Free Printable Hon IM1 Semester 2 Review

1.

Solve the following system:

2x-y=-1

y=x-1

a)

$\left(-2,-3\right)$

b)

$\left(4,\ 5\right)$

c)

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

d)

$\left(3,\ 4\right)$

2.

Solve the following system:

y=-3x+5

5x-4y=-3

a)

$\left(1,\ 2\right)$

b)

$\left(1,\ 5\right)$

c)

$\left(2,\ 5\right)$

d)

$\left(5,\ 1\right)$

3.

Solve:
y=8x+1
y=6x+3

a)

(1, 9)

b)

(4, 14)

c)

(0, 1)

d)

(2, 4)

4.

Which of the following is a solution to the systems of inequalities?

a)

(0, 0)

b)

(1, 1)

c)

(-4, -2)

d)

(4, -2)

5.

Which of the following is a solution to the systems of inequalities?

a)

(0, -2)

b)

(-3, 0)

c)

(-3, 2)

d)

(1, 1)

6.

This system has _____ solutions

a)

no

b)

1

c)

2

d)

Infinitely many

7.

Sam and Ellie graph two equations and the lines end up on TOP of each other, see pic. What type of solution does this system of 2 equations have?

a)

no solution

b)

1 solution

c)

infinite solutions

d)

just two solutions

8.

Which ordered pair is the solution of the system graphed below?

a)

(0, 2)

b)

(4, 0)

c)

(2, 4)

d)

(4, 2)

9.

Solve using the Addition Method (Elimination).

7x + 4y = -6

-7x - 6y = 30

Answers in (x,y)

a)

(6, -12)

b)

(12, 6)

c)

(12, 8)

d)

(6, 8)

10.

Solve using the Addition Method (Elimination).

8x + 2y = 30

7x + 2y = 24

Answers in (x,y)

a)

(6,-9)

b)

(-9,6)

c)

(3, 3)

d)

(-3, -3)

11.

Which set of equations matches the graph? (solution is the shaded region on the left)

a)

y ≤ 3x and y ≤ -2x + 4

b)

y > 3x and y > -2x + 4

c)

y < 3x and y > -2x + 3

d)

y > 3x and y < -2x + 4

12.

Solve the system of equations.

$y=-6x+5$
$-2x+y=5$

a)

(-3, -6)

b)

(-6, 3)

c)

(0, 5)

d)

(-3, 5)

13.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

a)

4x + 6y = 3
13.5x - 13y = 6

b)

x + y = 4
x - y = 6

c)

4x + 6y = 13
3x + 7y = 13.5

d)

4x - 6y = 13
3x - 7y = 13.5

14.

Evan needs to make 24 quarts of a 9% sugar solution. Solution A is 12% sugar, and Solution B is 6% sugar. How many quarts of each should Evan mix together?

a)

12 quarts Solution A, 12 quarts Solution B

b)

14 quarts Solution A, 10 quarts Solution B

c)

9 quarts Solution A, 15 quarts Solution B

d)

8 quarts Solution A, 16 quarts Solution B

15.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

16.

Lucy buys 8 bags of popcorn and 2 candies and the total cost is $58. Sarah buys 4 bags of popcorn and 5 candies from the same place and the total cost is $49. Find the cost of a bag of popcorn and the cost of a piece of candy.

a)

Candy = $6

Popcorn = $6

b)

Candy = $5

Popcorn = $6

c)

Candy = $6

Popcorn = $5

17.

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown? (a)

Choose from the below words

$y=1,200,000\left(1.04\right)^x$

$y=\ 1,200,000\left(0.04\right)^x$

$y=1,200,000\left(1.4\right)^x$

$y=1,200,000\left(0.06\right)^x$

18.

Which of the following exponential functions represents an initial value of 1450 and a decay of 18% for x years?

a)

$y=1450\left(0.18\right)^x$

b)

$y=1450\left(1.18\right)^x$

c)

$y\ =\ 1450\ -\left(0.18\right)^x$

d)

$y=1450\left(0.82\right)^x$

19.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

20.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

21.

Describe the translation.

$y\ =\ 6^x-\ 3$

a)

Up 3

b)

Down 3

22.

Describe the translation.

$y\ =\ 3^x+\ 7$

(a)

23.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=2^x$

$g\left(x\right)=2^{\left(x-4\right)}$

a)

Up 4 units

b)

Down 4 units

c)

Left 4 units

d)

Right 4 units

24.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=0.4^x-1$
$g\left(x\right)=0.4^x-2$

a)

Down 1 unit

b)

Down 2 units

c)

Up 1 unit

d)

Up 2 units

25.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=2^x$

$g\left(x\right)=-2^x$

a)

Down 3 units

b)

Stretch vertically

c)

Reflect over y-axis (horizontal reflection)

d)

Reflection over x-axis (vertical reflection)

26.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=0.25^x$
$g\left(x\right)=\left(2\right)0.25^x$

a)

Horizontal stretch by a factor of 2

b)

Horizontal compression by a factor of 2

c)

Vertical stretch by a factor of 2

d)

Vertical compression by a factor of 2

27.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=\left(\frac{2}{3}\right)^x$
$g\left(x\right)=\left(\frac{2}{3}\right)^{-x}$

a)

Right 1 unit

b)

Left 1 unit

c)

Reflect across the x-axis (vertical reflection)

d)

Reflect across the y-axis (horizontal reflection)

28.

Describe the transformation from f(x) to g(x).

$f\left(x\right)=3^x$
$g\left(x\right)=\frac{1}{2}\cdot3^x$

a)

Vertical shrink/compression

b)

Vertical stretch

c)

Reflection over y-axis

d)

Up 1/2

29.

Describe the transformations from f(x) to g(x).
Select all that apply.

$f\left(x\right)=6^x$
$g\left(x\right)=\frac{3}{7}\cdot6^x-2$

a)

Vertical shift down 2 units

b)

Vertical compression/ shrink

c)

Vertical stretch

d)

Reflection over x-axis

e)

Horizontal compression

30.

Describe the transformations from f(x) to g(x). Select all that apply.

$f\left(x\right)=10^x$ $g\left(x\right)=-3\cdot10^{\left(x+4\right)}$

a)

Reflection over x-axis

b)

Horizontal translation right 4 units

c)

Vertical stretch

d)

Horizontal translation left 4 units

e)

Vertical compression/ shrink

31.

Given the function $f\left(x\right)=7^x$ , find the value for $f\left(0\right)$ .

(a)

32.

If $f\left(x\right)=4^x$ , evaluate the function for $f\left(-2\right)$ .

a)

$-8$

b)

$-\frac{1}{8}$

c)

$\frac{1}{16}$

d)

0

33.

Which function represents the graph?

a)

$f\left(x\right)=2\cdot\left(4\right)^x$

b)

$f\left(x\right)=2\cdot\left(\frac{1}{4}\right)^x$

c)

$f\left(x\right)=4\cdot\left(2\right)^x$

d)

$f\left(x\right)=8\cdot\left(\frac{1}{4}\right)^x$

34.

Which function represents the table?

a)

$f\left(x\right)=120\cdot\left(\frac{1}{3}\right)^x$

b)

$f\left(x\right)=120\cdot\left(3\right)^x$

c)

$f\left(x\right)=-\frac{1}{3}x+120$

d)

$f\left(x\right)=-80x+120$

35.

Is the sequence arithmetic: -3, 3, -3, 3, ...

a)

Yes

b)

No

36.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

37.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

38.

Find the common difference: -18, -23, -28, -33, ...

a)

d = -5

b)

d = 5

c)

d = -3

d)

d = 3

39.

Find the common difference: 1, 201, 401, 601, ...

a)

d = 100

b)

d = 101

c)

d = 200

d)

d = 201

40.

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

a)

-1, 7, 15

b)

-5, 2, 9

c)

3, 12, 21

d)

-65, -73, -81

41.

Find the 35th term in the arithmetic sequence: -10, -14, -18, -22, ...

a)

-216

b)

-148

c)

-146

d)

-150

42.

Find 26th term in the arithmetic sequence: -15, -35, -55, -75, ...

a)

-515

b)

-490

c)

-535

d)

460

43.

What is a formula for the nth term in the sequence -4, -9, -14, ...?

a)

$a_n=-4-5\left(n-1\right)$

b)

$a_n=a_{n-1}+5$

c)

$a_n=-5-4\left(n-1\right)$

d)

$a_n=-4+5\left(n-1\right)$

44.

What is a formula for the nth term in the sequence 12, 20, 28, ...?

a)

$a_n=20+8\left(n-1\right)$

b)

$a_n=-4+8\left(n+1\right)$

c)

$a_n=12+8\left(n-1\right)$

d)

$a_n=12\left(8\right)^n$

45.

Given the sequence:
25, 21, 17, 13,...
Write the explicit equation that models the sequence.

a)

a_n = 4n + 29

b)

a_n = -4n + 25

c)

a_n= -4n + 29

d)

a_n = 4n + 25

46.

Write the explicit rule for the arithmetic sequence
12, 10, 8, 6, ...

a)

a_n = 12n - 14

b)

a_n= 2n - 14

c)

a_n= -2n + 14

d)

a_n= -12n + 14

47.

What is the common ratio of the geometric sequence -1, 6, -36, 216, ...?

a)

-6

b)

6

c)

12

d)

-4

48.

Find the common ratio: 64, -16, 4, -1, ...

a)

r = -8

b)

r = -1/4

c)

r = -4

d)

r = 4

49.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

50.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

51.

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

a)

384

b)

512

c)

768

d)

1,024

52.

What is the 11th term of the geometric sequence?

a)

-5120

b)

97,656,250

c)

19,531,250

d)

-19,531,250

53.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

54.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

55.

Find the product:
(2x+3)²

a)

2x+3+2x+3

b)

4x²+12x+9

c)

4x²+9

d)

16x²+9

56.

What is the perimeter of the rectangle?

a)

$25x^{2\ }-\ 20x$

b)

$10x-4$

c)

$20x\ -\ 8$

d)

44

57.

What is the area of the rectangle?

a)

$25x^{2\ }-\ 20x$

b)

$20x\ -\ 8$

c)

$10x\ -\ 4$

d)

44

58.

What is the leading coefficient of this polynomial?

a)

8

b)

-4

c)

-1

d)

1

59.

What is the value of the constant?
2x² + 4x − 5

a)

2

b)

4

c)

5

d)

−5

60.

Simplify the following and write in standard form:

$3\left(x+4\right)\left(x-1\right)\ -3\left(x-5\right)\left(x+2\right)$

61.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

62.

Find the product:
(x + 7)²

a)

x²+ 7x + 7x + 49

b)

x²+ 7x + 7

c)

7x²+ x + 7

d)

x² + 14x + 49

63.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

64.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

65.

If $7r^3-8r^2+42r-48$ is factored completely, one of the factors is:

a)

$\left(r^2-6\right)$

b)

$\left(r^2+6\right)$

c)

$\left(7r+8\right)$

d)

$\left(7r^2+6\right)$

66.

If $x^2+4x+3$ is factored completely. one of the factors is:

a)

$\left(x-3\right)$

b)

$\left(x+1\right)$

c)

$\left(x+4\right)$

d)

$\left(x-1\right)$

67.

Which of the following is a factor of $x^2-10x+24$ ?

a)

$\left(x-4\right)$

b)

$\left(x+4\right)$

c)

$\left(x+6\right)$

d)

$\left(x-2\right)$

68.

Which of the following is a factor of $x^2+7x-30$ ?

a)

$\left(x+2\right)$

b)

$\left(x+5\right)$

c)

$\left(x-10\right)$

d)

$\left(x-3\right)$

69.

If $2x^2-3x-2$ is factored completely, one of the factors is:

a)

$\left(2x-2\right)$

b)

$\left(2x+1\right)$

c)

$\left(x+2\right)$

d)

$\left(x-1\right)$

70.

Factor completely: $5x^2+13x-28$
Do not type any spaces in your answer!

(a)

71.

Factor: $16x^2-49$

a)

$\left(4x-7\right)^2$

b)

$\left(4x-7\right)\left(4x+7\right)$

c)

$\left(7-4x\right)^2$

d)

$\left(7x-4\right)\left(7x+4\right)$

72.

A rectangular area of a beach is given as $\left(7x^2+60x+32\right)ft^2$

Which expression represents the longer of the two sides of the rectangular area?

a)

$\left(7x+4\right)ft$

b)

$\left(x+16\right)ft$

c)

$\left(x+8\right)ft$

d)

$\left(7x+2\right)ft$

73.

The volume of a rectangular prism is given as $\left(6x^3+96x^2+360x\right)$ cubic inches. What is one possible expression for the height of the prism?

a)

$\left(x+10\right)inches$

b)

$\left(x-6\right)inches$

c)

$x\ inches$

d)

$\left(x+20\right)inches$

74.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

75.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

76.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

77.

find: BxA

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

78.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

79.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

80.

Evaluate the determinant of the matrix.

a)

$-30$

b)

$-10$

c)

$10$

d)

$-55$

81.

Evaluate the determinant of the matrix.

a)

$-5$

b)

$45$

c)

$-10$

d)

$10$

82.

Evaluate the determinant of the matrix.

a)

$9$

b)

$-1$

c)

$1$

d)

$19$

83.

Multiply.

a)

b)

c)

d)

No Product Exists

84.

What are the matrix dimensions?

a)

3 x 3

b)

2 x 3

c)

3 x 2

d)

2 x 2

85.

Perform the matrix multiplication, if possible.

a)

b)

c)

d)

Cannot be multiplied, dimensions not compatible.

86.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

87.

Find f(-2)

a)

-3

b)

6

c)

8

d)

-6

88.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

89.

Find f(2)

a)

f(2) = 0

b)

f(2) = 1

c)

f(2) = 3

d)

f(2) = 4

90.

Find f(2)

a)

3

b)

-2

c)

2

d)

infinite outputs

91.

What is the domain restriction of the blue piece of this function?

a)

x > 0

b)

x ≥ 0

c)

x > 2

d)

x ≥ 2

92.

What is the vertex?

a)

(3, 1)

b)

(0, 1)

c)

(1, 3)

d)

No vertex

93.

Describe the transformation of the equation below:

y = I x + 2 I - 5

a)

Left 2 up 5

b)

Right 2 up 5

c)

Left 2 down 5

d)

Right 2 down 5

94.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

95.

What are the transformations for the function below:

$f\left(x\right)=-3|x+1|-3$

a)

Reflection, vertical stretch factor of 3, left 1, and down 3

b)

Reflection, vertical compression factor of 3, right 1, and down 3

c)

Down 6 and right 1

d)

vertical compression, right 1, and down 3

96.

Describe the transformations of the equation above:

a)

Vertical stretch, shifts up 4 units

b)

Vertical stretch, shifts down 4 units

c)

Vertical compression, shifts up 4 units

d)

Vertical compression, shifts down 4 units

97.

What is the equation of the graph below? You can click the picture to zoom in!

a)

y = - | x + 2| + 4

b)

y = - | x - 2| + 4

c)

y = | x - 2 | + 4

d)

y = | x - 2| - 4

98.

f(x) = −|x+4|

a)

A

b)

B

c)

C

d)

D

99.

What is the vertex of the function?

$f\left(x\right)=-2\left|x+3\right|-2$

a)

$\left(-3,-2\right)$

b)

$\left(3,-2\right)$

c)

$\left(3,2\right)$

d)

$\left(-3,2\right)$

100.

What is the range of the graph?

a)

All real numbers

b)

$y\ge0$

c)

$y\le0$

d)

$x\ge0$

Hon IM1 Semester 2 Review

Total questions: 100

Worksheet time: 5hrs 55mins

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