Algebra II Honors Midterm Review

Name_____________________________________ Date___________________Period______________ Honors Algebra II Review for Midterm 1. To which sets of numbers does the C [A] d = number belong? 7c 2 − 16 2 cd [B] d = [A] natural numbers C real numbers

[B] irrational numbers real numbers [C] integers rational numbers real numbers

[C] d

=

C − cd cd 2

[D] d

=

cd

2

−C

Solve the equation. 7. 1 = 3b x − 4g + 1 − 2 x

[D] natural numbers integers rational numbers

[A] 14

2. Evaluate the expression for the given values of the variables. e − c e2 − ef e f h − f ; e = 11, f = 3

[B] 4 [C] 12 [D] 6

3. Evaluate the expression for the given value of the variable. 3x 2

− 8;

8. 4b x + 3g + 4 = 5b x + 5g + 5

x= 5

[A] 38 4. Simplify by combining like terms. 6 x + 4b x − 1g − 2b x − 3g [A]

[C] –3

− 12 x + 2

[D] –14

[B] 8 x − 10

9. The sides of a triangle are in the rati ratio o 3:4 :5. What What is the the leng length th of each each side side if

[C] 12 x − 10

the perimeter of the triangle is 54 cm?

[D] 8 x + 2 Solve the equation or formula for the indicated variable. 5. ay + p = a t + uy ,

[B] 9

Solve the inequality. Graph the solution. 10. 5x ≥ –15

fory 11.

6. C = 7c 2 d , for d 12.

3 4

b x − 15g ≥ x − 18 b

g

b x + 3g

18 > 6 − 2 − 3x + 4 + 18

Name_____________________________________ Date___________________Period______________ Honors Algebra II Review for Midterm function

Solve the equation. [C] 13. 4 4 − 3x

=

14. 3 x + 3

−

4x + 6

12

=

– 15

[A] x = 2 or x = 4

–4

–1

–3

4

2

6

8

9

–4

–1

–3

4

2

6

8

9

[B] x = –3 function [C] x = –4 or x = –2 [D] [D] no solution Solve the inequality. Graph the solution. 15. 3x + 2

>5

16. 4 5 − x

≥ 12

not a function 17. Identify the model of the relation

mb– 4, – 1g, b – 3, 6g, b2, 4g, b8, 9gr. Det

ermine whether the relation is a function. [A] –1

–4

4

–3

6

2

9

8

18. If f b x g = − x + 2, find f b– 3g. [A] 1 [B] –7 [C] 5 [D] 3 19. Find the slo pe of the line through the pair of points. b– 5, 2g, b – 3, 5g

not a function [B] –1

–4

4

–3

6

2

9

8

[A]

[B]

[C]

3 2 10 3 −

7 8

Name_____________________________________ Date___________________Period______________ Honors Algebra II Review for Midterm

[D]

2

[C]

3

Find the slope of the line.

[D]

3 4 −

3 4

y

20.

22. Write in standard form the equation of the line. Then graph the line. slope = 3; b – 5 6, g

10

10 x

–10

Find the point-slope form of the equation o f the line passing through the pair of points. 23. b – 6, – 2g

andb5 3 ,g

–10

[A] [B]

Find the point-slope form of the equation o f the line passing through the pair of points.

−2

−

24. b5, – 1g andb – 7, g3

1 2

[A] y − 1 = −3b x + 5g

[C] 2 [D]

[B] y + 1 = −3b x − 5g

1 2

[C] y + 1 = −

10

–10

1 3

b x − 5g

3

26. Find an equation for the line. through b2, 4g, x - intercept – 2

[B] y = − x + 1 4 3

b x + 5g

x. 25. y varies direc tly with If x is 64 when y is 160, find y when x is 68.

[A] y = x + 1

4

−

[D] y − 1 = −

10 x

–10

[B]

3

y

21.

[A]

1

[C] y = − x + 2


[D] y = x + 2 27. A candle is 4 inches tall and burns at a rate of 2 inches per hour. Identify the graph and equation that models the height after x hours.

). n i( t h g i e H

10

0

y

Number 10 x of hours

[A] y = – 2 x + 4 28. Graph the equation by writing two linear equations. y = − 2x + 3

y ). n i( t h g i e H

10

0

Number 10 x of hours

[B] y = 4 x − 2 s r 10 u o H f o r e b m u N 0

y

Height (in.)

10 x

29. Graph the absolute value equation. f b xg = −x −1 30. Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function. 2 2 1 y= x , y= x + 3 3 3 31. Write an equation for the horizontal translation. y 10

[C] y = 2 x + 4 s r 10 u o H f o r e b m u N 0

y

10 x

–10

–10 Height (in.)

[D] y = 4 x + 2

10 x

32. Write the equation of the translation of y= x.

Name_____________________________________ Date___________________Period______________

y

Honors Algebra II Review for Midterm 38. Locate the point

10

b4 ,

4, – 4g in a

three-dimensional coordinate system. [A]

z

10 x

–10

y

–10 x

[A] y = Gx + 4 G+ 4 [B] y = Gx + 4 G– 4 [B]

z

[C] y = Gx − 4 G+ 4 [D] y = Gx − 4 G– 4

y

Graph the inequality on a coordinate plane. 33. y

≤

x

4x − 8

34. y > 3 x − 6 [C]

z

35. Solve the system by the method of substitution. Rx + 2 y = 7

S 3x + y = 11 T

y

Solve the system of inequalities by graphing.

36.

37.

Ry | S |y |T

≥

3 5

≤

−

x

x +1

2 5

R| y > − 2 x 5 S |T y < x − 7

x −4

[D] none of these 39. Solve the system by elimination. R6x − 3 y − 2 z = – 29

| S |T

3x − 3 y + z = – 8 5x + 5 y − z = – 46


40. Solve the equation. L3 − 5O L17 11O X 4 + = M0 7P M 6 − 5P N Q N Q

[B]

y 10

41. For the parabola, identify points corresponding to P and Q. y 10

−10

10

x

10

x

10

x

−10

vertex: b − 2 , 5− g

Q

x = −2

P 10 x

–10

[C]

y 10

–10

−10

42. Graph the function. y = −4 x 2 + 5

−10

vertex: b − 2 , 3−g

43. Graph the quadratic function. Label the vertex and axis of symmetry. y = −x2 − 4x − 1

x=2

[D]

y 10

[A]

y 10 −10

−10

10

x −10

vertex: b− 2 3 ,g −10

vertex: b − 2 , 3−g x=2

x = −2

44. Graph the function. y

=

2b x − 5g

2

−

4

45. Write the equation of the parabola in vertex form.

Name_____________________________________ Date___________________Period______________ Honors Algebra II Review for Midterm y 5

50. 3x 2 − 5x − 12 51. Solve by factoring. 2 x − 10 x = –24

–5

5 x

–5

[A] y = − b x + 2g

2

[B] y = − b x − 2g

2

[C] y = − b x − 2g

2

[D] y = − b x + 2g

+2

−2

2

2

−2

+5

47. Write the equation in vertex form. 2 y = x 2 + 8 x + 22 3 48. Write the equation of the parabola in vertex form. vertex b9, – 5g, point b11, – 17g [A] y = −2b x + 11g [B] y = b x + 9g

2

2

+ 17

+5

[C] y = −3b x − 11g [D] y = −3b x − 9g

2

2

− 17

−5

Factor the expression. 49. x 2

− 6x − 7

[A]

− 33 − 19i

[B]

− 9 − 37i

[C]

− 33 − 37i

[D]

− 9 − 19i

+2

46. Identify the vertex an d y-intercept of the graph of the function. y = 0.28b x − 5g

52. Simplify the expression. b7 + 3igb− 3 − 4i g

53. Solve the equation using the Quadratic Formula. 2 − 5x + 7 + 9 x = 0


Reference: [1.1.1.4] [1] [C] Reference: [1.4.1.63] [12] no solution

Reference: [1.2.1.30] [2] –80

Reference: [1.2.1.34] [3] 7

Reference: [1.5.1.74] 5 11 [13] x = or x = 8 4

Reference: [1.2.2.39] [4] [D]

Reference: [1.5.1.72] [14] [D]

Reference: [1.3.1.47] at − p [5] y = a−u

Reference: [1.5.2.78] 7 [15] x < − or x > 1 3

–10

Reference: [1.3.1.48] [6] [A] Reference: [1.3.1.45] [7] [C]

–10

Reference: [1.3.2.57] [9] 13.5 cm, 18 cm, 22.5 cm

15

0

20

0

Reference: [2.1.2.22] [18] [C] 5

10

Reference: [2.2.1.30] [19] [A] Reference: [2.2.1.29] [20] [D]

Reference: [1.4.1.62] [11] x ≤ 27 10

–5

Reference: [2.1.2.17] [17] [C]

Reference: [1.4.1.61] [10] x ≥ –3 –5

0

5

10

Reference: [1.5.2.79] [16] x ≤ 2 or x ≥ 8

Reference: [1.3.1.46] [8] [D]

–10

–5

25

30

Reference: [2.2.1.29] [21] [D]

5

10

Name_____________________________________ Date___________________Period______________ Honors Algebra II Review for Midterm y 10

Reference: [2.2.2.34] [22] 3x − y = –21 y 10

10 x

–10

10 x

–10

–10

–10

Reference: [2.5.1.85] y [29] 10

Reference: [2.2.2.35] 5 5 [23] y + 2 = b x + 6g or y − 3 = b x − 5g 11 11 10 x

–10

Reference: [2.2.2.36] [24] [C] –10

Reference: [2.3.1.51] [25] 170

Reference: [2.4.1.59] [26] [D] Reference: [2.4.1.61] [27] [A] Reference: [2.5.1.79] [28]

R 3 x≥ ||− 2 x + 3, if 2 y=S 3 | 2 x − 3, if x< |T 2

Reference: [2.6.1.90] [30] The second function is the graph 1 2 of y= x moved up unit. 3 3

Reference: [2.6.2.98] [31] y = − x + 2 or y = x − 2

Reference: [2.6.2.103] [32] [B] Reference: [2.7.1.110]

Name_____________________________________ Date___________________Period______________

y

[33]

Honors Algebra II Review for Midterm Reference: [3.3.1.38] y

[37]

10

10

10 x

–10

10 x

–10

–10 –10

Reference: [2.7.2.120] y [34]

Reference: [3.5.1.52] [38] [B]

10

Reference: [3.6.1.65] [39] b – 6, – 3, 1g 10 x

–10

Reference: [4.3.1.32] . 4O L35 [40] X =M P N15. − 3Q

–10

Reference: [3.2.1.11] [35] b3, 2g

Reference: [5.1.1.6] [41] P ′b0.5, 35 . g, Q ′b3, 6g

Reference: [3.3.1.31]

Reference: [5.2.1.14] y [42]

[36]

y 10

–10

0

–10

10

10 x

10 x

–10

–10


Reference: [5.2.1.17] [43] [D]

Reference: [5.6.2.68] [52] [B]

Reference: [5.3.1.25] y [44]

Reference: [5.8.1.89]

10

[53]

10 x

–10

–10

Reference: [5.3.1.26] [45] [D] Reference: [5.3.1.29] [46] b5, 5g, y-intercept 12

Reference: [5.3.1.31] 2 2 [47] y = b x + 6g − 2 3

Reference: [5.3.1.33] [48] [D] Reference: [5.4.1.36] [49] b x + 1gb x − 7g

Reference: [5.4.1.39] [50] b3x + 4gb x − 3g

Reference: [5.5.1.46] [51] x = 4 or x = 6

5 ± i 227 18

Algebra II Honors Midterm Review

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