Free Printable Sem 1 HAT Finals Review Ideas

1.

Find the equation of the line in slope-intercept form.

a)

y = - 1/4x - 3

b)

y = 1/3x + 3

c)

y = - 1/4x + 2

d)

y = 1/3x -3

2.

What is the equation of the linear function?

a)

y = -3x + 10

b)

y = -3x + 16

c)

y = 3x + 10

d)

y = 3x + 16

3.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

(4, -7); m = -1/4

a)

y + 7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y + 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

4.

The line with the equation

$y-2=4(x+8)$ ,

contains the point

a)

$\left(-8,2\right)$

b)

$\left(8,2\right)$

c)

$\left(8,-2\right)$

d)

$\left(-2,8\right)$

5.

Solve the system using elimination.

2x + 3y = 12

5x - y = 13

a)

(-3, -2)

b)

(1.5, 2)

c)

(3, 0)

d)

(3, 2)

6.

Solve the system.

a)

(3, -2, 4)

b)

(2, -3, 1)

c)

(-3, 2, -1)

d)

Infinitely many solutions

7.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

8.

Which graph shows the solution to the system:

$3x\ +\ 7y\ <21$

$y\ \ge2x\ -4$

a)

b)

c)

d)

9.

Here is a system of inequalities:

$x\ +\ y\ <\ 3$

$y\ \ge\ x\ -\ 4$

Is the point (2, -6) a solution to the system?

a)

Yes, it is in the overlapping section

b)

No, it is only a solution to x + y < 3

c)

No, it is only a solution to $y\ \ge\ x-4$

d)

No, it is a solution to neither

10.

What is the axis of symmetry in the following graph?

a)

(-1, 0)

b)

X = 0

c)

x = -1

d)

X = 1

11.

If we have the equation y = ax²+ bx + c,

how can we can find the x-coordinate of the vertex?

a)

-a

b)

-b/a

c)

b/2a

d)

-b/2a

12.

What is the vertex of y = x²+ 4x + 3?

a)

(2, 1)

b)

(-2, 1)

c)

(0, 0)

d)

(-2, -1)

13.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

both

d)

neither

14.

How many solutions does this graph have?

a)

one

b)

two

c)

no real solutions

d)

cannot be determined

15.

What is the y intercept for the equation:
y = -8x² + 3x - 7

a)

(0, -8)

b)

(0, 3)

c)

(-8, -7)

d)

(0, -7)

16.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

17.

What is the range of the function graphed?

a)

(-∞, -3]

b)

(-∞, ∞)

c)

[-4, -1]

d)

[-3, ∞)

18.

What is the vertex of function f(x) = 3(x+4)²- 8?

a)

(4, -8)

b)

(-4, -8)

c)

(3, -8)

d)

(-4, 8)

19.

What are the x-intercept(s) of the function g(x) = -9(x - 3)(x + 2)?

a)

(3, 0) and (-2, 0)

b)

(-3, 0) and (2, 0)

c)

(3, -2)

d)

(-9, 0), (3, 0), and (-2, 0)

20.

What is the correct graph for the equation y = - 0.5x²+ 2

a)

b)

c)

d)

21.

Write a quadratic function in intercept form.

y = a(x - r1)(x - r2)

a)

$f\left(x\right)=-(x-6)(x-8)$

b)

$f\left(x\right)=-(x+6)(x+8)$

c)

$f\left(x\right)=(x+6)(x+8)$

d)

$f\left(x\right)=(x+6)(x-8)$

22.

What should be added to both sides of the following equation to complete the square?
x² + 12x = 5

a)

12

b)

6

c)

36

d)

5

23.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

No Real Solution

b)

c)

d)

24.

$x^2=8-5x$

Solve the quadratic equation by completing the square.

a)

$\frac{5\pm\sqrt{57}}{2}$

b)

$\frac{-5\pm\sqrt{57}}{2}$

c)

$-\frac{47}{4},\ \frac{67}{4}$

d)

$-\frac{67}{4},\ \frac{47}{4}$

25.

Solve the equation:
5x² - 35x + 60 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

26.

Solve the equation:
4x²+2x - 6 = 0

a)

x = 1 & -1.5

b)

x = -1 & 1.5

c)

x = (-2 ±√92)/8

d)

x = (-2 ± √100)/8

27.

If the discriminant equals 0, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

28.

Solve the equation:

$2\left(x\ +\ 2\right)^2\ -\ 5\ =\ 8$

a)

$x\ =\ \frac{-4\ \pm\ \sqrt[]{6}}{2}$

b)

$x\ =\ -2\ \pm\ \frac{\sqrt[]{26}}{2}$

c)

$x\ =\ -4\ \pm\ \sqrt[]{6}$

d)

$x\ =\ -2\ \pm\sqrt[]{26}$

29.

What does i² = ?

a)

$-1$

b)

$\sqrt[]{-1}$

c)

$1$

d)

$-\sqrt[]{1}$

e)

$i$

30.

$(1+3i)+(7-2i)$

a)

$8+i$

b)

$i+8$

c)

$8+5i$

d)

$8-5i$

31.

$\left(7\ +\ 3i\right)\ -\ \left(1-8i\right)$

a)

$6+11i$

b)

$6-5i$

c)

$6-5i^2$

d)

$31-53i$

32.

Simplify:

$(-2+i)^2$

a)

$3$

b)

$4+i^2$

c)

$3-4i$

d)

$4i^2$

33.

Simplify:

$(-2+i)^2$

a)

$3$

b)

$4+i^2$

c)

$3-4i$

d)

$4i^2$

34.

$(1-3i)(2+5i)$

a)

$22-i$

b)

$16-i$

c)

$17-i$

d)

$-2+7i$

35.

a)

b)

c)

d)

36.

What is the simplified form of the above?

a)

$\frac{7}{10}+\frac{11}{10}i$

b)

$\frac{13}{10}+\frac{1}{10}i$

c)

$\frac{5}{4}-\frac{3}{2}i$

d)

$\frac{7}{10}-\frac{11}{10}i$

37.

What is the conjugate of $7-2i$ ?

a)

$7+2i$

b)

$7-2i$

c)

$2-7i$

d)

$2+7i$

38.

√-36

a)

6

b)

-6

c)

-6i

d)

6i

39.

Match each sum with its factors.

a)

9x²+ 1

1.

2, (3x - i), (3x + i)

b)

18x² + 2

2.

3, (x - 2i), (x + 2i)

c)

3x²+ 12

3.

(6x - 5i), (6x + 5i)

d)

36x² + 25

4.

(3x - i), (3x + i)

40.

Solve for x:

a)

x = {-4, -1}

b)

x = {-1, -4}

c)

x = {2+i, 2-i}

d)

x = {-2+i, -2-i}

41.

What is the error and correct the error.
$\frac{4}{3-i}\times\frac{3-i}{3-i}=\frac{4\left(3-i\right)}{3^2+i^2}=\frac{12-4i}{10}$

a)

The error is $\frac{12-4i}{10}$ , it should be $\frac{12+4i}{10}$

b)

The error is $\frac{4\left(3-i\right)}{3^2+i^2}$ , it should be $\frac{4\left(3-i\right)}{6-1}$

c)

The error is $\frac{3-i}{3-i}$ , it should be $\frac{3+i}{3+i}$ .

42.

Given the function to the left, what is f(-5).

a)

1

b)

0

c)

-13

d)

-10

43.

Given the function to the left, what is f(2).

a)

-6

b)

-5

c)

2

d)

-7

44.

Which graph represents f(x)?

a)

b)

c)

d)

45.

a)

A

b)

B

c)

C

d)

D

46.

What function best describes this graph?

a)

f(x)= -√(x+4) -2

b)

f(x)= √(x-4) -2

c)

f(x)= -√(x-4) -2

d)

f(x)= √(x+4) +2

47.

Sketch the graph of each function.

a)

b)

c)

d)

48.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

49.

Find the domain and range of the function
Hint: Use a scratch graph to help you visualize things.

a)

Domain: (-∞, ∞) Range: [-∞, 4]

b)

Domain: [1, ∞) Range: (-∞, 4]

c)

Domain: [-1. ∞) Range: [4, ∞)

d)

Domain: [4, ∞) Range: [-1,∞)

50.

What is the equation of the graph? Up 4 to the right 5.

a)

y = √(x - 3)

b)

y = √(x) + 3

c)

y = √(x - 5) + 4

d)

y = √(x + 5) + 4

51.

What is the degree of this polynomial?

a)

0

b)

1

c)

2

d)

3

52.

What is the degree of the function graphed here?

a)

6

b)

4

c)

3

d)

5

53.

What is the lead coefficient of the polynomial?

$-4a^3+19a^4-a+12a^6+103$

54.

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)

55.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

56.

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)

57.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

58.

Divide (x² + 5x - 8) by (x + 3). What is the remainder?

a)

16

b)

12

c)

-14

d)

-16

59.

Which of the following is a COMPLETE list of all possible Rational Zeros for

f(x) = 3x⁵-5x²+x+6?

a)

±1, ±2, ±3, ±6

b)

±1/3, ±2/3, ±1, ±2, ±3, ±6

c)

1/3, 2/3, 1, 2, 3, 6

60.

(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

61.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

62.

List all the possible rational zeros
h(x) = x³- 5x²+2x+12

a)

1,2,3,4,6,12

b)

1,2,6,12

c)

1,2,3,4,6,12,-1,-2,-3,-4,-6,-12

63.

g(n) = n² + 5n

f(n) = n + 4

Find g(f(n))

a)

n² + 3n + 36

b)

n² + 13n + 16

c)

n² + 13n + 36

d)

n² + 3n + 20

64.

f(x) = 2x - 5

g(x) = -4x - 2

Find f(g(-2))

a)

25

b)

-25

c)

-7

d)

7

65.

Are the following inverses of each other?

a)

True

b)

False

66.

Write the following expression in radical form:

a)

a.)

b)

b.)

c)

c.)

d)

d.)

67.

Rewrite with positive exponents: $x^{-a}$

a)

$ax$

b)

$\frac{1}{x^a}$

c)

$\frac{a}{x}$

d)

$-ax$

68.

Simplify the following expression:

a)

5

b)

25

c)

125

d)

625

69.

Simplify

a)

A

b)

B

c)

C

d)

D

70.

√100x⁸y²

a)

10x⁴y√5

b)

10x⁴y²

c)

10x⁴y

d)

100x⁴y√5

71.

Solve the equation. Check for extraneous solutions.

$\sqrt[]{2-x}=x+4$

a)

-7 and -2

b)

No solution

c)

-2

d)

-7

72.

Divide:

a)

√12

b)

(4√3)/3

c)

√3

d)

(2√3)/3

73.

√28m⁴n³

a)

m²n√7n

b)

7m²n√n

c)

2m²n√7n

d)

7m²n²√n

Sem 1 HAT Finals Review Ideas

Total questions: 73

Worksheet time: 5hrs 16mins

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