Free Printable Pre-Aice Math 3 Midterm Review

1.

Solve for x:
4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

2.

Solve for x:
6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

3.

A toy company spends $1500 per day for factory expenses plus $8 to make each teddy bear. They sell the teddy bears for $12 a piece. Which equation could be used to find the number of bears t the company has to sell in one day to equal its daily cost?

a)

1500 + 8t = 12

b)

12 + 8t = 1500

c)

1500 + 8t = 12t

d)

8t = 12t + 1500

4.

a)

-14/9

b)

-9/14

c)

-21/6

d)

6/21

5.

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on the taxi ride. Select the equation that models how many miles, m, Katie can ride.

a)

1.75 + 0.65m < 10

b)

1.75 + 0.65m > 10

c)

1.75m + 0.65 < 10

d)

1.75m + 0.65 > 10

6.

Which situation can be represented by the inequality
15 + 6x ≤ 100?

a)

Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

b)

Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

c)

Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

d)

Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

7.

2x - 3 ≥ 4x - 1

a)

x ≤ -1

b)

x ≥ -1

c)

x ≤ 1

d)

x ≥ 1

8.

-1(2x + 4) ≥ 6

a)

x ≤ -5

b)

x ≥ -5

c)

x ≤ -1

d)

x ≥ -1

9.

-2x + 2 > 3x - 8

a)

x > -9

b)

x > 2

c)

x < -9

d)

x < 2

10.

What is the solution to the system?

a)

(6, 8)

b)

(8, 6)

c)

(-6, 8)

d)

No solution

11.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

same lines

12.

What is the solution to this system?
x - y = 6
y= 2x - 5

a)

(1,3)

b)

(-1,3)

c)

(-1,-7)

d)

(1,-7)

13.

A sporting goods store sells left handed (x) and right handed (y) gloves. In one month, 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

a)

x + y = 561

45x+52y=12

b)

x + y = 12

52x+45y=561

c)

x + y = 12

45x+52y=561

d)

x + y = 561

52x+45y=12

14.

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations. That models this situation.

a)

5q + 2z = 1.32

1z = 0.75

b)

5q + 2z = 1.32

3q + 1z = 0.75

c)

q + z = 1.32

q + z = 0.75

d)

5q + 2z = 0.75

3q + 1z = 1.32

15.

A plane has 646 total seats, which are divided into economy class and business class. For every 12 seats in economy class, there are 5 seats in business class. How many seats are there in economy class?

(a)

16.

What does the graph of the following function look like?

-14x+35y=-28

a)

The Number Line

b)

A line

c)

A parabola

d)

A plane

e)

A circle

17.

Find the vertex. y = x²+ 16x + 71

a)

V(-8, 7)

b)

V(-8, 3)

c)

V(8, 10)

d)

V(16, -2)

18.

Find the vertex y = x² - 2x - 5

a)

V(-2, 10)

b)

V(-1, 15)

c)

V(1, -6)

d)

V(1, -12)

19.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

20.

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

21.

Given y=2(x+3)(x-7), find the vertex.

a)

(2, -50)

b)

(10, 50)

c)

(-2, -18)

d)

(4, -42)

22.

Find the vertex y = (x - 5)(x - 1)

a)

(5, 1)

b)

(-5, - 1)

c)

(3, -4)

d)

(-3, 32)

23.

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

24.

Given the equation for this parabola:
y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

25.

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

26.

What is the axis of symmetry of the given function?

a)

y = 1

b)

y = -1

c)

x = 1

d)

x = -1

27.

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

28.

Solve by taking square roots:

5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no real solution

29.

Solve for x:

(x + 6)²= 49

a)

x=7,12

b)

x=±7

c)

x=1,-13

d)

x=43,-55

30.

What number goes in the blank to complete the square for this trinomial?

x² – 8x + ___

a)

-4

b)

-16

c)

4

d)

16

31.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

32.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

33.

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

a)

22-i

b)

16-i

c)

17-i

34.

(3+8i)(-2-i)

a)

2-19i

b)

23-i

c)

34+5i

d)

23-i

35.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

36.

Simplify

a)

(-10+6i)/17

b)

(1+50i)/61

c)

(-23+36i)/25

d)

(-21+33i)/34

37.

Simplify.

a)

b)

c)

d)

38.

Simplify i²³

a)

i

b)

-1

c)

1

d)

-i

39.

Simplify

a)

A

b)

B

c)

C

d)

D

40.

What is the complex conjugate of 4-3i?

a)

A. 1/(4-3i)

b)

B. 1/(4+3i)

c)

C. -4 + 3i

d)

D. 4 + 3i

41.

Find the values of k for which the following equation has two equal roots.

x^2+k=4x

a)

k = 4

b)

k = -1

c)

k = 2

d)

k = 6

e)

k = 2, 6

42.

Find the values of k for which the following equation has no real roots.

3kx^2-3x+2=0

a)

$k<\frac{3}{2}$

b)

$k\ =\ \frac{3}{2}$

c)

$k=\frac{3}{8}$

d)

$k>\frac{3}{8}$

e)

$k>\frac{3}{2}$

43.

Find the values of k for which the line

x^2-7x+2=kx+1

has two equal roots.

a)

k = -2, 3

b)

k = -4, 7

c)

k = -5, -9

d)

k = 2, 9

e)

k = -1, 7

44.

Find the set values of k for which $\frac{1}{2}x^2+2x-5=2x-k$ has two real roots

a)

k < -10

b)

k < -10 & k > 5

c)

-10 < k < 5

d)

k > -5

e)

k < 5

45.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

46.

(x − 3)(6x − 2)

a)

6x² − 20x + 6

b)

6x² + 20x - 6

c)

6x² +6

d)

6x + 6

Pre-Aice Math 3 Midterm Review

Total questions: 46

Worksheet time: 11hrs 20mins

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