Intermediate Algebra Test for the Internet. Evaluate: x y when x =and y =. a) b) 6 c) 77. Add: 9:6+( :). a).9 b) -.9 c). -.. Subtract: 8 ( ). a) - b) c) -. Multiply: a) 8. Divide: a) 8 9 8 b). 6 b) 0 7 6. Simplify: x [9 (x 6)]. c) c) 9 7 a) 7x +9 b) 7x 7 c) x 7 x +9 8 7. Simplify: 9a b. ab a) b 6 a 8. Solve: 6(x ) = + (x + 7). b) a b 6 c) 7b 6 6a 7b6 6a a) b) - c) 9. Money is borrowed at 6.% simple interest. After one year $7.76 pays o the loan. How much was originally borrowed? a) $80 b) $7. c) $60 $90.7 0. Solve: 9y 7 9. a) fyjy g b) fyjy g c) fyjy g y y 9
. Solve: x+ <7. a) x x< c) x <x. A painter can be paid in one of two ways: Plan A: $0 plus $8.00 per hour. Plan B: Straight $6.00 per hour. b) x x< x <x< For what values of n hours is plan B better than plan A? a) fnjn <8:7g b) fnjn >g c) fnjn <g fnjn >8:7g. Solve: j x j. a) fxj 7xg b) fxj x7g c) fxjx or x 7g fxjx 7or x g. Find the intersection: f; ; 9; ; ; 9g\f;; g. a) f; ; 9; ; ; ; 9g b) f; g c) f; ; g f; 9; ; 9g. Find the slope, if it exists, of the line containing the points (-,-) and (,6). a) b) c) 6. Find an equation of the line having the slope m = and containing the point (,-). a) y = x + 7 b) y = x + 7 c) y = x y = x + 7. Find an equation of the line containing the following pair of points: (,9) and (-,-7). a) y = 6 x b) y =x+ c) y =x 7 y = 6 x +7 8. Find an equation of the line containing the point (-,6) and parallel to the line x y =. a) y = x b) y = x +0 c) y = x y = x +
9. Find an equation of the line containing the point (,-) and perpendicular to the line x + y =. a) y = x + 9 b) y = x c) y = x +7 y = x 0. The cost of a taxi ride is $.60 for. miles and $8.0 for 8. miles. Find a linear equation that ts the data points. Express C, the cost of the taxi ride, in terms of M, the number of miles ridden. a) C =0:M+:6 b) C =0:8M+:6 c) C =0:M+: C =:M+0:6. What linear inequality does this graph illustrate? a) x y b) x +y c) x +y x y. Use the substitution method to solve for y: x y =, y=x 6. a) b) c) - -. Use the elimination method to solve for x. 8x y =, x +y=. a) - b) c) - -
. A chemist has one solution that is % acid and a second solution that is 8% acid. How many liters (L) of the 8% acid should be mixed with the % to get 80L of a solution that is 0% acid? a) 0 b) 0 c) 60 0. An airplane ew for hr with a -mph tail wind. The return trip against the same wind took 6hr. Find the speed of the plane in still air. a) 7 mph b) 00 mph c) 0 mph mph 6. Use matrices to nd z when solving x y + z =, x+y+z=8, x+y z=. a) - b) c) - 7. When solving the following system of equations using Cramer's rule, what is the value of D x? x y =, x +y=. a) b) c) 6 8. When solving the following system of equations using Cramer's rule, what is the value of D? x y +z=, x+y z=, x + y +z=9. a) - b) - c) 0-0 9. Add: ( x +x 6x)+(x x 9). a) x +x 0x +9 b) x + x x 9 c) x +x x 9 x x x 0. Subtract: (x 6x ) ( x x +). a) x x b) x 9x c) x x 9 x 9x. Multiply: (8a +b)(a b). a) 0a ab 6b b) 0a 6b c) a + b 0a +ab 6b
. Find one of the factors of m +m 08. a) m 9 b) m + c) m 8 m +9. Find one of the factors of 8a 8a 6a. a) a + b) a + c) a a. Solve: x x = 0. a) -, b) -, 6 c) -, -6,. Find the remainder when x x is divided by x +. a) b) c) - 6. Subtract and simplify: a) (x )(x +) x x x x x. b) x x 0 (x )(x )(x +) c) x + (x )(x ) x x +0 (x )(x )(x +) 7. Divide and simplify: a) 8. Solve: a) 9. Solve: a) b) y +7 y+ 8 x = x. x 8 y 9 y y +y+ y +. c) y 7 (y +) b) - c) x 6 = x +. b) y +7 (y +) c) 7 6 0. The sum of a number and times its reciprocal is 6. Find the numbers. a) -, b), c) -,-,
. Two pipes are lling a pool. One of them can ll the pool alone in 9 hr. The other can ll the pool alone in 6 hr. How long will it take them working together to ll the pool? a) hr b) 7 hr c) hr. Simplify: a) 7x x 6 7x. 6 9x b) 7 7x +6 c) 6 7x 6 7x 6. Approximate p to three decimal places. a).67 b).66 c).8.89. Add and simplify: p 8 + p 7 + p 08. a) 9 p b) 0 p c) p p. Rationalize the denominator: p. 6 a) 0 + p 6 b) 0 + p 6 c) 0+p 6 +p 6 6. Solve: p x +6= p x +. a) b) 0 c) 9 0 7. Multiply: ( + i). a) 7 + i b) 7 c) + i 7+i 8. Simplify: i. a) i b) i c) - 9. How long is a guy wire reaching from the top of a ft pole to a point on the ground 0ft from the pole? a) 8ft b) 0ft c) 6ft ft 0. Solve: x(x ) x(x +) =. a), b), c),6, 6
. Solve: x +x=7. Approximate the positive solution to the nearest tenth. a). b). c) 6... A student opens a history book to two facing pages. The product of the page numbers is 06. Find the smaller page number. a) 8 b) c) 9. Use the formula A = P ( + r) t. An investment of $8000 grows to $907.80 in years. What is the interest rate? a) 7.% b) 6.% c).6%.%. Find the vertex of the parabola y = x 8x +. a) (,-) b) (-,) c) (,-) (,-7). Find the quadratic equation that ts the data points (0,-), (,), and (-,0). a) y =x +x b) y =x x c) y =x x+ y =x x 6. Solve: (x + )(x ) (x +) <0. a) fxjx < or x>g b) fxj <x< or x>g c) fxj <x<g fxjx < or <x<g 7. Find the distance between (,-) and (-,). Give an approximation to three decimal places. a) 6. b) 8.8 c).7 9.87 8. Find the center and radius of the circle: x + y 6x +y =0. a) (,);6 b) (,-); c) (-,); (-,);6 9. Find the x-intercept of x + y =. a) (-,0) and (,0) b) (0,-) and (0,) c) (-,0) and (,0) (0,-) and (0,) 60. Find one of the solutions of y = x x, x = y 8. a) (-,6) b) (,-6) c) (-,) (,-6) 7
6. Given the function f described by f(x) =x x+,nd f( ). a) - b) 7 c) 6. A rectangle has an area of 7m and a perimeter of 68m. Find the length. a) 7m b) m c) 6m m 6. Find a formula for the inverse of f(x) = x 7 x+. a) x x +7 b) x 7 x 6. Convert = x to a logarithmic equation. c) x +7 x x x 7 a) = log x ( ) b) x = log ( ) c) =log x =log x 6. Given that log a =0:, and log a =0:770, nd log a 0 a).07 b) 0.089 c).6.06 66. Find log6:79. a).89 b) 0.790 c) 0.8.8 67. Find antilog e (0:). a) -.0 b).79 c).6.6 68. Find log using the change-of-base formula. a).978 b) 0.7 c).7.079 69. Solve: 6 x =:. a) 0.7 b). c) 0.60.66 70. Find the doubling time for the function N(t) =:e 0:0t. a) 7. b).9 c) 7. 6. 8
Answers for Intermediate Algebra.b.d.c.a.b 6.b 7.c 8.d 9.a 0.b.c.d.d.b.c 6.a 7.a 8.b 9.d 0.b.d.d.c.b.a 6.b 7.d 8.d 9.c 0.c.a.a.a.b.c 6.d 7.d 8.c 9.d 0.b.c.b.b.a.b 6.c 7.d 8.b 9.c 0.d.a.b.b.c.a 6.d 7.d 8.b 9.c 60.a 6.d 6.b 6.c 6.c 6.d 66.b 67.c 68.a 69.b 70.c 9