Project - Math 99 Final Practice Due Thursday 3 rd August

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1 Project - Math 99 Final Practice Summer 017 Project - Math 99 Final Practice Due Thursday rd August 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 400 when factored fully is:- A. 100(y 4 ) B. 100(y + )(y ) C. (y + 0)(y 0) D. Some other answer. The epression 4a b 8a b when factored fully is:- A. 4a b (1 a) B. 4a b ( a) C. a b (4 8a) D. 4ab(ab a b ) E some other answer 4. The epression when factored fully is:- A. ( + 8)( + ) B. ( )( + 4) C. ( 4)( ) D. ( + )( + 4) E some other answer 4y 4. Simplify 7 8 y 1 A 4 y B 4 y 4 C y 4 D y 10 E some other answer

2 Project - Math 99 Final Practice Summer Simplify the following epression. 4 p z 4 8z p 16 A. z z B C. z 4 p D. 5 4z 4 6. Simplify 4 16 A 4 B 4 C 1 4 D 4 E some other answer 7. Add and simplify the following epression A 1 B 1 C 4 4 D 4 4 E some other answer 8. When you add the fractions A. B. ( 1) 1 and simplify the result you get:- 5 C. ( 1) D. some other answer 9. What is the slope and y-intercept of the line with equation 4 + y 0 A. Slope and y-intercept 10 B. Slope 4 and y-intercept 0 C. Slope and y-intercept 10 D. Slope ½ and y-intercept For the line with equation 4y + 8 what is the slope of the line. A. B. 4 C.6 D.½ E. ½ 11. For the line with equation 4y 1 where does it cut the y ais? A. (0,1) B. (0,6) C. (0,) D. (0, ) E. (0, 4 )

3 1. Determine which of the following points, if any, satisfy the system of equations. y 4 7 y 4 A. The point (,1) B. The point (1, ) Project - Math 99 Final Practice Summer 017 C. The point ( 1, ) D. None of the points satisfy the system of equations 1. For the pair of equations + y 5 + 4y 10 Which is the only coordinates that satisfy both equations? A. (1,1) B. (1,) C. (,1) D. ( 1, ) E. ( 1, ) 14. Simplify the following radical epression 48 A. 4 B. 16 C. 1 D. 4 E some other answer 15. Simplify the following radical epression y z 6 6 A. y z y B. y z y C. y z D. 4 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. 4 y z 4 C. 4 y z yz D. Some other answer 17. 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 18. The solution to the radical equation Project - Math 99 Final Practice Summer 017 A. 1 B. 4 C. 17 D. Some other answer 19. When you epress as a comple number in the form a + bi you get :- A. 4 i B. 4 + i C i D. Some other answer 0. Epress as a comple number a + bi A 7 B 4 i C 4 + i D 0 + 5i E some other answer 1. 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 Summer 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. Add or subtract the following and simplify the answer where possible. (a) p p 6 (b)

6 . Solve the following equations. Project - Math 99 Final Practice Summer 017 (a) 7 5 (b) 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.

7 Project - Math 99 Final Practice Summer John traveled from his own home to his mother s home 00 miles away and then he returned back home that same day. During these journey s he noticed that his speed was 10 mph faster coming home than it was when he traveled to his mothers home. The total time spent on both parts of the journey was 9 hours. What were his speeds during this journey? First Journey Return Journey Rate Distance Time

8 Project - Math 99 Final Practice Summer (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

9 Project - Math 99 Final Practice Summer (a) Solve the pair of equations + y 10 by the substitution method. y 1 7.(b) Solve the system of equations y 10 by using the addition method. + y 5

10 8. If hamburgers and fries cost $.50 and 4 hamburgers and fries cost $6.50. What are the cost of a single hamburger and a single portion of fries? Project - Math 99 Final Practice Summer 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 $1.40 per pound. The total cost of all the seed used in the miture was $100. How much of each seed was used?

11 10. Solve the following Radical Equations. Project - Math 99 Final Practice Summer 017 (a) 4 (b) 17 9 b 11. Solve the quadratic equation by using the quadratic formula b 4ac a

12 Project - Math 99 Final Practice Summer Solve the quadratic equation by using the quadratic formula b b 4ac 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.

13 Project - Math 99 Final Practice Summer 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?

14 Answers Project - Math 99 Final Practice Summer 017 Section 1: Multiple Choice Questions 1. A. B.A 4.B 5.B 5.A 6.B 7.B 8.C 9.A 10.E 11.D 1. A 1.B 14.D 15.B 16.B 17.D 18.B 19.D 0.C 1.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. Add or subtract the following and simplify the answer where possible. (a) 6 p p 6. p +. (p+) 6p + (p+) (p+) p p (p+) p(p+) p(p+) 6p+p+9 p(p+) 9p+9 9(p+1) p(p+) p(p+) (b) +. ( ). (+) (+) ( ) ( ) (+) ( ) (+) (+)( ) 4 (+)( ) 4 4 (+)( ). Solve the following equations. 7 5 (a) +7 5 (b) ( + 7) ( 5)

15 Project - Math 99 Final Practice Summer 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 1 miles downstream. Find the speed of the water current. If you let speed of current, then upstream speed is 4, while downstream will be 4 +. Since the times are equal Distance Speed Time (4 + ) 18(4 ) mph Upstream 8 4 Downstream John traveled from his own home to his mother s home 00 miles away and then he returned back home that same day. During these journey s he noticed that his speed was 10 mph faster coming home than it was when he traveled to his mothers home. The total time spent on both parts of the journey was 9 hours. What were his speeds during this journey? Rate Distance Time First Journey X Return Journey Total Time (+10) (+10) + 00 (+10) (+10) Cross multiply 9( +10) 1( ) Use the quadratic formula to get the answers 10± So the solution is First 40 mph and Return 50 mph mph

16 Project - Math 99 Final Practice Summer (a) Draw on the grid the line with equation y 1. y (b) Draw on the grid the line with Equation + y 8 y (c) Use your diagram to find the solution to the system of equations. y 1 + y 8 Solution is the point (,) and y 7.(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 (, 4)

17 Project - Math 99 Final Practice Summer (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 ) 8. If hamburgers and fries cost $.50 and 4 hamburgers and fries cost $6.50. 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 $.50 gives us the equation + y.50 4 hamburgers and fries cost $6.50 gives us the equation 4 + y y.50 multiply by 4 6y y 6.50 leave equation alone 4 + y 6.50 add the equations 4y y 4 y $0.1 1 cents Put y $0.1 into + y.50 + (0.1) $1.57 Hamburger cost $1.57 each and fries cost $0.1 1 cents per portion.

18 Project - Math 99 Final Practice Summer 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 $1.40 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 y 100 Solve by the substitution method, let + y 600 be rewritten as y Put y into the equation y ( + 600) pounds Put 400 into y y pounds. So amount of sunflower seed 400 pounds y amount of peanut seed 00 pounds 10. Solve the following Radical Equations. (a) (b) Square both sides Solve the quadratic equation by using the quadratic formula a 5 b and c 7 b 4ac () 4(5)( 7) b b 4ac a b b 4ac a and or 7 5

19 Project - Math 99 Final Practice Summer Solve the quadratic equation by using the quadratic formula a 1 b 10 c 16 b b 4ac a b b 4ac a and For the quadratic y 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 -intercepts? Solve 8 0 ( 4)( + ) 0 At 4 and at coordinates(4,0) 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

20 Project - Math 99 Final Practice Summer 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 4)(t ) Solution are at t and t 4 seconds (c) How long does it take the ball to reach its maimum height? Use t b a 1 4 seconds h 1t t 1() () 6 18 h 18 feet