Free Printable Algebra 1 Diagnostic Test

1.

The table shows the cost of long distance calls based on the number of minutes used. Is there a constant rate of change, and if so what is it?

a)

Yes, 10 calls per minute

b)

Yes, $.10 per minute

c)

Yes, $.40 per minute

d)

Not a constant rate

2.

Find the rate of change

a)

1

b)

2

c)

11

d)

Not a constant slope/Non-Linear

3.

A 6-ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10-ounce package?

a)

25 pieces

b)

35 pieces

c)

75 pieces

d)

70 pieces

4.

The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class?

a)

12 girls

b)

15 girls

c)

5.3 girls

d)

27 girls

5.

What is the area of the shaded region?

a)

20 sq cm

b)

4 sq cm

c)

30 sq cm

d)

24 sq cm

6.

Solve the inequality.

x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

7.

Which equation matches the table?

a)

y = 3x + 9

b)

y = x + 9

c)

y = x + 3

d)

y = 12x - 3

8.

Which equation represents this graph? (hint: where is the y-int?)

a)

$y=\frac{1}{5}x+3$

b)

$y=-5x-3$

c)

$y=5x+3$

d)

$y=-3x+0.5$

9.

Maria has 25 dollars. She has to buy a gallon of milk which costs $3.50. She wants to spend the rest of her money on cereal. If each box of cereal costs $4.50, how many can she purchase?

a)

4 boxes

b)

5 boxes

c)

6 boxes

d)

7 boxes

10.

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

11.

2x+8 = 22

a)

14

b)

16

c)

8

d)

7

12.

Which property is illustrated by the following statement? (a – b) + (b – a) = 0

a)

Associative Property of Addition

b)

Commutative Property of Addition

c)

Additive Identity

d)

Additive Inverse

13.

The value of 6b when b = –2 is _____.

a)

4

b)

-12

c)

-3

d)

2

14.

The value of 3a – d when a = –2 and d = 3 is (a) .

15.

Which property is illustrated by the following statement? If r = s, then r + t = s + t.

a)

Addition Property of Equality

b)

Commutative Property of Addition

c)

Distributive Property

16.

If x + (–6) = 7, then x =

(a)

17.

Solve.

\frac{s}{-5}=9

(a)

18.

Solve.

3 + 5t + 2 = 50

(a)

19.

Solve the inequality.

x – 5 > –4

(a)

20.

$–4x\ ≤\ 12$

Solve the inequality.

a)

$x\ ≤\ -3$

b)

$x\ \ge\ -3$

c)

$x\ ≤\ 3$

d)

$x\ \ \ge3$

21.

$4+36\ \div\ \left(10-8\right)^2\ \times3\ +\ 7$

a)

37

b)

38

c)

100

d)

130

22.

Simplify the expression:
$7x^{2\ }-6\ +\ 4x\ +7\ -5x^{2\ }+x$

a)

$2x^{2\ }+5x\ +1$

b)

$2x^{2\ }+4x\ +\ 1$

c)

$12x^{2\ }+5x\ +1$

d)

$12x^{2\ \ }+\ 4x\ +1$

23.

Which graph represents the solution to the inequality

x+\ 6\ \le-9?

a)

A

b)

B

c)

C

d)

D

24.

What is the solution set of

\left|3x-2\right|=7\ ?

a)

$3$

b)

$-3,\ 3$

c)

$-\frac{5}{3},3$

d)

$-\frac{5}{3}$

25.

Calculate the slope of the line that passes through the points

(-4, 7) and (1, -7 ) .

a)

undefined

b)

-\frac{14}{5}

c)

0

d)

$\frac{14}{3}$

26.

Which describes the relationship between the two lines?

y\ =\ 2x\ -3\

y=\ \frac{1}{2}x\ +\ 3

a)

The lines are parallel.

b)

The lines are perpendicular.

c)

The lines intersect, but are not perpendicular.

d)

The lines are the same.

27.

$y\ +\ 5\ =\ \frac{1}{3}\left(x-9\right)$

Which equation is the same as the above equation, in slope-intercept form?

a)

$y\ =\ \frac{1}{3}x\ -14$

b)

$y\ =\ \frac{1}{3}x\ -8\$

c)

$y=\ \frac{1}{3}x\ -4$

d)

$y\ =\ \frac{1}{3}x\ +\ 2$

28.

What is the square root of 45 in simplest radical form?

a)

$9\sqrt{5}$

b)

$5\sqrt{9}$

c)

$5\sqrt{3}$

d)

$3\sqrt{5}$

29.

$\left(4x-5\right)\left(3x+2\right)$ Multiply the binomials:

a)

$12x^2+23x\ -10$

b)

$12x^2+7x-10$

c)

$12x^2-7x-10$

d)

$12x^2-23x\ -10$

30.

$3^0\left(3^{-2}\right)$ Evaluate the expression

a)

$-9$

b)

$0$

c)

$\frac{1}{9}$

d)

$\frac{1}{81}$

31.

Solve this equation.

$\frac{2\left(r-3\right)}{4}-8=50$

a)

$r=87$

b)

$r=119$

c)

$r=113$

d)

$r=78$

32.

Solve the following:
-2 x (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

33.

Solve the following:
(2 + 7 - 1) ÷ 2²

a)

16

b)

2

c)

72.25

d)

8.75

34.

-6k + 7k=

a)

k

b)

-k

c)

12k

d)

-12k

35.

In the equation y=mx+b,
what does m represent?

a)

Nothing in particular

b)

The y-intercept

c)

The x-intercept

d)

Slope

36.

Name the y intercept

a)

4

b)

-1

c)

1

d)

-4

37.

What is the next term in the sequence:
3, 9, 15, 21, ...

a)

24

b)

27

c)

30

d)

33

38.

Which of these numbers could NOT be a common denominator for these three fractions?
1/3 and 2/5 and 3/10

a)

15

b)

30

c)

60

d)

90

39.

Simplify
(1/3)(21m + 27)

a)

63m + 9

b)

7m + 9

c)

7m + 81

d)

7m + 27

40.

What are the coordinates of point H?

a)

(-4, 2)

b)

(4, -2)

c)

(-2, 4)

d)

(4, 4)

41.

What is the origin?

a)

The point furthest away from the center of the coordinate plane

b)

The four regions of a coordinate plane

c)

the x-axis

d)

Where the x-axis and y-axis intersect

42.

What type of slope does the graph have?

a)

Positive

b)

Negative

c)

Zero Slope

d)

Undefined

43.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

44.

What type of slope does the following graph have?

a)

Postive

b)

Negative

c)

Zero Slope

d)

Undefined

45.

Find the slope of:
(1,8) and (3,12)

a)

2

b)

1/2

c)

9/7

d)

-2

46.

Is it a function?

a)

It IS a function.

b)

It IS NOT a function

47.

What is the x-intercept of the graph of $3x-4y=12?$

a)

$-4$

b)

$-3$

c)

$3$

d)

$4$

48.

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

a)

$\frac{2}{9}$

b)

$\frac{4}{9}$

c)

$\frac{4}{3}$

d)

$\frac{4}{6}$

49.

Add the fractions:
1/3 + 1/5 =

a)

8/15

b)

2/5

c)

1/2

d)

1/3

50.

Write an algebraic expression for "8 less than a number".

a)

8x

b)

x - 8

c)

8 - x

51.

Simplify:
$5\left(x-3\right)$

a)

$5x-3$

b)

$5x-15$

c)

$-5x+15$

d)

$-5x+3$

52.

Which equation matches the graph?

a)

y = 60x

b)

y = 40x

c)

y = 80x

d)

y = 20x

53.

What is the slope of the line?

a)

$\frac{3}{4}$

b)

$-\frac{4}{3}$

c)

$-\frac{3}{4}$

d)

$\frac{4}{3}$

54.

Factor completely.

x^2+8x-9

a)

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

b)

$\left(2x+3\right)\left(x-3\right)$

c)

$\left(x-9\right)\left(x+1\right)$

d)

$\left(x-1\right)\left(x+9\right)$

55.

Factor Completely:

x^2-2x-35

a)

$\left(x+7\right)\left(x-5\right)$

b)

$\left(x-7\right)\left(x+5\right)$

c)

$\left(x-7\right)\left(x-5\right)$

d)

Prime

56.

Factor completely:
x² - 5x + 3

a)

(x + 3) (x + 1)

b)

(x - 3) (x - 1)

c)

prime

d)

(x - 3) (x + 1)

Algebra 1 Diagnostic Test

Total questions: 56

Worksheet time: 3hrs 41mins

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