7 ft. , sketch a right triangle and label the two given sides.

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1 Math 421A Review for Final Exam *This is NOT enough for you to prepare for the exam. Re-do your assignments and tests, and do the textbook end of chapter reviews!! CHAPTER #1: Measurement 1. Which referent could you use for 1 inch? a. The thickness of a dime c. The width of your hand b. The length of a small paper clip d. The diameter of a tennis ball 2. Convert the following: (a) 11 yd to in 100 in to ft and in (c) 26 feet to the nearest tenth of a cm (d) 2.5m to yards 3. The bobsled track at the Canada Olympic Park in Calgary is 1475 m long. What is this length to the nearest tenth of a yard? 4. Determine the surface area and volume of this square 5. Determine the volume and surface area of this right pyramid to the nearest unit. cone to the nearest unit. 7 ft. 5 m 3 m 5 ft. 6. The radius of a volleyball is approximately 11 cm. Determine the surface area of a volleyball to the nearest square centimeter. CHAPTER #2 - Trigonometry 1. If tan D 4, sketch a right triangle and label the two given sides If cos A 0. 75, describe in words what this value means in terms of the relationship between certain sides of the right triangle. 3. Solve for the indicated angle or side in each of the following triangles. Round sides to one decimal place and angles to the nearest whole number. L 12.2 m M l 66 N 4. Ryan stands 10 m away from a cell phone tower. When he looks up, the angle of inclination is 67 o. What is the height of the tower, to the nearest tenth of a meter? Include a diagram with your solution.

2 CHAPTER #3 Factors & Products 1. Factor the trinomial. 2. Identify the greatest common factor of the terms in the trinomial. s 2 t 2 3. Expand and simplify: 4. Complete: 5. Complete. 6. Which multiplication sentence does this set of algebra tiles represent?

3 7. Which set of algebra tiles represents? 8. Expand and simplify: 9. Expand and simplify: (2x 3)(2x + 3) a. 4x 2 6x 9 c. 4x 2 12x 9 b. 4x 2 9 d. 4x Expand and simplify the following (a) (p - 3)(p + 5) (c) (d) (x 4)(x + 4) 11. Factor the following polynomials: (a) x 2 10x + 24 (c) x x + 30 (d) 4m 2 n +9mn Chapter #4: Roots and Powers 1. Put a check mark in the boxes of all the number systems that each of the following numbers belong - 6 Irrational Numbers Rational Integers Whole Numbers Natural Numbers

4 Distance from home (km) 2. Write all answers in simplest radical form. (a) (c) (d) 3. A cube has a volume of 108 cm. Determine the edge length of the cube as a radical in simplest form. 4. Write each power in radical form and then evaluate. Do not just use a calculator. (a) (c) (d) 5. Simplify each power so it is written with a positive exponent and then evaluate. (a) (c) (d) 6. Simplify each expression. (a) (c) 7. Evaluate if a = -1 and b = 2 Chapter #5: Relations and Functions 1. (a) Explain why the points on this graph are not joined. The independent variable is 2.(a) Calculate the rate of change between points BC. Round to the hundredth. Natasha's Drive C D 4 A 3 2 B 1 E O Time (min) Which section of the graph represents Natasha travelling the fastest? How do you know? (c) Explain what is happening between D and E. (d) Explain what is happening between A and B.

5 Mass (kg) Speed (m/s) 3. (a) Identify if the following are linear relations. Explain your reasoning. Cost of Renting a Paddle Boat Number of Total Cost ($) Days (n) 1 $54 3 $ s Speed of a Hot Air Balloon 5 $170 7 $ t Time (s) 4. Use the graph to the right to determine (a) the range value when the domain value is 3 the domain value when the range value is 1 5. State the domain and range for each of the following relations. Also identify if the relation is a function (i) 80 Ages and Masses of Animals E F (ii) 60 C D G A B Age (years) (iii) { (3, 4), (4, 4,), (5, 4)} (iv)

6 6. The equation represents the total cost, C dollars, for a sports banquet when n people attend. (a) Determine C(46). What does your answer represent? Determine the value of n when C(n) = What does your answer represent? 7. (a) What is the vertical intercept? (c) (d) (e) Calculate the rate of change. What does the rate of change represent? Write the equation that represents this graph. Use the equation to calculate the altitude of the helicopter at 45 seconds. (f) Use the equation to calculate the time that has passed if the altitude is 120 m. Chapter #6: Linear Functions 1. Find the slope in each of the following situations: (a) (3, 2) and (3, 9) (c) y = 8x 3 (d) (e) 2. Write the equation of this line in slope point form.

7 3. Graph each of the following lines based on the given information: (a) contains the point (1, -2 ) and has a slope of 4 4. Write the equation of these lines in slope intercept form. (a) 5. Line ST passes through the points S (4, -1) and T (-8, 3). Line PQ passes through the points P (3, 4) and Q (6, 5). Are the two lines parallel, perpendicular or neither? Show work to justify your answer. 6. A line has a slope of 1 4 and a y-intercept of -7. (a) Write the equation of this Re-write the equation from line in slope intercept form part (a) in general form. 7. Determine the equation of the line, in slope point form, that passes through the point ( - 4, 3 ) and has a slope of Write the equation, in slope point form, of the line that goes through the points ( 0, -2 ) and ( -1, 1 ) 9. Determine the equation of the line that goes through the point ( -1, 3 ) and that is perpendicular to the line. Write the equation in slope point form.

8 Chapter #7: Systems of Linear Equations 1. Circle the ordered pair that is a solution to the system of equations. ( 0, - 1 ) ( 3, 1) ( 1, -3 ) ( 1, 3) ( -3, 1 ) 2. Solve the system of linear equations by graphing. 3. Solve the system of linear equations using the substitution method. 2x y + 15 = 0-4x + 3y = Solve the system of linear equations using the elimination method. Answers Chapter #1 Measurement: 1. B 2. a) 396in b) 8 ft 4 in c) cm d) 32.8 yards yds (use 1 yd = m) 4. Surface area = 95 ft 2 Volume = 54.5 ft 3 5. Surface Area = m 2 Volume = 16m cm 2 Chapter #2 Trigonometry: 1. 4 θ 3 2. The length of the side adjacent to anglea is 0.75 (or 75%) of the length of the hypotenuse. (cosa = ¾) 3. a) 5.4m b) 31.4 c) m Chapter #3 Factors and Products: 1. D 2.B 3.A 4.B 5.B 6.D 7.B 8.C 9.B 10. a. 6x 2 24x b. p 2 + 2p 15 c. 16x 2 24x + 9 d. x a. 3pq 2 (4 6q 2 3p 3 q 3 ) b. (x 6)( x 4) c. (x + 10)(x + 3) d. mn(4m + 3) Chapter #4 Roots and Powers: Irrational Numbers x x Rational x x Integers x x Whole Numbers x Natural Numbers x

9 2. a) b) c) d) a) 9 b) 16 c) 32 d) - 5. a) b) 8 c ) 2 d) 6. a) b) c) 7. Chapter #5 Relations and Functions: 1. a) You cannot have half a person, so it is a discrete graph b) number of people 2. a) 0.13km/min b) 0A steepest c) She is returning home d) she is not moving 3. a) Paddle boat linear because the x values increase by 1 each time and the y values increase by 58 each time b) graph non linear because it is a curved graph c) equation linear because the x is to the power of one 4. a) 2 b) (i) domain: {4,10,13,16,19,20} range: {20,25,50,60,70,80} (ii) domain: [xεr} range: {y 3} (iii) domain: {3,4} range: {4} (iv) domain: { -3 x 3} range: {-3 y 4} 6. a) 756 cost for 46 people b) 121 number of people who attend when it costs $ a) 360 b) - 3 c) helicopter descends at a rate of 3 metres per second d) y = -3x e) 225m f) 80s Chapter #6 Linear Relations: 1. a) 2/3 b) Undefined c) 8 2. y + 2 = -3/2(x 3) a) y = -3 b) y = 1/2x Slope of ST is -1/3 slope of PQ is 1/3 so neither 6. a) y = -1/4x 7 b) x + 4y + 28 = 0 7. y 3 = 5(x + 4) 8. y 1 = -3(x + 1) OR y + 2 = -3x 9. y 3 = -1/3(x + 1) Chapter #7 Systems of Linear Equations: 1. (1, -3) 2. (-4, 6) 3. (-4, 7) 4. (2,1)