MTH1W Course Review Final PDF

**Tips on how to prepare for the Culminating:** - Complete all of the review questions included in this package - Review your notes and create summary sheets about the key terms and concepts covered in each unit - Make corrections to old tests and assignments - Complete any incomplet...

**Tips on how to prepare for the Culminating:** - Complete all of the review questions included in this package - Review your notes and create summary sheets about the key terms and concepts covered in each unit - Make corrections to old tests and assignments - Complete any incomplete worksheets in your binder - Look through your notes and worksheets, and retry any examples or questions you found challenging ***Practice Questions:** \*Complete on a separate sheet of paper\** **[B: NUMBERS]** **B1: Development of Number and Number Sets** 1\. Given the Venn Diagram on the right: a. What is the Set of A? b. What is the Set of B? c. Is B ⊆ A? Explain how you know. 2\. Complete the following by writing ⊆ 𝑜𝑟 ⊈ to make each statement true:  a. {2,4,5,8,9} \_\_\_\_\_ {1,2,3,5,6,7,8,9} b. {2,3,7,8,9,10,11} \_\_\_\_\_ {1,2,3,5,6,7,8,9,10,11} 3\. Complete the following by writing ∈ 𝑜𝑟 ∉ to make each statement true: a. {11} \_\_\_\_\_ {1,2,3,5,6,7,8,9,12, 14,16,17,18} b. {27} \_\_\_\_\_ {12,13,15,22, 23,26,27,28,29,30,31} 4\. What is the difference between RATIONAL and IRRATIONAL numbers? **B2: Powers** 5\. Express the following numbers in scientific notations a. 8000000 b. 740000 c. 943000000 d. 0.04 e. 0.000006 f. 0.00257 6\. Simplify first using exponent laws. THEN evaluate if possible. a. [5 × 5^4^]{.math.inline} b. [( − 9)^7^ ÷ ( − 9)^4^]{.math.inline} c. [\[( − 2)^4^\]^3^]{.math.inline} d. [6^2^ ÷ 6^7^ × 6^3^]{.math.inline} e. [\$\\frac{(3\^{2})\\ \\times \\ 3\^{3}}{3\^{8}}\$]{.math.inline} f. [(*k*^2^)^3^ × *k*^2^]{.math.inline} g. [(3*y*^2^)^4^]{.math.inline} h. [\$\\frac{(x\^{2})\\ \\times \\ 3x\^{5}}{6x\^{10}}\$]{.math.inline} i. [\$\\frac{(8x\^{3})(4xy\^{4})}{(2x\^{6})(14y\^{3})}\$]{.math.inline} **B3: Number Sense and Operations** 7\. Evaluate. a. [\$\\frac{9}{2} \\times \\frac{8}{3}\\ \$]{.math.inline} b. [\$\\frac{17}{3} - \\frac{5}{12}\\ \$]{.math.inline} c. [\$\\frac{9}{4} \\div \\frac{11}{3}\\ \$]{.math.inline} d. [\$\\frac{7}{6} + 2\\frac{8}{3}\\ \$]{.math.inline} e. 3[\$\\frac{4}{5} - \\frac{8}{3} \\times \\frac{7}{5}\\ \$]{.math.inline} f. [\$\\frac{1}{2}(\\frac{2}{3})\^{3}\\ \$]{.math.inline} 8\. What should a store charge for two plants if they want their prices just slightly lower than a store that charges \$14.98 for three plants? **[C. ALGEBRA]** **C1: Algebraic Expressions and Equations** 9\. Simplify the following expressions. a. [7*m* + 6*m*^2^ − 2*m* + *m*^2^ ]{.math.inline} b. [3*k* − 5 + 8 − *k* + 1 − 4*k*]{.math.inline} c. [(4*m* − 1) + (3*m* − 8)]{.math.inline} d. [(4*v* − 9) − ( − 6*v* + 5)]{.math.inline} e. [2(*a*^2^ + 5*a* + 3)]{.math.inline} f. [ − 5*y*(3*y*^2^ − 7*y* − 2)]{.math.inline} g. [5(4*x* − 6) − 2(3*x* − 7)]{.math.inline} 10\. Expand and simplify the following expressions using the distributive property. a. 5(x + 3) b. 4(b + 2) c. w(2w + 1) d. q(q + 4) e. 3c(6 -- 4c) f. --p(2p -- 1) g. --5(a^2^ -- 4a -- 2) h. 2d(d^2^ -- 3d -- 1) i. 3(x + 3) + 2(x + 1) -- 5x 11\. a) Expand and simplify an expression for the area of the following rectangle. b\) What is the area if x= 3 cm? 12\. Johnny gets paid \$500 every two weeks. After his paycheck is deposited, he has to pay his cell phone bill of \$30 and buy a gift for his friend. If Johnny has \$390 left in his account, how much did he spend on the gift? 13\. A submarine hovers at 240 metres below sea level. If it descends 160 metres and then ascends 390 metres, what is its new position? 14\. The length of a rectangular field is three times its width. a. Write an expression for the perimeter of the field b. Find the perimeter of the field if it is 300m wide. c. Find the length and width of the field if the perimeter is 1600m. 15\. Solve each of the following equations below. a. [2*y* − 7 = 13]{.math.inline} b. [4 + 5*x* =  − 21]{.math.inline} c. [2(*x* − 2) = 4*x* − 2]{.math.inline} d. [3*x* − 8 = 7*x* + 10]{.math.inline} e. [2(*x* − 8)=  − 4(2*x* − 1)]{.math.inline} **C2: Coding** 16.  17. **C3: Application of Relations** 18\. Determine whether each of the following table of values is linear or non-linear. Explain how you know.  19\. Find the slope of a line passing through the points. Then write the equation of the line. a. (4, 4) and (7, −2) b. (−3, 2) and (3, −12) c. (−3, −5) and (6, 7) d. (0, 6) and (4, 16) 20\. Find the slope and y-intercept of each of the following lines. Then write the equation of the line. 21\. Graph each pair of lines below on the same grid. Then determine the Point of intersection. a. [*y* = 2*x* + 1 ]{.math.inline}and [*y* = 3*x* − 1]{.math.inline} b. [*y* = 2*x* − 2]{.math.inline} and [\$y = - \\frac{1}{4}x + 7\$]{.math.inline} 22\. Sasha is a hotel manager. Their responsibilities include renting rooms for conferences. The hotel charges \$250 per day plus \$15 per person. a. Create an equation that represents the cost of renting the conference room per day (Define your variables) b. How much would it cost if 85 people attended the conference? c. How many people could attend if a company renting the space has a budget of \$3000? 23. The following table on the right shows the Cost, *C*, to park in a downtown parking lot based on the number of hours, *t*, your car is parked for. a. What is the rate of change? b. What does the rate of change represent in this situation? c. Write an equation relating *C* and *t*. 24\. Cersei and her brother Tyrion decide to race home. Cersei is a faster runner than Tyrion, so she gives him a head start. Their distance-time graphs are shown. a. How much of a head start did Tyrion get? b. How fast does Cersei run? c. How fast does Tyrion run? d. For what length of the race will each runner win? For what length of the race will they tie? e. What is the point of intersection? What does it represent? **C4: Characteristics of Relations** 25\. What inequality is represented on each number line below?  26\. What is the resulting equation in each situation? a. reflecting y = 2x across the x-axis and then translating down 8 units b. reflecting y = [\$\\frac{- 3}{5}x\$]{.math.inline} across the x-axis and then translating up 2 units c. rotating y = -4x clockwise 90° around the origin, then translating right 3 units 27\. Perform the following transformations of y = 3x. Then write an equation for the new line. Use a different colour for each transformation. a. Translate up 2 units b. Reflect in the x-axis c. Rotate 90° around the origin **[D: DATA]** **D1: Collection, Representation and Analysis of Data** 28\. Find the mean, median, mode, and range for each set of data below.\ a) 72, 43, 15, 66, 32, 72, 52, 19, 28, 81 b\) 5,28,16,32,5,16,48,29,5,35 29\. Create a box and whisker plot for the data set below. Show all calculations. a\) 17,29,32,9,30,14,8,39,11,32,23 b\) 24, 34, 98, 44, 72, 56, 52, 50, 38, 22, 20, 60 30\. The table shows the heights and arm spans for a group of students: a\) Draw a scatter plot of the data and line of best fit. b\) Describe the relationship between a person's height and arm span. c\) Identify any outliers and explain how they are different from the rest of the data. 31\. The table shows the values of some used cars: a\) Identify the independent and the dependent variable b\) Draw the scatter plot of the data and line of best fit. c\) Describe the relationship between the age of the car and\ its value. d\) Jane bought a 7-year-old car for \$28,000. Did she pay too much? Explain. 32\. The following data show the final marks for 10 students in a math class and the average number of hours they studied math per week. a\) Draw the scatter plot of the data and line of best fit. b\) Is there a relationship between the final mark and the number of hours of study per week? Explain. c\) Estimate the study time for a student whose final mark is 71. **D2: Mathematical Modelling** **33.** **[E: GEOMETRY AND MEASUREMENT]** **E1: Geometric and Measurement Relationships** 34\. Calculate the surface area of the following shapes. 35\. Calculate the volume of the following shapes.  36\. Calculate the circumference and area of the circles below. 37\. Find the perimeter of each composite figure.  38\. Find the area of each composite figure. 39\. Find the missing angle(s) in each question below.  40\. Calculate the length of the missing side in each triangle. **[F: FINANCIAL LITERACY]** **F1: Financial Decisions** 41. Consider the following options for a \$500 investment: i\. 2% monthly simple interest for 6 months ii\. 2% monthly compound interest for 6 months 42. You must take out a \$10,000 loan to buy a used car. The simple interest rate on this loan is 1.3% monthly. How much interest would you be paying if you did not pay off any of the loan in 2 years? 43. You invested \$10,000 in an ETF that returns 2.1% simple interest monthly. a\. What will the total value of the investment be after 3 years? b\. How long would you need to invest to have \$12,000? 44. The following is a list of expenses and income for a university student. Put the following information in a monthly budget table and describe the situation this person is in. Gifts from family: \$500 semi-annually Part Time Job at Walmart: \$1000 monthly Textbooks: \$100 monthly Food: \$700 monthly Transportation: \$25 bi-weekly Clothing: \$300 monthly Cell Phone Bill: \$50 monthly Rent: \$6000 yearly Utilities: \$50 monthly 45. The following is two options you found while shopping at a local grocery store. You found 12 cans of Pepsi for \$4.88 but you also found 24 cans of Pepsi for \$7.99. Which is the better buy? Justify your decision.