a 1. (a b)(a b) a b (a 1)(a 1) a b a 1. Complete the calculation then simplify the following epressions. (a) p 5 p p 1 p p+5+p+1 p+ p+6 p+ (p+) p+ (b) 16. ( )(+) (+) ( ) (+) +. Solve the following equations. 7 5 (a) +7 5 (b) + 5 ( + 7) ( 5)

14 Project - Math 99 Final Practice Fall 017. Vecca can paddle her kayak mph in still water. It takes her as long to paddle 8 miles upstream as it takes her to paddle 1 miles downstream. Find the speed of the water current. If you let speed of current, then upstream speed is, while downstream will be +. Since the times are equal 8 18 Distance Speed Time 8( + ) 18( ) mph Upstream 8 Downstream (a) Draw on the grid the line with equation y 1. y (b) Draw on the grid the line with Equation + y 8 y 5 0 (c) Use your diagram to find the solution to the system of equations. y 1 + y 8 Solution is the point (,) and y

15 Project - Math 99 Final Practice Fall (a) Solve the pair of equations + y 10 by the substitution method. y 1 Use + y 10 to get y +10 Substitute y +10 into the equation y 1 ( +10) Substitute into the equation y +10 () So the Solution is (, ) 6.(b) Solve the system of equations y 10 by using the addition method. + y 5 y 10 multiply by 6y 0 + y 5 multiply by 9 + 6y 75 Add the equations Put 5 into + y 5 (5) + y y 5 y y y 5 So the Solution is (5, 5 )

16 7. If hamburgers and fries cost $.0 and hamburgers and fries cost $6.80. What are the cost of a single hamburger and a single portion of fries? Let cost of Hamburgers Let y cost of fries hamburgers and fries cost $.0 gives us the equation + y.0 hamburgers and fries cost $6.80 gives us the equation + y 6.80 Project - Math 99 Final Practice Fall y.0 multiply by 6y y 6.80 leave equation alone + y 6.80 add the equations y 1.60 Put y $0.0 into + y.0 + (0.0) $1.50 Hamburger cost $1.50 each and fries cost $0.0 0 cents per portion y y $0.0 0 cents 8. A pet store owner wants to make 600 pounds of mied bird seed, the sunflower seeds cost $.0 per pound and the peanut seeds cost $1.0 per pound. The total cost of all the seed used in the miture was $100. How much of each seed was used? amount of sunflower seed y amount of peanut seed 600 pounds of mied bird seed gives us the equation + y 600 Total cost was $100 gives us the equation. + 1.y 100 Solve by the substitution method, let + y 600 be rewritten as y Put y into the equation. + 1.y ( + 600) pounds Put 00 into y y pounds. So amount of sunflower seed 00 pounds y amount of peanut seed 00 pounds

17 9. Solve the following Radical Equations. Project - Math 99 Final Practice Fall 017 (a) 16 (b) Square both sides Solve the quadratic equation by using the quadratic formula a 5 b and c 7 b ac () (5)( 7) b b ac a b b ac a and or Solve the quadratic equation by using the quadratic formula a 1 b 10 c 16 b b ac a b 10 b ac a and

18 1. For the quadratic y 8 Project - Math 99 Final Practice Fall 017 (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 -intercepts? Solve 8 0 ( )( + ) 0 At and at coordinates(,0) and (,0) (d) What are the coordinates of the verte? b a 1 y (1) (1) Coordinates of Verte (1, 9) (e) Sketch the quadratic use appropriate scales. y

19 Project - Math 99 Final Practice Fall The height h, in feet of a ball after t seconds is given by the model h 1t t (a) What is the height of the ball after 5 seconds? h 1t t 1(5) (5) feet (b) How long does it take the ball to reach a height of 16 feet? h 1t t 16 0 t 1t (t 6t + 8) 0 (t )(t ) Solution are at t and t seconds (c) How long does it take the ball to reach its maimum height? Use t b a 1 seconds (d) What is the maimum height the ball reaches? h 1t t 1() () 6 18 h 18 feet