Class: Date: Mock Final Exam Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Two terms of an arithmetic sequence are t = 0.6 and t 1 = 89.6. What is t 1? t 1 = 4.7 B. t 1 = 18.8 C. t 1 = 1 t 1 = 119.1. Determine t 11 of this arithmetic sequence: 0,, 0, 6,... t 11 = 80 C. t 11 = 1 B. t 11 = 170 t 11 = 0. An arithmetic series has S 1 = 79, d = 1, and t 1 = 6; determine the first terms of the series. 6 19 B. 6. 19.. C. 1 8 16 9 4. 4096 is a term in which geometric sequence?, 4, 8, 16,... C., 1, 7, 4,... B. 4, 4, 144, 864,..., 6, 1, 4,.... In a finite geometric sequence, t 1 = and t 4 = 40. If the last term is 640, how many terms are in the sequence? 9 B. 8 C. 10 6 6. A geometric series has t 1 = and S = 6. Determine the common ratio. r=0. C. r=0. B. r= r=0. 7. Determine the common ratio of a geometric series that has these partial sums: S 4 =., S =.7, S 6 =.87 r=1 B. r= C. r= 0. r=0. 8. Determine the common ratio of this infinite geometric series: 6 +4 +96 +84 + Does the series converge or diverge? r=4, so the series diverges. C. r=6, so the series diverges. B. r=4, so the series converges. None of the above 9. For which values of the variable, x, is this radical defined? x 4 x 0 B. x ò C. x 0 the radical is never defined 10. Write this radical in simplest form: 411a 11 b 1 Then state the values of the variables, a and b, for which the radical is defined. a b 17ab ;a ò,b ò C. a b 17ab ;a ò,b 0 B. a b 17ab ;a ò,b 0 a b 17ab ;a 0,b ò 1
11. Simplify this expression: 9 4 B. C. 9 1 4 1 1. Simplify by adding or subtracting like terms: 79w 4 w w 7w 7 6w w w w +w C. 6w w B. 6w w +6w w w Ê ˆ Ë Á,a 0 1. Expand and simplify this expression: a a a a C. a B. a a a +w +w,w ò 14. Expand and simplify this expression: Ê f g ˆ Ë Á,f 0,g 0 9fg 0 fg B. f 0 fg +4g C. f+0 fg +4g f 0 fg 4g 1. Solve this equation: x= 0+x x = and x = B. x = C. x = x = 16. Simplify this expression: +9 7 8 B. 18 4 7 7 6 6 9 14 16 7 7 6 C. 18 4 7 7 6 6 9 14 16 7 7 6 17. Solve this equation: 4 x = x+4 x = 4 B. x = 8 C. x = x = 16 18. Factor this polynomial expression: 147(x ) 48(y+1) (14x+8y+1)(14x 8y 9) C. (14x+8y 1)(14x 8y 9) B. (14x+8y+1)(14x 8y 9) (14x+8y 1)(14x 8y 9) 19. Factor this polynomial expression: (x ) +9(x ) (x+1)(6x ) B. (x )(x+) C. (x+)(x ) (x 1)(6x+) 0. Solve by factoring: 1x 1x+9=0 x = 1 or x = 9 4 B. x = 1 or x = 9 4 C. x = 1 or x = 9 4 x = 1 or x = 9 4 1. Solve this equation: (x 1) 7=4 x=1± 17 B. x=1± 1 C. x= 1± 1 x= 1± 17
. Solve this quadratic equation: 4x +x 9=0 Give the solution to decimal places. x=1.6 or B. x=1.00 or x= 1.6 x=. C. x=. or x= 1.00 x=.00 or x= 4.0. Calculate the value of the discriminant for this equation: 4x +6x+1=0 0 B. 4 C. 6 4. Determine an equation of a quadratic function with the given characteristics of its graph: coordinates of the vertex: V(4, 4); passes through A(, ) y= (x 4) +4 B. y=(x 4) 4 C. y=(x+4) +4 y= (x+4) +4. Write this equation in standard form: y= x +0x+8 y= (x+) +7B. y=( x +) +7C. y= (x+) + 1 y=(x+0) +18 6. Write this equation in standard form: y= x +1x 16 y= (x+) 4 B. y=(x ) 4 C. y= (x ) 4 y= (x+) +4 7. Which graph represents the quadratic function y= x +x? C. B.
8. Use the graph of y=x 4 to determine the roots of x 4=0. x= and x= B. There are no real roots. C. x=± x= 4 9. Determine the x-intercepts, the equation of the axis of symmetry, and the coordinates of the vertex of the graph of y= x x+ x-intercepts: and 1; axis of symmetry: x= 1; vertex: ( 1, 4) B. x-intercepts: and 1; axis of symmetry: x= 1; vertex: ( 1, 4) C. x-intercepts: and 1; axis of symmetry: x=1; vertex: (1,4) x-intercepts: and 1; axis of symmetry: x= 1; vertex: ( 1,4) 0. Does the quadratic function y=(x+10)(4 x) have a maximum value or a minimum value? What is that value? minimum value; 484 C. maximum value; 484 B. minimum value; 40 maximum value; 40 1. Write an inequality to describe this graph. x + y < 9 B. x y > 9 C. x y < 9 x + y > 9. Solve the quadratic inequality: x 4x+ x 1, x ò C. x 1orx, x ò B. x orx 1, x ò 1 x, x ò 4
. Which inequality below is represented by this number line? 4x 17x+1>0 B. 4x 17x+1 0 C. 4x 17x+1 0 4x 17x+1<0 4. Solve this quadratic-quadratic system algebraically. y=x 4x+ y= (x 1) 1 ( 1, 1) and (, 7) C. (7, 1) and (1, ) B. (1, 1) and (7, ) ( 1, 1) and (7, ). Write an inequality to describe this graph. y<(x 1) B. y (x+1) + C. y (x+1) + y>(x 1) 6. This is a graph of y= 1. Determine an equation of the quadratic function y=f(x). f(x) y=(x+) 9 C. y=x 9 B. y=(x+) y=(x+) +9
7. Determine the reference angle for the angle 90 in standard position. 90 B. 0 C. 110 70 8. Point P(, 0) is a terminal point of an angle θ in standard position. Determine the value of sin θ. undefined B. 1 C. 0 9. Determine the exact value of cos 0. 1 B. C. 1 40. Solve the following triangle, rounding side lengths to the nearest tenth of a unit and angle measures to the nearest degree. Diagram not drawn to scale. A=1, b = 19, a =. B=, C=6, c =.0 C. B=68, C=174, c = 8.7 B. B=18, C=84, c =.0 B=, C=7, c = 8. 41. While flying, a helicopter pilot spots a water tower that is 7.4 km to the north. At the same time, he sees a monument that is 8. km to the south. The tower and the monument are separated by a distance of 11.4 km along the flat ground. What is the angle made by the water tower, helicopter, and monument? 91 B. 11 C. 40 48 6
4. For XYZ, determine the measure of Z to the nearest degree and the measure of XZ to the nearest tenth of a centimetre. Z = 8 ; XZ = 7. cm C. Z = ; XZ = 8.0 cm B. Z = 0 ; XZ = 1.1 cm Z = 9 ; XZ = 4.8 cm 4. Simplify this rational expression and state the non-permissible values of the variable. m 16 m +6m+8 m+4 m+ ; m= 4 and m= C. m 4 ; m= 4 and m= m+ m 4 B. m+ ; m=4 and m= m+4 ; m= 4 and m= m+ 44. Solve. h+ h 14 h h 6 = h h h =1orh = 1 B. h = 1 C. h =1 h = 4. Simplify this expression: a bc ab b 8ab 6a b a b bc 7,a 0,b 0 C. bc,a 0,b 0,c=0 7 a B. 8 c a,a 0,b 0,c 0 8 c,a 0,b 0 b b 46. Simplify. pq p q + p+q p q pq p+q,p 0,q 0 C. p q +p +q,p 0,q 0 pq B. 1,p 0,q 0 p q +p +q +pq pq,p 0,q 0 7
47. Simplify. a a 144 a 1 a +10a 4 a a,a 10 10a 10 a+1 B.,a 1 10a+1 ( ) a+1 C.,a 1,a 1,a (a+1)(a 1)(a ) a +a 1,a 1,a 1,a (a+1)(a 1)(a ) 48. Solve. 1 b 1 b = x= ± 1 B. x= ± 1 4 C. x= ± 1 no solution 49. Andres runs 6 km on pavement and then 1 km on gravel. His speed on pavement is twice as fast as his speed on gravel. If he finishes his run in 10 min, what is his speed on the gravel surface? Give the answer to 1 decimal place where necessary. 1.1 km/h B. km/h C. 1 km/h 1.9 km/h 0. Karen and Benjamin are ecologists studying forest regeneration. Working together, they can count the seedlings on a research site in h. It takes Karen 8 h to count the seedlings on her own. How long would it take Benjamin to count the seedlings on his own? Give the answer to 1 decimal place where necessary. 1.6 h B. 10 h C. 6 h.7 h 1. The graph of which absolute value function would have x-intercepts and and y-intercept 4? y= x 4 C. y= x 4 B. y= x 4 y= 4x +. How many solutions does the equation y= x have when y=1? 6 B. 4 C.. Solve this equation: 9 4 x = x = 0 9 and x = 4 9 B. x = 9 0 and x = 4 9 C. x = 0 9 and x = 4 9 no solution 4. Identify the vertical asymptotes of the graph of the reciprocal of the quadratic function y= x +6x. y= and y=1 C. x= and x=1 B. x= no vertical asymptotes 8
. This is the graph of the absolute value of a function f(x). What is an equation for f(x)? f(x)=x 6 B. f(x)=x 6 C. f(x)=(x+) 6 f(x)= 6x + 6. Solve. d d 8d 9 = d 81 a = 1ora = B. a =1ora = 9 C. a =1ora = a = 1ora =9 7. Angle θ is in standard position and its terminal arm lies in Quadrant 4. The sine of its reference angle is 4 6. Determine the exact value of cosθ. 0 6 B. 6 0 C. 4 0 0 4 8. Point P(, 6) is on the terminal arm of an angle θ in standard position. Determine the exact value of sin θ. 40 6,or 10 B. 8 40,or 4 10 C. 6 40,or 10 40,or 1 10 9. Solve. w = 1 w 0 w=10 B. w= C. w=10orw= 10 no solution 9
60. This is the graph of the reciprocal of a linear function. Which graph below represents the linear function? C. B. 10