Free Printable Algebra 2 Review Day #2

1.

Given the sequence 2, 8, 14, 20, 26, ... What is the common difference?

a)

2

b)

4

c)

6

d)

8

2.

How many of these sequences have a common difference of -4?

-19, -15, -11, -7, -3,...

19, 15, 11, 7, 3...

3, 7, 11, 15, 19...

-3, 7, -11, 15, -19,...

a)

0

b)

1

c)

2

d)

3

3.

What number follows 20 in this arithmetic sequence?

8,11, 14, 17, 20

a)

5

b)

23

c)

26

d)

29

4.

Find the missing term in the geometric sequence: 8, 20, 50, 125, _____.

a)

75

b)

200

c)

250

d)

312.5

5.

Describe the pattern in the sequence. Find the next three terms.

13, 15, 17, 19,...

a)

Add 2; 23, 25, 27

b)

Multiply by 2; 38, 76, 152

c)

Add -2; 17, 15, 13

d)

Add 2; 21, 23, 25

6.

Is the sequence geometric? If so, identify the common ratio.

6, 12, 24, 48

a)

yes, 2

b)

yes, -2

c)

yes, 4

d)

no

7.

What is the fifth term of the geometric sequence?

5, 15, 45,...

a)

135

b)

1875

c)

1215

d)

405

8.

Find the next four terms of the arithmetic sequence 16, 24, 32,...

a)

40, 48, 56, 64

b)

36, 40, 44, 48

c)

35, 40, 45, 50

d)

40, 44, 50, 56

9.

What are the next four terms of the arithmetic sequence 122, 111, 100, ...?

a)

89, 78, 67, 56

b)

95, 90, 85, 80

c)

92, 88, 84, 80

d)

99, 88, 77, 66

10.

What is the eleventh term of an arithmetic sequence in which a1 = 3 and d = 6?

a)

63

b)

39

c)

69

d)

36

11.

Find the 8th term of a geometric sequence for which a1=2 and r = 7?

a)

823,543

b)

11,529,602

c)

1,647,086

d)

5,764,801

12.

What is the difference between an arithmetic sequence and a geometric sequence?

a)

One is the sum of the numbers and one is just a list of numbers.

b)

One has a common difference and one has a common ratio.

c)

One you can write an nth term and one you cannot.

d)

None of these are correct.

13.

Evaluate.

a)

290

b)

278

c)

250

d)

295

14.

Evaluate.

a)

539

b)

364

c)

346

d)

361

15.

The sum of this arithmetic series is 595. a₁=28, and a_n=91. How many terms are there (what is n)?

a)

9

b)

10

c)

11

d)

12

16.

What is the sum of the first 10 terms for the following geometric series:
1+1/2+1/4+1/8+1/16+...

a)

0.999

b)

0.002

c)

9.8

d)

1.998

17.

Find the sum of a geometric series where

a₁=4, r = -2 , a_n = 16,384

a)

-10,921.3333333

b)

10,922

c)

10,924

d)

-10,924

18.

Find the sum of the first 25 terms of the series: 6+14+22+30+...

a)

450

b)

2650

c)

2550

d)

550

19.

What is the formula for the nth term of the sequence 3, -6, 12, -24, 48, ...?

a)

$a_n=-2\left(3\right)^n$

b)

$a_n=3\left(-2\right)^n$

c)

$a_n=-2\left(3\right)^{\left(n-1\right)}$

d)

$a_n=3\left(-2\right)^{\left(n-1\right)}$

20.

What is the 16th term of the following sequence?

\left\{10,\ 12,\ 14,\ 16,\ 18,\ ...\right\}

a)

36

b)

38

c)

40

d)

42

21.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

22.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

23.

Factor
x² - 5x - 36

a)

(x - 4)(x + 9)

b)

(x - 6)(x + 6)

c)

(x + 4)(x - 9)

d)

(x -12)(x + 3)

24.

Factor
k² - 2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

25.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

26.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

27.

Factor:
4h² - 17h + 4

a)

(2h - 2)²

b)

4(h + 4)(h + 1)

c)

(2h - 2)(2h + 2)

d)

(h - 4)(4h - 1)

28.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

29.

Solve
4m² - 100 = 0

a)

m=25 or m=-25

b)

m=96

c)

m=5 or m = -5

d)

m=-96

30.

Factor:
x² + 0x - 144

a)

(x + 12)²

b)

(x - 12)(x + 12)

c)

(x - 12)²

d)

12²

31.

Factor:
p² - 14p

a)

p(1 - 14)

b)

2p(p - 7)

c)

p²(1-14)

d)

p(p - 14)

32.

What is the GCF of the trinomial?
3x²- 9x -120

a)

3

b)

2

c)

6

d)

9

33.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

34.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

35.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

36.

Solve for the values of x:

(2x - 1)(x + 4) = 0

a)

x=1/2, x= -4

b)

x=1/2, x= 4

c)

x= 1, x=-4

d)

x=-2.5, x=4

37.

Find the roots of this quadratic function:

2x²-x=0

a)

2 and 7

b)

1/2 and 0

c)

2 and 0

d)

-7/2 and 0

38.

Which is a common factor of 12x and 27?

a)

x

b)

12

c)

3

d)

9

39.

Factor using GCF or monomial factoring:

2n²-8n³

a)

2n²(n-4n²)

b)

2n²(1-4n)

c)

2n³(10-8n²)

d)

3n(1-4n)

40.

What is the GCF of the terms below?

24x³ + 36x²

a)

8x

b)

6x²

c)

12x²

d)

4x

e)

12x³

41.

The equation of a circle is: $\left(x-3\right)^2+\left(y-2\right)^2=16$

a)

The radius is 32 units.

b)

The radius is 16 units.

c)

The radius is 8 units.

d)

The radius is 4 units.

42.

What is the center of the circle: $\left(x+5\right)^2+\left(y-3\right)^2=9$

a)

$\left(5,\ 3\right)$

b)

$\left(5,\ -3\right)$

c)

$\left(-5,\ 3\right)$

d)

$\left(-5,\ -3\right)$

43.

What is the equation of the circle?

a)

$\left(x+1\right)^2+\left(y+1\right)^2=4$

b)

$x^2+y^2=4$

c)

$\left(x+4\right)^2+\left(y+4\right)^2=16$

d)

$x^2+y^2=16$

44.

Select all the equations for a circle with a diameter of 12.

a)

$\left(x+8\right)^2+\left(y-4\right)^2=36$

b)

$\left(x-2\right)^2+\left(y+14\right)^2=144$

c)

$x^2+y^2=36$

d)

$x^2+y^2=144$

e)

$\left(x+6\right)^2+\left(y+6\right)^2=24$

45.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

46.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

47.

What is this?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

48.

Use the quadratic formula to find the solutions for

y = 2x² - 9x + 5

a)

-8.14 and 6.14

b)

-4.07 and 3.07

c)

3.9 and 0.6

d)

ZERO solutions

49.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

50.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

51.

$3x^2-10x+1=0$

Solve using the quadratic formula. Leave your answer in exact form.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

52.

a)

i

b)

-1

c)

1

d)

-i

53.

$x^2+81=0$

a)

$\pm\sqrt{9i}$

b)

$\pm9$

c)

$\pm9i$

d)

$\pm3i$

54.

Your Turn!

i^{22}

a)

$\sqrt{-1}$

b)

$-1$

c)

$-i$

d)

1

55.

$i^{79}$

a)

i

b)

1

c)

-1

d)

-i

56.

$\sqrt{-18}$

a)

$3i\sqrt{2}$

b)

$9i\sqrt{2}$

c)

$-3\sqrt{2}$

d)

$-9i\sqrt{2}$

57.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

58.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

59.

Simplify
2i - 7i + 10

a)

10 - 5i

b)

5i

c)

10 + 9i

d)

10 + 5i

60.

Adult humans have how many teeth?

a)

26

b)

32

c)

36

d)

42

Algebra 2 Review Day #2

Total questions: 60

Worksheet time: 4hrs 33mins

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