Bridge Seminar in Mathematics

All Star Summer Bridge Program Summer 2021 Name _______________ MATH 0330 – Bridge Seminar in Mathematics Date ________________ POST-ASSESSMENT (FINAL EXAM) – TAKE HOME Show as much work as possible to receive credit. You are encouraged to demonstrate your highest level of knowledge. You may use a graphing calculator or online graphing utility. This is an open book/open notes exam. You must show work to receive credit. Use notebook paper to answer the following questions. Use the labels provided to organize the paper. You may print if you wish; and attach extra paper as needed for more space to solve problems and graphs. Scan and upload your completed exam. UNIT I (MATH 0330 Weeks 1 & 2; MATH 0330Q Weeks 1 – 3) 1. Find the prime factorization of 70. 2. Simplify the fraction 16 48 to lowest terms. 3. Perform the given operations with fractions. Give answers in lowest terms. a) 3 3 ∙ 4 9 b) 10 ÷ c) 7 9 − 3 2 1 18 4. A driver who travels at a constant speed of r miles per hour for t hours will travel a distance of d miles, given by the formula 𝑑 = 𝑟𝑡. How far will a driver travel at a speed of 30 mph for 6 hours? 5. Translate each phrase into an algebraic expression: a) eleven less than twice of a number b) the product of eight and a number 6. Plot the numbers on the number line given. The first one is done as an example. A. 2.5 B. 2 2 C. −0.25 D. 5 3 A 7. Perform the operations indicated. a) −4 + (−7) b) 5 8 − 3 4 c) 2 ∙ (−3) ∙ (−5) 8. The lowest elevation in North America is 272 ft below sea level. The highest elevation is 20,320 ft above sea level. Find the difference in elevation between the highest and lowest points in North America. Difference in elevation: ________ ft 9. The temperature in Austin was 82oF at 2 pm. The temperature dropped 6oF per hour for the next five hours. What was the temperature at 8 pm? Show your work! Temperature: _________oF 10. Use the rules for order of operations to simplify the expressions, collecting like terms and writing without parentheses. a) 2𝑥 + 7𝑥 − (5𝑥 + 6) b) [7(𝑥 − 5) − 19] − [4(𝑥 + 6) + 10] c) |2−5|+3∙(−2) 32÷8∙2 UNIT II (MATH 0330 Week 2; MATH 0330Q Weeks 4 – 6) 1. Express 42.5% as a decimal and a reduced fraction. 42.5% = ________________ 42.5% = _________________ As a decimal 2. Express 9 20 9 20 As a reduced fraction as a decimal and a percentage. = ____________________ As a decimal 9 20 = _________________ As a percentage 3. Express 0.008 as a percentage and a reduced fraction. 0.008 = _________________ As a percentage 0.008 = ________________ As a reduced fraction 4. Answer the following questions by translating into an equation OR setting up a ratio. Write the equation or ratio for full credit. a) What percent of 175 is 7? b) 150 is 24% of what number? c) What number is 8% of 500? 5. A car normally depreciates 35% of its value in its first year. A car is worth $18,200 after its first year. What was its original value? 6. On a test with 70 questions, Joe answered 70% of the questions correct. How many questions did Joe answer incorrectly? 7. Solve the equations showing each step. a) 𝑧 + 8 = −7 b) 11𝑦 − 3 = 63 c) 5(𝑑 − 2) = 7(𝑑 + 4) d) 7 2 1 3 5 𝑥 − 2 𝑥 = 3𝑥 + 2 − 2 𝑥 8. Graph the inequalities a) 𝑥 ≥ −1 b) −2 < 𝑥 ≤ 3 9. Solve the inequality. a) 3𝑥 − 2 ≥ 7 b) 5 − 9𝑦 < 2 − 8𝑦 10. Mary’s financial aid stipulates that her tuition not exceed $1,000. If the college charges a $120 admission fee and $280 per course, what is the greatest number of courses Mary can register for? Mary can register for at most _________ courses. UNIT III (MATH 0330 Week 3 & 4; MATH 0330Q Weeks 7 – 9) 1. A linear equation that describes a line is given: 2𝑥 + 3𝑦 = 18 a) Find the x-intercept. State the x-intercept as an ordered pair. b) Find the y-intercept. State the y-intercept as an ordered pair. c) Find the slope of the line. d) Graph the line: 2. The value, V, in dollars of a shopkeeper’s inventory software program is given by 𝑉 = −60𝑡 + 350 where t is the number of years since he bought the program. After how many years is the program worth $110? 3. Find the slope of the line (if it exists) that passes through each pair of points: a) (1, −2 3 1 ) 𝑎𝑛𝑑 (4, 3) b) (-2, 5) and (-7, 5) Population in 1,000s 4. The graph below shows data regarding the population of a town. At what rate is the population changing? Number of years after 2000 5. Find the equation of the line in y = mx + b form with the given properties. a) The line has a slope of -3 and a y-intercept of (0, 5) b) The line has a slope of 3 and passes through the point (-7, 0) c) The line passes through the points (11, 12) and (9, 2) 5 6. Graph the line that has a slope of 𝑚 = − 3 and a yintercept of (0, 7) 7. Determine whether the lines are parallel, perpendicular, or neither. Line B: y – 3x = -11 Line A: 3x -1 = y Slope of Line A: ___________ Slope of Line B: ___________ The lines are __________________________________ Write parallel, perpendicular, or neither. 8. Evaluate the following expressions. 1 0 a) (8) 1 1 b) (25) 1 −2 c) (3) 9. Simplify the expressions – use only POSITIVE exponents. a) 3𝑥 −6 b) (6𝑑4 )2 c) 𝑥5𝑘6 𝑥𝑘 13 d) (𝑎3 𝑏 5 )(𝑎4 𝑏 −4 ) 10. Evaluate the polynomial 𝑥 3 − 9𝑥 2 + 𝑥 when 𝑥 = −1 11. Perform the indicated operations. a) (8x + 5) – (3×2 + 2x – 3) b) (3x + 1)(x + 5) c) (x2 + x + 7)(x – 7) d) (4a + 5)(4a – 5) 12. Find an expression for the total area of the figure below. Remember: Area = length x width. d 4 Area = _______________________ 6 d UNIT IV (MATH 0330 Week 5; MATH 0330Q Weeks 10 – 12) Factor each expression. 1) 2𝑥 2 − 4𝑥 2) 𝑥 2 + 4𝑥 + 3 3) 4𝑥 2 − 25 4) 8𝑥 3 − 12𝑥 2 + 6𝑥 − 9 5) 𝑥 3 − 6𝑥 2 − 16𝑥 6) 4𝑥 2 + 8𝑥 + 3 7) 25y2 + 81 8) xy − 4y − 3x + 12 Simplify. 9. Solve the quadratic equations by factoring and then using the zero-product property. 10) 𝑥 2 + 7𝑥 + 6 = 0 11) 𝑥 2 − 5𝑥 = 18 + 2𝑥 12) (x+4)(x+5) = 0 13) 16×2 = 81 Draw and label a picture. Set up an equation. Solve. 14) A rectangular bench is 5 times as long as it is wide. If the area of the bench is 80 ft2, find the length and width of the bench. 15) The length of a rectangular garden is 5 ft greater than the width. The area of the garden is 66 ft2. Find the dimensions of the garden.
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