Free Printable Pre Semester Exam

1.

Simplify the following expression:

a)

A

b)

B

c)

C

d)

D

2.

Perform the operation

a)

A

b)

B

c)

C

d)

D

3.

Perform the operation

a)

A

b)

B

c)

C

d)

D

4.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

5.

Simplify $\frac{7n}{3n-18}+\frac{n+3}{3}$

a)

$\frac{8n+3}{3n-15}$

b)

$\frac{n^2+4n-18}{3\left(n-6\right)}$

c)

$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$

d)

$\frac{7n+n+3}{3n-18+3}$

6.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

7.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

8.

Simplify $\frac{7n}{3n-18}+\frac{n+3}{3}$

a)

$\frac{8n+3}{3n-15}$

b)

$\frac{n^2+4n-18}{3\left(n-6\right)}$

c)

$\frac{7\left(n+3\right)}{3\left(3n-18\right)}$

d)

$\frac{7n+n+3}{3n-18+3}$

9.

Find the restriction(s) for the above expression

a)

$n=0$

b)

$n\ne0$

c)

$n=-24$

d)

n can be any real number

e)

$n\ne-24$

10.

Choose the correct simplification of the original expression of $\frac{12a^2+54a}{54a}$

a)

$x-4$

b)

$\frac{2a+9}{9}$

c)

$\frac{2a+5}{2}$

d)

$\frac{4}{3\left(a+2\right)}$

11.

Simplify the expression above.

a)

$\frac{4x³}{x+2}$

b)

$\frac{4x³}{x+10}$

c)

$\frac{2x³}{5x+1}$

d)

$\frac{2x³}{x+5}$

e)

The expression cannot be simplified.

12.

Simplify the expression $\frac{x^8y^{12}}{x^4y^{15}}$

a)

$\frac{x^4}{y^3}$

b)

$\frac{x^{12}}{y^3}$

c)

$x^{12}y^{27}$

d)

$\frac{y^3}{x^4}$

e)

$x^4y^3$

13.

Simplify:

13-\left(12-6\div3\right)\ =?

a)

11

b)

3

c)

$\frac{7}{3}$

d)

none of these

14.

$What\ is\ the\ value\ of\ \left(-4\right)\ \times\left(7-11\right)$

a)

16

b)

12

c)

14

d)

20

15.

$What\ is\ the\ value\ of\ 19\ -\left(1+5\right)\ -3$

a)

15

b)

10

c)

15

d)

20

16.

$What\ is\ the\ value\ of\ \frac{9}{7}+\frac{8}{7}-\frac{2}{7}$

a)

$\frac{2}{7}$

b)

$\frac{17}{7}$

c)

$\frac{15}{7}$

d)

0

17.

Simplify the expression

a)

(4 - 2ab² + 3b³) / 4b²

b)

(4a - 2a²b² + 3ab³) / 4ab²

c)

(4 - 2ab² - 3b³) / 4b²

d)

(4a - 2a²b² - 3ab³) / 4ab²

18.

Find the LCD: $\frac{1}{3a}+\frac{1}{6a^2}$

a)

12

b)

18a

c)

$6a^2$

d)

$3a^2$

19.

$Simplify:\ \ \frac{x^8y^{12}}{x^4y^{15}}$

a)

$\frac{x^4}{y^3}$

b)

$\frac{x^{12}}{y^3}$

c)

$x^{12}y^{27}$

d)

$\frac{y^3}{x^4}$

20.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

21.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

22.

What does "m" represent in y=mx+b?

a)

y-intercept

b)

slope

c)

macaroni

d)

nothing

23.

What is the x-intercept of the equation 3x - 2y = 6

a)

(2, 0)

b)

(0, 2)

c)

(-3, 0)

d)

(0, -3)

24.

Find the equation of this line

a)

y = 2x

b)

y = 0.5x

c)

y = 2x + 6

d)

y = 2x + 3

25.

Find the equation of this line.

a)

y = -3x + 5

b)

y = -5x + 15

c)

y = -3x - 15

d)

y = your mum

26.

If 2x+3y = 12 and 3x-2y=5 then

a)

x = 2, y = 3

b)

x = 2, y = -3

c)

x = 3, y = 2

d)

x = 3, y = -2

27.

If the system of equations kx - 5y = 2, 6x + 2y = 7 has no solution, then k =___

a)

-10

b)

-5

c)

-6

d)

-15

28.

A driving range charges $4 to rent a golf club plus $2.75 for every bucket of golf balls you hit. Write an equation that shows the total cost c of hitting b buckets of golf balls.

a)

c = 2.75b + 4

b)

c = 2.75b

c)

c = 4b- 2.75

d)

c = 2.75b - 4

29.

Belinda's car needed repairs. The mechanic charged him $140 for the parts and an additional $48 an hour for labor. Write an equation that models this situation.

a)

y = 140x +48

b)

y = -48x +140

c)

y = 48x +140

d)

y = 48x

30.

What could this represent? 7x + 2 = 30

a)

Buying pet turtles for $7 each plus two cans of turtle food cost $30.

b)

Seven bags of candy plus 2 extra snickers bars equals 30 dollars.

c)

Two yoyos plus seven frisbees is thirty cents.

d)

Buying seven calculators plus $2 per bundle of pencils is $30.

31.

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.

a)

h = 2C + 15

b)

C = 15h + 2

c)

h = 15C + 2

d)

C = 2h + 15

32.

Find the slope and starting point.

a)

Slope: $\frac{2}{3}$ Starting Point: $\left(0,\ 4\right)$

b)

Slope: $\frac{3}{2}$ Starting Point: $\left(0,\ 4\right)$

c)

Slope: $\frac{2}{3}$ Starting Point: $\left(4,\ 0\right)$

d)

Slope: $-\frac{2}{3}$ Starting Point: $\left(0\ ,\ 4\right)$

33.

How many solutions does this equation have?

6x - 3 = 6x + 9

a)

One Solution

b)

No Solution

c)

Many Solutions

34.

How many solutions does this equation have?

8y - 4 = 8y - 4

a)

One Solution

b)

No Solution

c)

Many Solutions

35.

How many solutions does this equation have?

3z + 7 = 7 + 3z

a)

One Solution

b)

No Solution

c)

Many Solutions

36.

How many solutions does the following equation have?

−2x + 9 + 6x = −3x + 2

a)

One Solution

b)

No Solutions

c)

Infinitely Many Solutions

d)

Two solutions

37.

How many solutions does the following equation have?

−2x + 9 + 6x = −3x + 2

a)

One Solution

b)

No Solutions

c)

Infinitely Many Solutions

d)

Two solutions

38.

Maximum, how many solutions can a quadratic equation have?

a)

1

b)

3

c)

4

d)

2

39.

What is the formula to find the roots of a quadratic equation $ax^2+bx+c=0$ ?

a)

$x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}$

b)

$\frac{b\pm\sqrt[]{b^2-4ac}}{2a}$

c)

$x=\frac{-a\pm\sqrt[]{a^2-4bc}}{2b}$

d)

$\frac{-b-\sqrt[]{b^2-4ac}}{2a}$

40.

Choose the correct options among the given conditions in the quadratic equation $ax^2+bx+c=0$ .

a)

When $b^2=4ac$ , there is unique solution.

b)

When $b^2-4ac>0$ , the roots are rational number.

c)

When $b^2-4ac<0$ , the roots are irrational number.

d)

When $b^2=4ac$ , there is no solution.

41.

Choose the discriminant of the equation $x^2-x-20=0$ .

a)

9

b)

81

c)

1

d)

80

42.

Solve the equation by factoring.

a)

x = {-5,-3}

b)

x = {5,-3}

c)

x = {-5,3}

d)

x = {5,3}

43.

Solve the equation using the quadratic formula.

4x² +9x = 12x

a)

x = {0, 3/4}

b)

x = {0, -3/4}

c)

x = {0, 4/3}

d)

no solution

44.

Which graph is a parabola?

a)

b)

c)

d)

45.

Which equation would give the graph of a parabola?

a)

y = 2x - 3

b)

y = x₂+ 1

c)

y = x²+ 4

46.

How can you tell whether a parabola is facing up or facing down by looking at the equation?

a)

The vertex tells you the direction of the opening

b)

The value of "a" tells you the direction of the opening.

c)

All parabolas open upward

d)

All parabolas open downward

47.

If the a value is positive in the equation of y = ax²+ c, which direction does the graph open?

a)

up

b)

down

c)

left

d)

right

48.

Which letter in a equations y = ax²+ c represents the y-intercept?

a)

a

b)

b

c)

c

49.

What is the y-intercept of the parabola y = 5x² - 3

a)

5

b)

3

c)

- 3

d)

-5

50.

What is the y-intercept of the parabola?

a)

-4

b)

4

c)

-3

d)

0

51.

The graph of y = x² + 1 could be?

a)

b)

c)

d)

52.

What is the equation of this graph?

a)

y = x²+ 1

b)

y = - x² + 1

c)

y = x²

d)

y = - x²

53.

What is the equation of the following graph?

a)

y = 2x²

b)

y = x²+ 2

c)

y = x²- 2

d)

y = - 2x²

54.

Which of the following graphs could be y = 5x² + 1?

a)

b)

c)

d)

55.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

56.

What is the simplifies form of (11 - 7i) - (-3 + 12i)

a)

8 - 19i

b)

8 + 5i

c)

13- 19i

d)

14 -19i

57.

What is the simplified form of (-6i)(3i)

a)

-18

b)

-18i

c)

18

d)

-18i²

58.

A complex number can be expressed as a + bi. What does a represent?

a)

the real part of the complex number

b)

the imaginary part of the complex number

c)

depends on the sign of the number

d)

the square root of the complex number

59.

a)

i

b)

5i

c)

-i

d)

-5i

60.

Simplify the number by using the imaginary number i.

\sqrt{-40}

a)

$2i\sqrt{10}$

b)

$-2i\sqrt{10}$

c)

$8i\sqrt{5}$

d)

$-8i\sqrt{5}$

61.

$-50x^2\ -8=0$

Solve

a)

$x=\pm\frac{2}{4}i$

b)

$x=\pm\frac{2}{5}i$

c)

$x=-\frac{2}{5}i$

d)

$x=\pm\frac{4}{5}i$

62.

Find

i^{1222}

a)

1

b)

-1

c)

i

d)

-i

63.

a)

A

b)

B

c)

C

d)

D

64.

a)

A

b)

B

c)

C

d)

D

65.

Simplify $\frac{14}{7-6i}$

a)

$\frac{98+84i}{85}$

b)

$\frac{35+21i}{34}$

c)

$\frac{7+7i}{6}$

d)

$\frac{112+96i}{85}$

Pre Semester Exam

Total questions: 65

Worksheet time: 6hrs 57mins

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