Free Printable Semester 1 HAT Review

1.

Level 1: For the equation

y - 3 = 2(x + 4),

the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

2.

Level 3: Write an equation in point slope form that passes through the following points.

(1, 4) and (-1, 1)

a)

y-4=3/2(x-1)

b)

y+4=3/2(x-1)

c)

y=3/2x+4

d)

x-4=3/2(y-1)

3.

Level 4: Which is NOT a correct point-slope equation for the line?

a)

y - 0 = 1/2(x + 2)

b)

y - 1 = 1/2(x - 0)

c)

y + 2 = 1/2(x + 2)

d)

y - 2 = 1/2(x - 2)

4.

What is the y-intercept of the line 2x+4y=12

a)

(0,6)

b)

(3,0)

c)

(6,0)

d)

(0,3)

5.

Convert the following equation to standard form.

y=\frac{1}{4}x+4

a)

$x+4y=8$

b)

$x-4y=-16$

c)

$y=x+16$

d)

$4y+x=8$

6.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

a)

x + y ≤ 8

b)

x + y > 8

c)

2x + 3y ≤ 6

d)

x + y ≤ 10

7.

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

a)

2x + 3y ≤ 18

b)

x + y ≤ 6

c)

x + y ≤ 9

d)

3x + 2y ≤ 18

8.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.

a)

x+y≤300
7.5x+5.5y≥2000

b)

x+y<300
7.5x+5.5y≥2000

c)

x+y≤300
7.5x+5.5y≤2000

d)

x+y>2000
7.5x+5.5y≤300

9.

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

a)

x≥0

y≥0

x+y≥6

3x+2y≥15

b)

x≥0

y≥0

x+y≤6

2x+3y≤15

c)

x≥0

y≥0

4000x+y≤6

2x+600y≤15

d)

P=4000x+3000y

10.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

11.

Find f(0)

a)

-3

b)

18

c)

4

d)

0

12.

On the graph, which portion of the piecewise function is represented in red?

a)

x

b)

0.5x + 2.5

c)

-1

d)

0.5x + 2

13.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

14.

Match the graph with the correct equation.

a)

b)

c)

d)

15.

Describe the transformation

$f\left(x\right)+3$

a)

3 Units Up

b)

3 Units Down

c)

3 Units Left

d)

3 Units Right

16.

Describe the transformation

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

a)

2 Units Up

b)

2 Units Down

c)

2 Units Left

d)

2 Units Right

17.

Describe the transformation

$f\left(x+5\right)$

a)

5 Units Up

b)

5 Units Down

c)

5 Units Left

d)

5 Units Right

18.

Describe the transformation

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

a)

6 Units Up

b)

6 Units Down

c)

6 Units Left

d)

6 Units Right

19.

Describe the transformations

$g\left(x+4\right)-6$

a)

4 Units Left

6 Units Up

b)

4 Units Left

6 Units Down

c)

4 Units Right

6 Units Up

d)

4 Units Right

6 Units Down

20.

Describe the transformations

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

a)

Reflected across the x-axis

2 Units Up

b)

Reflected across the x-axis

2 Units Down

c)

Reflected across the y-axis

2 Units Up

d)

Reflected across the y-axis

2 Units Down

21.

Describe the transformation

$3h\left(x\right)$

a)

Vertically Stretched by a factor of 3

b)

Vertically Compressed by a factor of 3

c)

Horizontally Stretched by a factor of 3

d)

Horizontally Stretched by a factor of 3

22.

Describe the transformations

$g\left(-x\right)-4$

a)

Reflected across the x-axis

4 Units Left

b)

Reflected across the x-axis

4 Units Down

c)

Reflected across the y-axis

4 Units Left

d)

Reflected across the y-axis

4 Units Down

23.

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

a)

(-2, 5)

b)

(-6, 5)

c)

(-4, 3)

d)

(-4, 7)

24.

If the blue function is f(x)=x², then the red function must be

a)

g(x)=x²-5

b)

g(x)=x²+5

c)

g(x)=(x-5)²

d)

g(x)=(x+5)²

25.

a)

g(x)=x³+1

b)

g(x)=x³-1

c)

g(x)=(x-1)³

d)

g(x)=(x+1)³

26.

What are the transformations of this functions compared to the parent function y = √(x)?

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

27.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

28.

Solve:
|x + 3| > - 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

29.

Solve.
|2x - 1| = 7

a)

x = -3 or x = 4

b)

x = 4

c)

x = 4 or x = -4

d)

no solution

30.

Solve.
|2x - 1| = -7

a)

x = -3 or x = 4

b)

all real numbers

c)

x = 3 or x = -3

d)

no solution

31.

Solve.
-5|x - 4| > 20

a)

x < 8 and x > 0

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

32.

| x - 2 | > 3
Is this an "and" or an "or" problem?

a)

and

b)

or

33.

$2x+y-2z=12$
$3x-y-4z=26$
$x+3y+z=0$

Solve the system

a)

(-4, 10, 2)

b)

(10, -4, 2)

c)

(10, 4, -2)

d)

(4, -10, -2)

34.

$4x-6y-z=11$
$3x-6y=15$
$9x=27$

Solve the system

a)

(3,-5,1)

b)

(3,1,-5)

c)

(3,-1,7)

d)

(3,7,-1)

35.

Convert to vertex form:

y = x² + 4x + 10

a)

y = (x + 4)² + 6

b)

y = (x + 2)² + 6

c)

y = (x + 4)² - 6

d)

y = (x + 2)² - 6

36.

Solve by completing the square:
v² + 6v − 59 = 0

a)

{-5 + 5√2, -5 - 5√2}

b)

{5 + 5√2, 5 - 5√2}

c)

{-3 + 2√17, -3 - 2√17}

d)

{3 + 2√17, 3 - 2√17}

37.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

38.

Simplify √800.

a)

10√8

b)

5√32

c)

12√2

d)

20√2

39.

Simplify √56

a)

4√14

b)

2√14

c)

2√27

d)

4√7

40.

Solve the following equation by completing the square:
n² = 18n + 40

a)

{11, -11}

b)

{16, 2}

c)

{20, -2}

d)

{10, -4}

41.

Given $0=6x^2-12x+14\$ , solve by completing the square.

a)

$\frac{\pm2i\sqrt[]{3}}{3}$

b)

$\frac{-2}{3}$

c)

$\pm\frac{i\sqrt[]{3}}{3}$

d)

$\pm\frac{\sqrt[]{3}}{3}$

42.

Identify the vertex and whether the graph opens up or down.

a)

(5, 2); opens up

b)

(5, 2); opens down

c)

(-5, 2); opens up

d)

(-5, 2); opens down

43.

Find the vertex of

f(x) = -x²- 4x + 12

(hint: this is standar form. You need opposite b over 2a!)

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

44.

What is the axis of symmetry for the following equation?
y=4x²-8x+9

a)

x=-8

b)

x=1

c)

x=-2

d)

x=4

45.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (-1,4); point (1,0)

f\left(x\right)=a\left(x-h\right)^2+k

a)

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

b)

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

c)

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

d)

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

46.

Write the vertex form of the equation that has the indicated vertex and passes through the given point.
Vertex (1,-2); point (-1,14)

f\left(x\right)=a\left(x-h\right)^2+k

a)

$f\left(x\right)=-2\left(x-14\right)^2-1$

b)

$f\left(x\right)=\left(x+14\right)^2$

c)

$f\left(x\right)=4\left(x-1\right)^2-2$

d)

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

47.

Factor the expression: 21z² - 70z + 49

a)

7(3z - 7)(z - 1)

b)

7(3z + 7)(z + 1)

c)

7(3z - 7)(z + 1)

d)

7(3z + 7)(z - 1)

48.

Factor the expression: -2h² + 4h + 70

a)

-2(h + 7)(h + 5)

b)

-2(h - 7)(h - 5)

c)

-2(h + 7)(h - 5)

d)

-2(h - 7)(h + 5)

49.

Factor the expression: 10v² + 11v - 8

a)

(5v + 8)(2v + 1)

b)

(v + 8)(v - 1)

c)

(5v + 8)(2v - 1)

d)

(10v - 8)(v + 1)

50.

Factor: 3x² - 5x - 2

a)

(3x + 1)(x - 2)

b)

(3x + 2)(x - 1)

c)

(3x - 1)(x + 2)

d)

(3x - 2)(x + 1)

51.

Factor: 6x² - 7x - 10

a)

(3x + 2)( 2x - 5)

b)

(3x - 2)( 2x + 5)

c)

(6x - 5)(x + 2)

d)

(6x + 5)(x - 2)

52.

Factor: 8x² + 31x - 4

a)

(8x - 1)(x + 4)

b)

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

c)

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

d)

(8x - 2)(x + 2)

53.

Factor: 4x² - 17x + 15

a)

(2x - 5)(2x - 3)

b)

(4x - 3)(x - 5)

c)

(4x - 5)(x - 3)

d)

(2x + 5)(2x - 3)

54.

Factor:
4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

(x+1)(4x-9)

55.

Solve: $x^4+9x^2-52=0$ Hint: Try u-substitution!

a)

None of these are correct

b)

$-\sqrt{13}\ ,\ -\sqrt{11},\ 1\ ,\ 32$

c)

$-\sqrt{7}\ ,\ 2\sqrt{2},\ 1\ ,\ 4$

d)

$-i\sqrt{11}\ ,\ i\sqrt{11},\ 4\ ,\ 8$

e)

$-i\sqrt{13},\ -2,\ \ 2,\ \ i\sqrt{13}$

56.

Solve: $x^4-14x^2+33=0$

Hint: Try u-substitution!

a)

$\pm\sqrt{11}\ ,\ \pm\sqrt{3}\ \$

b)

$\pm\sqrt{7}\ ,\ \pm\sqrt{3}\ \$

c)

$-\sqrt{3}\ ,\ \sqrt{1},\ \ 3\ ,\ 11$

d)

$\pm\sqrt{13}\ ,\ \pm\sqrt{5}\ \$

57.

Factor over the set of real numbers: $f\left(x\right)=27x^3-125$

a)

$\left(27x-5\right)\left(x^2+5x+25\right)$

b)

$\left(3x-5\right)\left(x^2+15x+25\right)$

c)

$\left(3x-5\right)\left(9x^2+15x+25\right)$

d)

$\left(3x-5\right)\left(x+\frac{5+5\sqrt[]{3}}{6}i\right)\left(x+\frac{5-5\sqrt[]{3}}{6}i\right)$

58.

Complete the formula
a³-b³=

a)

(a-b)(a²+ab+b²)

b)

(a+b)(a²-ab+b²)

c)

(a-b)(a²-ab+b²)

d)

(a+b)(a²+ab+b²)

59.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

60.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

61.

Factorize 343x³ - 125y³.

a)

(7x - 5y)(49x² + 35xy + 25y²)

b)

(7x - 5y)(49x² + 70xy + 25y²)

c)

(7x + 5y)(49x² - 35xy + 25y²)

d)

(7x - 5y)³

62.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

63.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

64.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

a)

1.25 seconds

b)

1.4 seconds

c)

2.5 seconds

d)

2 seconds

65.

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.

a)

-9, 7

b)

√75

c)

9, -7

d)

15, -5

66.

Determine the vertex for y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

67.

Find two consecutive odd integers such that the square of the smaller is 10 less than 5 times the larger.

a)

just 0 and 2

b)

0 and 2 AND 5 and 7

c)

just 5 and 7

d)

0 and 1 AND 5 and 6

68.

After t seconds, a ball tossed in the air from the ground level reaches a height of h given by the function $h\left(t\right)=-16t^2+144t.$ What was the highest point the ball reached? (only write the number)

(a)

69.

(5 + 2i) + (3 - 6i)

a)

8 + 4i

b)

8 - 4i

c)

15 - 12i

d)

8 + 8i

70.

Simplify i¹⁸ (hint: every group of 4 "i's" = 1)

a)

i = √-1

b)

i² = -1

c)

i³ = - i ...or - √-1

d)

i⁴ = 1

71.

a)

10

b)

-10

c)

10i

d)

-10i

72.

i¹³

a)

-1

b)

1

c)

i

d)

-i

73.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

74.

Simplify: (3 + 2i ) - (5 - 7i )

a)

5i + 2i

b)

-2 + 9i

c)

-2 - 5i

d)

8 + 5i

75.

Simplify: $\sqrt[]{-64}-\sqrt[]{-25}$

a)

7i

b)

3i

c)

-3

d)

-13

76.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

77.

Simplify

a)

(-8i+1)/10

b)

(8+i)/11

c)

(34-77i)/109

d)

(21-38i)/58

78.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of f(g(4)).

a)

182

b)

40

c)

61

d)

None of the Above

79.

$f\left(x\right)=x^2\ and\ g\left(x\right)=2x\ +\ 3$ Write an expression that represents the following composition: $g\left(f\left(x\right)\right)$

a)

$2x^2+3$

b)

$x^2$

c)

$2x\ +3$

d)

$2x^3+2x^2$

80.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

81.

Rewrite into rational exponent form
√10

a)

10²

b)

10^½

c)

10

d)

10¹

82.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

83.

Do not use a calculator, simplify: $-32^{\frac{1}{5}}$

a)

2

b)

-2

c)

-3

d)

±2

84.

Rewrite using a radical: $x^{\frac{1}{5\ }}$

a)

$5\left(\sqrt{x}\right)$

b)

$^5\sqrt{x}$

c)

$\sqrt{x^5}$

d)

$\frac{1}{\sqrt{x^5}}$

85.

Without using a calculator, simplify: $\left(\frac{64}{25}\right)^{-\frac{1}{2}}$

a)

$\frac{5}{8}$

b)

$\frac{50}{128}$

c)

$-\frac{8}{5}$

d)

$\frac{8}{5}$

86.

Solve: $x^{3\ }+\ 5\ =\ 13$

a)

±2

b)

2

c)

$x=2,\ and\ x=1\pm2i$

d)

8

87.

a)

A

b)

B

c)

C

d)

D

88.

Simplify $\sqrt{80x^2y}$
Don't forget absolute value bars if necessary (EVEN - EVEN - ODD Rule)

a)

$4\left|x\right|\sqrt{5y}$

b)

$4x\sqrt{5y}$

c)

$2\left|x\right|\sqrt{10y}$

d)

$2x^2\sqrt{10y}$

89.

Simplify and don't forget absolute value bars if necessary (EVEN - EVEN - ODD Rule)

a)

$2m^2\left|n\right|^{\ \ 6}\sqrt{m^3n^2}\$

b)

$2m^9n^{2\ }$

c)

$2m^2n\ \ ^6\sqrt{m^3n^2}$

d)

$2\left|m^3\right|n^2\sqrt{m^2n}$

90.

Simplify, $2\cdot\ ^3\sqrt{-1000xyz^9}$ (cube root)
Don't forget absolute value bars if necessary (EVEN - EVEN - ODD Rule)

a)

$-20z^3\cdot\ ^{\ 3}\sqrt{xy}$

b)

$-10z^3\cdot\ ^{\ 3}\sqrt{xy}$

c)

$-20xyz^3$

d)

$-10xyz^3$

91.

Simplify $\sqrt{28xy²}$ .

Don't forget absolute value bars if necessary (EVEN - EVEN - ODD Rule)

a)

$2\left|y\right|\sqrt{7x}$

b)

$2y\sqrt{7x}$

c)

$\left|y\right|\sqrt{28x}$

d)

$4y\sqrt{7x}$

92.

Write in exponential form
$^3\sqrt{x^7}$

a)

$x^{\frac{7}{3}}$

b)

$x^{\frac{3}{7}}$

c)

$3x⁷$

d)

$7x³$

93.

What function best describes this graph?

a)

$f\left(x\right)=-\sqrt{x+4}-2$

b)

$f\left(x\right)=\sqrt{x-4}-2$

c)

$f\left(x\right)=-\sqrt{x-4}-2$

d)

$f\left(x\right)=\sqrt{x+4}+2$

94.

Solve for x. $2\left(5-x\right)^{\frac{1}{3}}-1=3$

a)

x = -3

b)

x = 3

c)

x = -27

d)

No Solution

95.

Solve

a)

-9

b)

-2,3

c)

5

d)

0

96.

Find the inverse function for $y\ =\ 2x\ +\ 8$ .

a)

$y^{-1}\ =\ \frac{x\ +\ 8}{2}$

b)

$y^{-1}\ =\ \frac{x\ -\ 8}{2}$

c)

$y^{-1}\ =\ \frac{-x\ -\ 2}{8}$

d)

$y^{-1}\ =\ \frac{x\ -\ 2}{8}$

97.

For the inverse function for $y\ =\ 2x^3\ +\ 1$ .

a)

$y^{-1}\ =\ \sqrt[]{\frac{x\ -\ 1}{2}}$

b)

$y^{-1}\ =\ \sqrt[3]{\frac{x\ -\ 2}{1}}$

c)

$y^{-1}\ =\ \sqrt[3]{\frac{x\ +\ 1}{2}}$

d)

$y^{-1}\ =\ \sqrt[3]{\frac{x\ -\ 1}{2}}$

98.

Solve: $\sqrt[]{2x+5}=3-\sqrt[]{x-6}$

(a)

99.

Solve $\sqrt[]{2x+7}=\sqrt[]{x+3}+1$ . Enter your solution as a number, or numbers, separated by commas.

(a)

Semester 1 HAT Review

Total questions: 99

Worksheet time: 5hrs 42mins

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