# Find the distance between the pair of points. 2) (7, -7) and (3, -5) A) 12 3 units B) 2 5 units C) 6 units D) 12 units B) 8 C) 63 2

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1 Sample Departmental Final - Math 9 Write the first five terms of the sequence whose general term is given. 1) a n = n 2 - n 0, 2,, 12, 20 B) 2,, 12, 20, 30 C) 0, 3, 8, 1, 2 D) 1,, 9, 1, 2 Find the distance between the pair of points. 2) (7, -7) and (3, -) 12 3 units B) 2 units C) units D) 12 units Solve the equation. 3) log 8 ( + 2) - log 8 = B) 8 C) 3 2 D) 2 3 Simplif. ) B) + 2 C) + 2 D) - 2 Solve the equation. ) = B) 22 C) D) -8 ) = 8-3 B) - 3 C) 3 D) 3 Using the change of base formula, rewrite the following epression using common logarithms. 7) log 2 log 2 log B) log log 2 C) log 2 D) log 2 Solve. 8) Jim can run miles per hour on level ground on a still da. One wind da, he runs miles with the wind, and in the same amount of time runs miles against the wind. What is the rate of the wind? mph B) mph C) mph D) 3 mph 1

2 9) = + -3 B) -2 C) 3 D) 8 ) = 0 1, 1 B) -1, 1, -, C) -1, 1, -i, i D) -i, i, -i, i 11) = B) 3 C) 9 D) 12) A painter can finish painting a house in 7 hours. Her assistant takes 9 hours to finish the same job. How long would it take for them to complete the job if the were working together? hours B) hours C) 8 hours D) 1 3 hours 13) How man real solutions are possible for a sstem of equations whose graphs are a parabola and a circle? 1, 2, or 3 real solutions B) 0, 1, 2, or 3 real solutions C) 0, 1, 2, 3, or real solutions D) 1, 2, 3, or real solutions Use the square root propert to solve the equation. 1) ( + 2) 2 = 11 9 B) -2-11, C) - 11, 11 D) 2-11, Solve. 1) One number is 2 less than a second number. Twice the second number is 8 less than 3 times the first. Find the two numbers. 12 and 1 B) -1 and -12 C) 11 and 13 D) 13 and 1 1) = B) 37 C) 18 D) 17) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. 1 thousand automobiles B) thousand automobiles C) thousand automobiles D) 2 thousand automobiles Find the eact value. 18) ln e B) 1 C) e D) e 2

3 19) log,000 2 B) 0 C) D) 1 Identif whether the equation, when graphed, will be a parabola, circle, ellipse, or hperbola. 20) 2 = parabola B) circle C) ellipse D) hperbola 21) = 1 parabola B) circle C) ellipse D) hperbola Graph the function. 22) = log 2 B) C) D) Use the quadratic formula to solve the equation. 23) ( - 8) = 3-13, + 13 B) , C) - 19, + 19 D) ,

4 2) = - - i 7, - + i C) - i 7, - + i B) - i 7, + i D) - - i 7, + i Sketch the graph of the equation. Find its verte. 2) = 2 - verte (, 0) B) verte (0, -) C) verte (0, ) D) verte (-, 0) Rationalize the denominator and simplif. Assume that all variables represent positive real numbers. 2) B) C) D) Perform the indicated operation. Write the result in the form a + bi. 27) ( + i) - (-2 + i) -8-3i B) 8 + 3i C) + i D) 8-3i

5 Find the indicated term for the sequence whose general term is given. 28) a n = (-1)n n + 9 ; a B) - 7 C) 1 21 D) Sketch the graph of the equation. Find its center and radius. 29) ( + ) = 1 center (0, ); radius = B) center (-, 0); radius = C) center (0, -); radius = D) center (, 0); radius = Rationalize the denominator and simplif. Assume that all variables represent positive real numbers. 30) B) 7 3 C) 21 D) Multipl, and then simplif if possible. 31) ( 2 - ) 2-2 B) 7-2 C) -3-2 D) 7 + 2

6 Solve the sstem. 32) z = z = 2 z = 3 (3,, ) B) (,, 3) C) (, 3, ) D) Find the value of the logarithmic epression. 33) log B) 1 2 C) 2 D) - 1 Find the power of i. 3) i 28 -i B) i C) -1 D) 1 Solve the equation for. Give an eact solution. 3) ln = e B) 3.2 C) 3.2 D) e 3.2 3) log = 3. e 3. B) 3. C) 3. D) 3. e Match the function with its graph. 37) f() = B) (-3, ) (3, -) C) D) (3, ) (-3, -) -

7 Graph the solution of the sstem of linear inequalities. 38) - < + < 3 B) C) D) Solve the equation. Give an eact solution. 39) e ( + 2) = e + 2 B) ln 7 C) e D) ln - 2 Solve the equation for the specified variable. 0) V r 2 h = 1 3 ; for h h = V r2 B) h = V 3r 2 C) h = Vr 2 3 D) h = 3V r 2 Epress as the logarithm of a single epression. 1) log 2 + log 2 log 2 3 B) log 2 12 C) log 12 D) log 3 Write the series with summation notation. 2) (-9) -9i B) i = 1 (-9i + 3) C) i = 1 9i D) i = 1 i = 1 (-9i + ) 7

8 Write the first five terms of the geometric sequence whose first term, a 1, and common ratio, r, are given. 3) a 1 = ; r = 1 3, 3, 9, 27, 81 B) 3, 9, 27, 81, 23 C), 12, 3, 8, 32 D), 13 3, 1,, Find the inverse of the one-to-one function. ) f() = 3 + f -1 () = - B) f -1 () = C) f -1 () = D) f -1 () = 3 - ) f() = f -1 () = B) f -1 () = C) f -1 () = 7-3 D) f -1 () = 7-3 For the given functions f and g, find the composition. ) f() = 3 - ; g() = -2 Find (f g)() B) C) D) Find the indicated term of the sequence. 7) If the second term of an arithmetic progression is -11 and the sith term is 9, find the fifteenth term. 9 B) -1 C) D) Epress as the logarithm of a single epression. Assume that variables represent positive numbers. 8) log b q - log b r log b q r B) log b (q - r) C) log b q log b r D) log b q r 8

9 Determine which graph is the graph of a one-to-one function. 9) B) C) D) Write an equation to describe the variation. Use k for the constant of proportionalit. 0) w varies directl as the square of and inversel as the cube of. w = k2 3 B) w = k3 2 C) w = k D) w 2 3 = k For the given functions f and g, find the composition. 1) f() = 2 + ; g() = + 2 Find (g f)(3). 2 B) 28 C) 120 D) 0 Write in terms of i. 2) i B) ±20 C) 20i D) i 20 Find the indicated term of the sequence. 3) The fifteenth term of the arithmetic sequence whose first term is - and whose common difference is -3 B) -9 C) 38 D) - 9

10 ) Find the seventh term of the geometric sequence 1, 2,,... 1 B) 128 C) 12 D) Write as a logarithmic equation. ) 3 2 = 9 log 3 9 = 2 B) log 2 9 = 3 C) log 3 2 = 9 D) log 9 3 = 2 Match the equation with its graph. ) = ( - 2) ( + 3) B) C) 8 2 D)

11 Identif the domain and then graph the function. 7) f() = - 3 [0, ) B) [0, ) C) [3, ) D) [-3, ) Use the graph of the following function f() to find the value. 8) Find such that f() = B) -3 C) 7 D) 11

12 Write an equation of the circle with the given center and radius. 9) (, -1); 13 ( - 1) 2 + ( + ) 2 = 19 B) ( - ) 2 + ( + 1) 2 = 13 C) ( + 1) 2 + ( - ) 2 = 19 D) ( + ) 2 + ( - 1) 2 = 13 Given the matri in echelon form, find the solution for the sstem. 0) (12, -1, -2) B) (, 7, -2) C) (-2, -1, 12) D) (9, 3, -2) Find the surface area of the figure. 1) 3 m m 7 m 1 m2 B) 18 m2 C) 122 m2 D) 8 m2 Find the variation equation for the variation statement. 2) z varies jointl as and the cube of ; z = 90 when = and = -3 = 3 B) = 3 C) = -3 D) = -3 Use the given right triangle to find the trigonometric function. 3) cos A B) 3 C) 3 D) 3 Use the properties of eponents to simplif the epression. ) 3/ 1/ 3/ B) C) 1/2 D) 1 12

13 The graph of an eponential function is given. Match the graph to one of the following functions. ) f() = 2-1 B) f() = 2 ( - 1) C) f() = 2 D) f() = Simplif. Assume that all variables represent an real number. ) B) + C) - + D) + Complete the indicated row operation. 7) Replace R2 in with 3R1 + R2. B) C) D) Solve the problem. 8) A bacteria culture starts with units and triples ever da. Write the general term of the sequence that describes the growth of this culture. Find the number of bacteria units there will be at the beginning of the fourth da. an = 3() n - 1 ; 192 units B) an = (3) n ; 32 units C) an = (3) n - 1 ; 8 units D) an = () n ; 2 units 9) At a certain time of da, the angle of elevation of the sun is 0. Find the height of a pole whose shadow at that time is 13 feet long ft (13 3)/3 feet B) 13 2 feet C) 13 3 feet D) 2 feet 70) Find the sum of the first nine negative integers. - 3 B) - C) - D) - 13

14 Simplif the radical epression. Assume that all variables represent positive real numbers. 71) 320k7q8 8k7q8 k B) 8q k7 C) 8k3q k D) 8k3q Use the partial sum formula to find the partial sum of the given geometric sequence. 72) Find the sum of the first five terms of the geometric sequence 1, 2,, B) 279 C) 2 D) 31 Use radical notation to write the epression. Simplif if possible. 73) 1 1/2 2 - B) 1 C) - 1 D) Find the unknown side of the right triangle. 7) B) 1 C) 2 3 D) 1 Provide an appropriate response. 7) How do ou find Dz when solving a sstem of equations using Cramer's Rule? Replace the -column values with the constant-column values. B) Replace the -column and -column values with the constant-column values. C) Replace the z-column values with the constant-column values. D) Replace the -column values with the constant-column values. 1

15 Graph the equation. 7) ( - 1) ( + 1) 2 9 = 1 B) C) D) Find the volume of the figure. 77) 2 in. 1π/3 in.3 B) 8π/3 in.3 C) 32π/3 in.3 D) π in.3 If the function is one-to-one, list the inverse function. 78) f = {(-3, 1), (3, -1), (-2, 1), (2, -1)} f -1 = {(1, -3), (-3, 3), (1, -2), (-1, 2)} B) f -1 = {(1, -3), (-1, 3), (1, -2), (-1, 2)} C) f -1 = {(1, -3), (-1, 3), (1, 3), (-1, 2)} D) not one-to-one 1

16 Graph the equation. 79) = 1 B) C) D) Find the square root. Assume that all variables represent positive real numbers. 80) B) 2 C) 12 D) Complete the square b adding the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. 81) (-1) = ( - )2 B) = ( - )2 C) = ( - 8)2 D) (-) = ( - 8)2 Add. 82) B) 1 C) D) 72 1

17 Solve the nonlinear sstem of equations for real solutions. 83) 2-22 = = 1 (2, 3), (2, - 3), (-2, 3), (-2, - 3) B) ( 3, 2), ( 3, -2), (- 3, 2), (- 3, -2) C) ( 3, 2), ( 3, -2) D) ( 3, 2), (- 3, -2) Solve the inequalit. Graph the solution set and write the solution set in interval notation. 8) - + < 0 (-, -) B) (-, -) (, ) C) (-, ) D) (, ) ) > 0 (-7, -3) B) (-3, ) C) (-, -7) (-3, ) D) (-, -7) Find the sum of the terms of the infinite geometric sequence. 8) 3, 3, 3 1,... 3 B) C) 1 D) 3 Use the product rule to multipl. 87) B) 1 C) 12 D) 2 17

18 Write with positive eponents. Simplif if possible. 88) 1 -/ B) 32 C) 1 32 D) not a real number Find the volume of the figure. 89) Cone 8 in. 3 in. 2π in.3 B) 72π in.3 C) 8π in.3 D) 1π in.3 Sketch the graph of the quadratic function. Give the verte and ais of smmetr. 90) f() = - 1 ( + 2)2-1 verte (-1, -2); ais = -1 B) verte (1, 2); ais = C) verte (-2, -1); ais = -2 D) verte (2, -1); ais =

19 Answer Ke Testname: MATH 9 1) A 2) B 3) D ) D ) D ) A 7) B 8) B 9) C ) B 11) B 12) A 13) C 1) B 1) A 1) D 17) D 18) B 19) C 20) D 21) C 22) D 23) C 2) B 2) D 2) C 27) B 28) C 29) B 30) B 31) B 32) B 33) A 3) D 3) D 3) C 37) C 38) A 39) D 0) D 1) A 2) D 3) A ) D ) D ) A 7) C 8) D 9) D 19

20 Answer Ke Testname: MATH 9 0) A 1) A 2) C 3) D ) D ) A ) B 7) C 8) C 9) B 0) A 1) C 2) C 3) D ) C ) C ) B 7) D 8) C 9) C 70) C 71) C 72) D 73) B 7) D 7) C 7) D 77) C 78) B 79) B 80) D 81) B 82) D 83) B 8) C 8) C 8) B 87) C 88) C 89) A 90) C 20

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