Math 80a exam 1 review (Part I)

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1 Math 80a exam 1 review (Part I) This is a preview of the test. Any questions from the homework are possible on the exam. i) Please practice every problem on this review two or three times, ii) Find problems like them in the homework and practice those. iii) Create your own exam using homework problems, place two hours on a timer, and take the exam. iv) Practice the problems you missed and find ones like them to practice. v) Create a new exam and take it. Repeat if needed. 1. Simplify Evaluate the following expression using the Order of Operations. 1 (6 ) 3. Evaluate the variable expression when a = and b = 6. 5a 6b. Evaluate the variable expression when a = 7, b = 1, and c =. 9 b c + a 5. 1 Solve for z. (x + 3z) = 5y 6. a) Solve for p. A = pt 3p b) Solve for C. F = 9 C c) Solve for x. x + 9y = 11 d) Solve for y. 1 x 1 3 y = 1 7. Apply the formulas for determining a child's body surface area and a child's dose of medication. S is a child's body surface area. k is the weight of the child in kilograms. C is the child's dose of medication in milligrams. D is the usual adult dose in milligrams. S = k+7 k+90 C = body surface area in square meeters 1.7 xd a) Find the body surface area, to the nearest hundredth, of a child with a weight of 6 kg. b) If the usual adult dose of a medication is 50 mg, what is the child's dose, to the nearest unit, for a child that weighs 6 kg. Page 1

2 8. Translate into a variable expression. Three more than one-half of the square of p 9. Translate into a variable expression. The product of four and the total of x and seven 10. Translate into a variable expression. The quotient of six less than m and twice m 11. Translate the following into a variable expression. 5 less than the product of z and. 1. Translate the following into a variable expression. Then simplify. A number decreased by the difference between three and the number. 13. Translate the following into a variable expression. times the difference between a and Translate the following into a variable expression.8 divided by the difference between a and Is a solution of x 8 8? 16. Solve: 5w Solve: x Solve: 1x 59 6x Solve: x x Solve. 8 x 3 x Solve: x6 x.. Solve: x Solve: 9 31 n 6n.. Solve: 9.3x x. 5. x 3 5 Solve: 3 x Solve: [6 (1 + x)] + 10x = (10 3x) + 8x 7. Solve: 3x 1 9 Solve. x x+3 6 = 3 8. Solve: 1 5 (3x 1) = x #30-37 Solve, Graph, and Write in interval notation x and x x 8 k x x and x x or x x < 3 and x x 3

3 Answers: A a) p = t 3 c) x = 9 y + 11 b) Any of the following: C = 5f d) y = 3 x y x z = = 10y 3 3 x 3 = 5f 160 = 5 (f 3) a) 0.96 m b) 11 mg 6. all real numbers p x m 6 m 11. z 5 1. p (3 p); p ( a 5) 1. 8 a Yes x 3. x 3. n /3 9. 3, 6 30.,, 31. 5, 1, 1 3., 1,, Empty number line. 3. [,1] 35. (, ) Empty number line. -5/ -1/7-1/ [-5,9]

4 Math 80a exam 1 review (Part II) Word Problems: 1. Translate. Do NOT solve. a) 5 less than twice a number is seven more b) The product of six and a number is 30 times than the number. the difference of 1 and the number.. A piggy bank contains 9 coins in quarters and nickels. The have a value of $5.05. Find the number of each coin type. a) Express in terms of x: # quarters # nickels b) Equation (SOLVE!): c) # quarters = and # nickels = 3. Turtle and Vince combine their coins to find they have all dimes and quarters. They have 8 more quarters than dimes, and the coins are worth a total of $5.15. How many dimes and quarters do they have? a) Express in terms of x: # quarters # dimes b) Equation (SOLVE!): c) # quarters = and #dimes =

5 . A collection of 5 cent and 3 cent stamps has a value of $ The number of 3 cent stamps is two more than four times the number of 5 cent stamps. Find the number of each stamp type. a) Express in terms of x: # 5 cent stamps # 3 cent stamps b) Equation (SOLVE!): c) # of 5 cent stamps = and # of 3 cent stamps = 5. in 009, there were about 1 acres of farmland in Crane County. This was 3% less than the number of acres of farmland in 000. Calculate the number of acres of farmland in Crane County in 000. a) Express in terms of x: Number of acres of farmland in 009 in 000 b) Equation (SOLVE!): c) Number of acres of farmland in 009 in A 16-ft steel beam is to be cut into two pieces so that one piece is 1 foot longer than twice the other. Find the length of each piece. a) Express in terms of x: One of the pieces The other piece b) Equation (SOLVE!): c) One of the pieces The other piece 5

6 7. A total of $7000 is deposited into two simple interest accounts. On one account, the annual simple interest rate is 10%, and on the second account, the annual simple interest rate is 15%. How much should be invested in each account so that the total annual interest earned is $800? a) Define your variable. Principle Rate = Interest 1st account nd account Total b) Equation (SOLVE!): c) Amount invested at 10% Amount invested at 15% 8. How many liters of a 10% alcohol solution must be mixed with 0 L of a 50% solution to obtain a 0% Solution? b) Equation (SOLVE!): c) Liters of 10% Liters of 50% Liters of 0% 6

7 9. Find three consecutive even integers such that the sum of the least integer and the greatest integer is 1 more than the middle integer. a) Write in terms of x: 1st integer, nd integer, 3rd integer b) Equation and solve: c) 1st integer, nd integer, 3rd integer 10. Two planes start at the same time from the same point and fly in opposite directions. The first plane is flying 100 mph faster than the second plane. In 3 h, the two planes are 1050 mi apart. Find the rate of each plane. a) Picture: b) c) equation and answer. 11. A bicyclist traveling 15 mph heads out at 8 A.M. At 10 A.M. a motorcyclist heads out in the same direction traveling 5 mph. At what time will the motorcyclist pass the bicyclist? a) Picture: b) c) equation and answer. 1. To pass Algebra, a student must have an average of at least 70 on five tests. On the first four tests, the student has the scores of 75, 79, 6, and 71. What possible scores on the fifth test would guarantee a passing grade in the class 7

8 Answers for Word Problems. 1. a) x-7=7+x b) 6x=30(1-x). a) Express in terms of x: # quarters X # nickels 9-X b) Equation (SOLVE!): 5x+5(9-x)=505 c) # quarters = 18 and # nickels = a) Express in terms of x: # quarters 8+x # dimes x b) Equation (SOLVE!): 10x+5(8+x)=505 c) # quarters = 17 and # dimes = 9. a) Express in terms of x: # 5 cent stamps x # 3 cent stamps +x b) Equation (SOLVE!): 5x+3(+x) =1016 c) # of 5 cent stamps = 10 and # of 3 cent stamps = 5. a) Express in terms of x: Number of acres of farmland in 009 x 0.3x in 000 x b) Equation (SOLVE!): 1 = x.3x c) Number of acres of farmland in acres in acres 6. A 16-ft steel beam is to be cut into two pieces so that one piece is 1 foot longer than twice the other. Find the length of each piece. a) Express in terms of x: One of the pieces 1+x The other piece x b) Equation (SOLVE!): 1+x+x=16 c) One of the pieces 11 The other piece x 0.15(7000-x) 0.10x+0.15(7000-x)=800 $5000 at 10% and $000 at 15% 8. 10x + 50(0) = 0(x + 0), L 9.a) Write in terms of x: 1st integer x, nd integer x+, 3rd integer x+ b) Equation: x+(x+)=1+(x+) c) 1st integer 10, nd integer 1, 3rd integer a) picture b) 3x (x + 100)3 3x + 3x = 1050 D1 R T D R T c) equation and answer. 15 mph for the second plane and 5 mph for the first plane 8

9 11. A bicyclist traveling 15 mph heads out at 8 A.M. At 10 A.M. a motorcyclist heads out in the same direction traveling 5 mph. At what time will the motorcyclist pass the bicyclist? a) picture b) 15(t + ) 5t D D 1 R T R T 15(t + ) = 5t c) equation and answer. 11:00 am 1. x 61, 61 or higher 9

10 Math 80a exam 1 review (Part III) 1. Find the x - and y -intercepts for: 6xy a) x -intercept:, a) y -intercept:,. a) Write in y mx b form: 3xy 8 d) Graph: b) Find the x and y intercepts. c) Find: slope = 3. Graph; find slope: x b) Graph; find slope: y slope = slope = 10

11 . Graph the line through, 3 with slope Find the slope of the line going through the point 7, and ( 6, ) 6. Determine whether the pair of lines are parallel, perpendicular, or neither. a) y 3x 5 y 3x b) y 3x 5 y 3x c) 1 y x 5 3 y 3x d) 1 y x 5 3 y 3x 7. Find the equation of the line:,7 and(1, 3) in y mx b a) through form. b) through 5,7 with slope= 0. c) through 3,7 with undefined slope. d) through point 3, and is parallel to e) through the line 3x y 3., 3 and perpendicular to y 7. f) through, 3 and parallel to y 7. 11

12 8. A Jet plane left a runway that was 0.5 miles above sea level and ascended at a rate of 500 miles per hour. Write a linear equation that models the plane's height, H, in terms of time, t. 9. After two months of use, Biff s Spiffy Persian Monkey s bike had dropped to $300 in value. After six months, the value had declined to $13. a) Find a linear equation that models the data. b) Slope =. Verbally interpret. c) y-intercept. = (, ) Verbally interpret. d) When will Biff s Spiffy Persian Monkey s bike have a value of $100? 10. Graph the following a) yx 3 b) x 3 c) y Find the x- intercept of the function, f x 3x 9 1

13 1. Let f x x 5x 7, find f. 13. Let gx 7x 5, find 3 g h and simplify. 1. Given f x x 3, find a number, c, such that c 5 f. 15. Determine whether the relation is a function. Give the domain and range of the relation. 5,,, 3, 0,1, 3,, 7,11 Function? YES or NO Domain: Range: 16. Determine if the following graph is a function and then find the domain and range. 10 y x Function? YES or NO Domain: Range: 13

Answers for part III. 1. a. (,0) b. (0,-1). a) y = 3 x b) (8/3,0) (0,-) c) m=3/ d) 3. a. m= undefinded b. m= 0. 5. m = 6 13 6. a. parallel b. neither c. perpendicular d. neither 7.

14 Answers for part III. 1. a. (,0) b. (0,-1). a) y = 3 x b) (8/3,0) (0,-) c) m=3/ d) 3. a. m= undefinded b. m= m = a. parallel b. neither c. perpendicular d. neither 7. a) y = x 1 b) y=7 c) x=3 d) y = 3x + 11 e) x= f) y=3 8. H=500t a) V=-m+38 b) m=-$/month, The value of the monkey s bike decreases $ every month. c) (0,$38) The initial price of the bike was $38. D) 6.76 months 11. (-3,0) 1. f( ) = g(3h ) = 1h c=

Math 80a Exam #1 Review

Math 80a Exam #1 Review 4 2) 1 zx 6x Math 80a Exam 1 Review This is a preview of the test Any questions from the homework are possible on the exam i) Please practice every problem on this review two or three times ii) Find problems