North Seattle Community College Computer Based Mathematics Instruction Math 102 Test Reviews

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1 North Seattle Community College Computer Based Mathematics Instruction Math 10 Test Reviews Click on a bookmarked heading on the left to access individual reviews. To print a review, choose print and the page numbers indicated. Check the Math 10 calendar for test dates.

2 Math 10: College Algebra REVIEW TEST 1 Name: Show all work in this solution space: Your final answer here: 1. Multiply and simplify: ( y ). Solve the equation ( 6) 7 -. Give eact solutions.. Simplify: 1 i 1 + i. Write your answer in the form a + bi 4. Multiply: ( 1 48). Simplify: y +1 y y y 1 y +

3 Simplify: ( 16) Simplify: Solve for : Solve for : 1.8 < Write your answer in interval notation. 10. Find the equation of the line through the origin perpendicular to the line. y 4 0 Give your answer in standard form.

4 11. Simplify and rationalize the denominator: 8 8 y 4 z y z 7 4 (, y, and z are positive numbers.) 1. Solve for : Solve: Which of the following is NOT a function? [A] {(, 8), (, ), (1, )} [B] y 1 [C] y 4 0 [D] y 1. Find f ( ) given f ( ) + 6

5 16. Find the domain and range of the function g( ) 17. Find the domain of the function: f ( ) 1 ( ) 18. Find the domain and range of the function graphed below a. Domain y b. Range 19. Sketch the graph the function: f ( ) 4 Label all intercepts with their co-ordinates. 0. Sketch the graph the function: y ( ) + Label all intercepts with their co-ordinates

6 ANSWERS TO MATH 10 REVIEW TEST y + y. or y + 0y ( y 4)( y + 4)( y ) or 4 9. [ 1., 10.9) y 0 i 11. y z 1. 0, z D , 16. Domain: (, ] ; range: [ 0, ) 17. (, 0) U ( 0,) (, ) 18. a. reals b. y > ( 0, -4) 4 (, ( 0, 7) (, ) y ( ) +

7 MATH 10: College Algebra REVIEW TEST Name: Date: Score: QUESTION (Show all work) ANSWER 1) Write the equation log 16 4 in eponential form. 1 ) Write as a single logarithm: (a) 7 log + 8log b (b) log + 4( log log y) b b b y b (a) (b) ) (a) Evaluate: log (a) (b) Simplify and evaluate ( 1 log 8 + log 1 log ) 8 (b) 4) (a) Find the eact value of log 8 (a) (b) Find the eact value of log (b) (c) Find the eact value of log 1 (c) ) Solve: log 6) Solve:

8 MATH 10 REVIEW Test Page ANSWERS 7) Find the value of rounded correct to decimal places: e 8 8) Find the value of rounded correct to decimal places if 0 9) Evaluate: log 9 1 to decimal places 10) 1 Solve for the eact value of : ) Solve for the eact value of : + log ( 1) 1 log

9 MATH 10 REVIEW Test Page ANSWERS 1) Sketch the graph of ( ) 1 f + Label all intercepts with their coordinates. 1) 1 1 Sketch the graph of y Label all intercepts with their coordinates. 14) Sketch the graph of y log ( + ) Label all intercepts with their coordinates. 1) The amount of money $A obtained at the end of n years when a principal of $P is invested at a rate r compounded annually, is given by the formula: A P 1 + r ( ) n If a person invests $0 at 4% interest compounded annually, find the amount obtained at the end of 1 years. Round your answer to the nearest dollar.

10 MATH 10 REVIEW Test Page 4 ANSWERS 16) If P is the number of bacteria present, after t minutes, the population growth of a bacterial colony is described by the formula: 0.1t P 1000e Find the number of bacteria present after 10 minutes (to the nearest whole.) 17) 1 Solve for : ) Solve for : ) Solve for : ( 1) 9 0) Find all solutions for where:

11 MATH 10 REVIEW Test Page ANSWERS 1) 1 1 Solve for : ) Solve for w: w 1 + w 1 w ) Find all points of intersection between the circle + y 0 and the line + y 0 4) Sketch the graphs of the system y 4 y 8 Algebraically find all point(s) of intersection of the two graphs and label these on your sketch.

12 MATH 10 REVIEW Test Page 6 ANSWERS 1) ( 1 ) ) (0, ) ) (a) log b ( 7 y 8 ) 14) (b) log b 4 y (-, 0) (0, 1) ) (a) - 1) $40 (b) 4) (a) 8 16) 0 bacteria (b) 6 (c) -. ) 8 17),1 6) ) 1, 7) ) 8, -6 8) ) ±, ± 4 9).0 1) 1 10) 1 ) 1, 11) (-1 is etraneous) ) (1, 1) 1) 4) (, - 4) and (4, 0) y 8 (0, ) (0, 0) (0, -8) (, -4) (4, 0) y 4

13 MATH 10: College Algebra TEST REVIEW Name: Date: Score: QUESTION (Show all work) ANSWER 1) Find the equation of the circle of radius 7 with its center at the origin. ) Find the center and radius of the circle 4 + 4y 40y ) Find the verte of the parabola y + 4) Find the verte of the parabola y 10 ) Find the coordinates of the verte for the function y

14 6) Which equation describes an ellipse? [A] y + y 6 [B] y 4y + 0 [C] y + 11y [D] 4y y 4 7) Find an equation of the parabola in standard form with verte ( -, ), ais of symmetry y, and passing through the point (,-1) 8) Graph the parabola: y ( ) + 9) Sketch the graph of ( + ) + ( y + 4) 9 10) Graph: y + 6y 0 MATH 10 TOPIC 1 PRACTICE TEST Page

15 11) Find the center, vertices, and foci for the ellipse: + y ) Obtain an equation for an ellipse with major ais of length 8 and foci at (7,1) and (1,1). 1) Graph: ( 4) 9 + ( y ) ) Graph and show the asymptotes: y ) Simplify the equation and graph: + y y ) Determine the vertices, asymptotes, and foci of the hyperbola defined by ( + ) ( y + ) 4 1. MATH 10 TOPIC 1 PRACTICE TEST Page

16 17) Evaluate: ) Use Cramer s rule to solve: 4y 11 + y 6 19) y + 4 z Write the augmented matri for the system y + 6z 6 + y + 4z 6 Then perform elementary row operations to complete the first column of the solution. 0) Write the partial fraction decomposition of ( + )( + 4) MATH 10 TOPIC 1 PRACTICE TEST Page 4

17 1) Solve the system: + y + 4z 4 y + 4z 4 + y + 1z 4 ) Use Cramer s rule to solve: + y z y z y z 16 ANSWERS 1. + y center (4, ); radius 1. ( ) + (y 1) 7 y MATH 10 TOPIC 1 PRACTICE TEST Page

18 . 1 4, y ( -1, 11) y (-, 0) 10 ( y + 1) ( + ) vertices: (, ), ( 4, ) foci: 6 6. [A] Note the coefficients of the squared terms ( ) 8 y ( + ) 18., y ,, 9, Circle with center (-, -4), radius Circle with center (-, -), radius 1 1. inconsistent 11. Center : (0, 0), Vertices : ( 0, 9)(, 0, 9), Foci : ( 0, ),( 0, ). (-4,, 1) MATH 10 TOPIC 1 PRACTICE TEST Page 6

19 MATH 10: College Algebra REVIEW Test 4: TOPIC 18 Name: Date: Score: QUESTION (Show all working) 1) Use a calculator to find tan 7 correct to the nearest thousandth. ANSWER ) Find the angle A, to the nearest degree, if sin A ) Find the eact value of angle B if tan B 4) Solve the triangle ABC, given that C is a right angle, and: a and c 6 B 6 C A ) Find the measure of θ given that sin θ 1 and cos θ 6) Find. BCD and ACD are similar. C B 4 D 9 A 7) In the diagram of the rectangular prism shown, find size of AGD to the nearest degree. E F A B 6 cm H G cm D 4 cm C

20 8) Find the eact value of sin A, cos A, and tan A C B A 9) Find the value of the side labeled correct to the nearest tenth ) Find the value of the side labeled correct to the nearest tenth ) Find the value of the side labeled correct to the nearest tenth θ 1) Find the value of the side labeled correct to the nearest tenth ) Find the angle θ correct to the nearest degree. 1 1 θ 18 MATH 10 REVIEW TEST 4 Page

21 14) Find the angle θ correct to the nearest degree θ 1) Use the Area Rule to find the area of the triangle ABC (to the nearest whole), C given A 7, b and c 8. A 7 8 B 16) Use the Area Rule to find the area of the triangle ABC (to the nearest whole), given A 7, a 1 and c 14. [HINT: You will need to find B] C A 7 b 14 1 B 17) Two ships leave port at the same time. One travels 00 miles in a direction S4 E, while the other travels 70 miles in a direction S W. How far apart are the ships, to the nearest mile? MATH 10 REVIEW TEST 4 Page

22 18) A 1 ft ladder reaches 10 ft up the wall against which it leans. Find the (acute) angle, to the nearest degree, that the ladder makes with the ground ) A person standing on the top of a cliff, looking out to sea, spots a boat. The angle of depression from observer to boat is. If it is known that the cliff is 46 feet in height, how far out to sea (from the cliff) is the boat, to the nearest foot? θ θ 46 ft ft 0) To estimate the altitude of a hot air balloon, Junee takes two measurements. Initially she finds that the angle of elevation to the balloon is 68. After traveling 10 ft closer to the balloon, she finds that the angle of elevation to the balloon is 7. What is the altitude of the balloon, to the nearest 10 ft? θ y ft 68 α 7 10 ft 1) A kite is flying at an altitude of 10 ft above the ground, and makes an angle of elevation of 7 with the ground. Find the length of the string needed to fly the kite, correct to the nearest foot. 10 ft 7 MATH 10 REVIEW TEST 4 Page 4

23 MATH 10: College Algebra REVIEW Test 4: TOPIC 18 Name: Date: Score: QUESTION (Show all working) ANSWER 1) Use a calculator to find tan 7 correct to the nearest thousandth..7 ) Find the angle A, to the nearest degree, if sin A ) Find the eact value of angle B if tan B 0 tan ) Solve the triangle ABC, given that C is a right angle, and: a and c 6 b b cos B A ( 4 ) 1 B cos B 6 A B 6 C A A 6 B 4 b. ) Find the measure of θ given that sin θ 1 and cos θ 10 sin θ 1 so θ is 0 or 10. But cos θ, so θ must be 10. 6) Find. C 6 BCD and ACD are similar. So: B 4 D 9 A 7) In the diagram of the rectangular prism shown, find size of AGD to the nearest degree. E F DG A B tang 6 1 G tan G 6 cm D H 4 cm C G cm

24 8) Find the eact value of sin A, cos A, and tan A C sin A b sin A cos A tan A B A cos A tan A 9) Find the value of the side labeled correct to the nearest tenth.. tan16 8 8tan ) Find the value of the side labeled correct to the nearest tenth.. sin sin ) Find the value of the side labeled correct to the nearest tenth. θ By the Law of Sines: 48 8 θ sin 48 sin sin 48 8 sin ) Find the value of the side labeled correct to the nearest tenth. By the Law of Cosines: cos cos ) Find the angle θ correct to the nearest degree. 6 Using the Cosine Law, cosθ cosθ 16 θ cos θ 6 ( 9 ) θ 1 18 MATH 10 REVIEW TEST 4 Page

25 14) Find the angle θ correct to the nearest degree. Using the Sine Law, sinθ sin 64 6 sin 64 sinθ θ sin θ 0 ( ) 6 θ or θ Since θ must be smaller than 64 (the side opposite each angle), θ 0 1) Use the Area Rule to find the area of the triangle ABC (to the nearest whole), C given A 7, b and c 8. Area,A 1 8 sin7 8 units A 7 0 (not 10 ) 8 sq. units 8 B 16) Use the Area Rule to find the area of the triangle ABC (to the nearest whole), given A 7, a 1 and c 14. [HINT: You will need to find B] By the Law of Sines: sinc sin B C 14 sin7 sinc b 1 Area sin sin7 1 A 7 C sin 1 9 units 14 C B 9 sq. units ( B 4 ) 17) Two ships leave port at the same time. One travels 00 miles in a direction S4 E, while the other travels 70 miles in a direction S W. How far apart are the ships, to the nearest mile? By the Law of Cosines: cos cos miles MATH 10 REVIEW TEST 4 Page

26 18) A 1 ft ladder reaches 10 ft up the wall against which it leans. Find the (acute) angle, to the nearest degree, that the ladder makes with the ground. 10 sinθ 1 θ sin ) A person standing on the top of a cliff, looking out to sea, spots a boat. The angle of depression from observer to boat is. If it is known that the cliff is 46 feet in height, how far out to sea (from the cliff) is the boat, to the nearest foot? θ 90 6 tan tan6 978 θ 46 ft 10 ft 1 θ ft 0) To estimate the altitude of a hot air balloon, Junee takes two measurements. Initially she finds that the angle of elevation to the balloon is 68. After traveling 10 ft closer to the balloon, she finds that the angle of elevation to the balloon is 7. What is the altitude of the balloon, to the nearest 10 ft? α θ By the Law of Sines, y 10 sin 68 sin 7 10sin 68 y sin ) sin sin ft (to nearest 10 ft 68 α 7 10 ft y θ ft 1100 feet 1) A kite is flying at an altitude of 10 ft above the ground, and makes an angle of elevation of 7 with the ground. Find the length of the string needed to fly the kite, correct to the nearest foot. 16 ft 10 sin7 10 sin ft 7 MATH 10 REVIEW TEST 4 Page 4