ALGEBRA X Final Exam Review Packet
Multiple Choice Match: 1) x + y = r a) equation of a line ) x = 5y 4y+ b) equation of a hyperbola ) 4) x y + = 1 64 9 c) equation of a parabola x y = 1 4 49 d) equation of an ellipse 5) y = 9x+ 6 e) equation of a circle 6) If log ( 5x + 1) = 4, then x =? a) 7/5 b) 1 c) 17/5 d) e) 7) Find x, if 4 log 8 = x a) b) / c) / d) 1/ e) 4 8) Solve: x ( x ) log log = log a) x = -1, b) x = - c) x = d) x = 1,- e) none of these ( 4x 7) 9.) Solve for x: 5 = 15 a) 5/ b) c) 5 d) e) -1 10) Solve: x + x = 7 a) x = 1 b) x = c) x = -, 1 d) x = -1, 11) Solve: log x (4 x ) = a) x = 0, 4 b) x = 0 c) x = 0, -4 d) x = 4 Page of 14
1) The coordinates of the vertex of the parabola with equation ( ) y = x 4 6 are: a) (-4,-10) b) (-4,6) c) (4,-6) d) (4,6) e) (4,10) 1) The graph of y = (x - ) + is a) b) c) d) 14) Determine the vertex and the direction the graph opens of the equation y = x + 8x 1. a) (-4, -1); Upwards b) (4, -17); Downwards c) (8, -1); Upwards d) (-4, -17); Upwards e) (-4, 15); Upwards 15) Determine the radius of the circle with center (0,4) and a point on the circle (-,0). a) 10 b) 7 c) 5 d) -5 e) none of these 16) Find the coordinates of the midpoint of (7,) and (-5,1). a) (6,) b) (1,1) c) (6,1) d) (1,) e) (,-1) Page of 14
17) The length of the major axis of x y + = 1 4 5 is a) 14 b) c) 10 d) 4 e) none of these 18) Solve the following system of equations: x y = 1 x = y+ a) {(-9,-11), (1,1)} b) { (1, 11), (,1)} c) {(,1), (-,-5)} d) {(-9,-11), (1,-1)} e) {(1,), (-5,-)} 19) Find the 7nd term of the sequence 5, 11, 17,... a) 47 b) 41 c) 45 d) 0,816 e) 404 0) What is sum of the first five terms in the geometric series whose first term is 4, the common ratio is -, and the fifth term is 4? a) -44 b) 44 c) -484 d) 484 e) none of these 1) The value of the sum (k 1) is 5 k = a) 16 b) 7 c) 4 d) 5 e) none of these ) Find the sum of the infinite geometric series 1 1 1 1 +... 4 8 a) -1/ b) c) / d) / e) none of these ) In the sequence 7, 1, 19,...a n, which term, n, has the value of 157? a) n = 6 b) n = 4 c) n = 5 d) n= 94 e) none of these Page 4 of 14
4) The common ratio for the geometric sequence -4,, -1, 1/, -1/4... is a) r = b) r = 1/ c) r = - d) r = -1/ e) none of these 5) If y varies inversely as x, and y = 4 when x = 0, find y when x =. a) /5 b) 80 c) 5/ d) 0.5 e) 40 6) Find the smallest positive angle co-terminal with 416. a) 6 b) 4 c) 56 d) 04 7) Point P(5, -6) is on the terminal side of an angle in standard position with measure θ. Find tan θ. a) 5 6 b) 6 5 c) 5 61 61 d) 6 61 61 8) The terminal side of an angle in standard position passes through the point (5, -1). Find the sine ratio of the angle. a) 1 b) 1 5 1 c) 5 d) 1 1 1 9) Find the value of cos 10. a) b) 1 c) d) 1 0) Change 48 to radian measure. a) 96π b) 48π c) 15 π 4 d) 4 π 15 1) Given triangle ABC, C = 90, A = 0, and AC = 15 cm. Find AB. a) 0 cm b) 5 cm c) 10 cm d) 15 cm Page 5 of 14
) In right triangle ABC with C = 90, if a = 4.8 in and B = 9, find side c to the nearest tenth. a) 1.9 in b) 19. in c) 15.6 in d) 9.4 in ) x 4 x + x 0 x 1 1 x equals a) 1 x + 5 b) x + 5 c) 1 x + 5 d) x x + 1 4) Subtract: x + - x 1 5x + 10 x + 6 a) 8x + 4 b) -x + 14 c) -x + 14 d) -x + 4 15(x + ) 15(x + ) x + 1 5) If log n = 9, then n = A) 81 B) - C) 9 D) 6) If log(x + 4) log(x - 7) = log, then x = A) B) -7 C) 18 D) x+ 1 7) If e = 10, then x is approximately: A) 4.5 B).65 C) 0 D).4 8) Solve for x: 4 = 8 x 9 x x+ Page 6 of 14
Free Response Functions 1. Describe the following: a. {(,), (4,5), (1,)} b. {(,), (4,5), (,7)} Function or relation? Domain: Range: Function or relation? Domain: Range:. State the domain of : 6 f( x) = x +. Let f ( x) = x 4. Find f 1 ( x ). 4. Let f ( x) = x + 4x and g( x) = x. Determine the following: a. f (g()) b. ( f )( x) c. g + ( f g)() d. g( f ( x)) 5. If y varies directly as x; and y =8 when x =7, find x when y =96. 6. If y varies inversely as x, and y =6 when x =, find y when x =. 7. How do you know if the inverse of a function is a function? Page 7 of 14
Rational Expressions/Equations 8. Simplify and state all restrictions: x + x 7 a. + x 4 x 4x b. 1 x x c. y y y + 15 y 5 + y 6 d. x + x + 6 5x + 10 x + 9. Solve for x. 4 a. = x + 5 x+ x x 9 b. Solve for: x + 15 = 4 5 Logarithms 10. If log 5 =.68 and log 5 =.4, then find log 5 6. 11. Convert 5 = to logarithmic form. 1. Solve each equation for x. a. log (4x + ) = b. x x+ = c. x log log ( ) log 4 log ( ) + log (x+ ) = 1 Page 8 of 14
d. (6x-5) = 7 e. ln( 5 ) = 4 x f. 1000 = 50(1.04) x 1. Evaluate the following: a. log 9 1. b. log 9 c. log 4 64 d. log 1 81 14. Expand as a sum/difference of simple logarithms: x y ln z 4 Conics 15. Find the equation of the graph: 16. Let y = ( x+ 5). a. Identify the vertex. b. What is the distance between the focus and the directrix? Page 9 of 14
17. Find the axis of symmetry for y = ( x ) + 5. 18. Put into standard form and identify the conic: x + 1x y 9 = 0 19. Determine the radius of the circle with a center of (0, ) and a point on the circle of (-4, 0). 0. Find the coordinates of the midpoint of (5, -) and (-9, 8). 1. Consider the equation: ( x ) ( y+ 4) + = 1 9 49 a. Identify the center. b. Determine the length of the major and minor axis. c. Sketch the conic. 10 8 6 4-10 -8-6 -4-4 6 8 10 - -4-6 -8-10 Page 10 of 14
. Consider the equation: ( y ) ( x+ ) = 1 16 4 a. Identify the center. b. Identify the slopes of the asymptotes.. Identify the graph of the following equations (which conic is it?) a.) x = 6y y+5 d.) x y + = 1 5 6 b.) y = x+ e.) x + y = r c.) x y = 1 49 16 4. Solve the following system of equations. x + y = 5 y = x 1 Page 11 of 14
5. Sketch: y = x 6x+ 6 6. Sketch: x + 10x+ y + y = 10 10 8 6 4-10 -8-6 -4-4 6 8 10 - -4-6 -8-10 10 8 6 4-10 -8-6 -4-4 6 8 10 - -4-6 -8-10 Sequences and Series 7. Find the nd term of the sequence 4, 8, 1, 8. Insert two arithmetic means between 15 and 6. 9. Find in the geometric series where a 1 =, r = - S 6 Page 1 of 14
0. Evaluate 6 k = (k + 1) 1. Find the sum of the infinite geometric series: + 1 + ½ + ¼ +. Find the sum of the first 10 natural numbers.. In the sequence, 8, 1,, what term has a value of 8? 4. Find r for the geometric sequence -6,, -/, /9, Trigonometry 5. Find the smallest positive co-terminal angle of 790. 6. (7, 4) is on the terminal side of an angle θ. Find tan θ. Page 1 of 14
7. (8,-15) is on the terminal side of an angle θ. Find sin θ. 8. Find the exact value of cos 150. 9. Find the approximate value of tan 168 (use a calculator). 40. Change 6 to radians. 41. Given triangle ABC, C = 90, A = 0, and AB = 16 cm. Find AC. 4. Given a circle with radius 6 cm, find the length of an arc intercepted by a central angle of 5 π. 18 4. Convert to degrees: 7 π 15 44. In right triangle ABC, C = 90, a = 14.6, and B = 5. Find c to the nearest tenth. Page 14 of 14