Free Printable Final Exam Study Guide - Number Sets and Properties

1.

Write a number that satisfies the given condition. An integer between 1.4 and 2.8. The integer between 1.4 and 2.8 is

(a)

2.

Give a number that satisfies the given condition. A rational number between 1.6 and 1.8. Choose the correct answer below.

a)

1.7

b)

-1.85

c)

1

d)

-1

e)

1.85

3.

Give a number that satisfies the given condition. A whole number greater than 4.8. Choose the correct answer below.

a)

7

b)

4

c)

3

d)

1

4.

Give a number that satisfies the given condition. An irrational number that is between $\sqrt{8}$ and $\sqrt{35}$ . Choose the correct answer below.

a)

- $\sqrt{31}$

b)

$\sqrt{39}$

c)

$\sqrt{11}$

d)

$\sqrt{7}$

5.

Decide whether the statement is true or false. Every integer is a rational number. Choose the correct answer below.

a)

The statement is false because the rational numbers fall between the integers on a real number line.

b)

The statement is true because any integer can be rewritten as a fraction.

c)

The statement is false because the integers fall between the rational numbers on a real number line.

d)

The statement is true because any fraction can be rewritten as an integer.

6.

List all numbers from the given set that are natural numbers. Use the set: { $-9$ , $0$ , $\sqrt{36}$ }. Select every correct number.

a)

$-9$

b)

$0$

c)

$\sqrt{36}$

7.

List all numbers from the given set that are whole numbers. Use the set: { $-9$ , $0$ , $\sqrt{36}$ }. Select every correct number.

a)

$-9$

b)

$0$

c)

$\sqrt{36}$

8.

List all numbers from the given set that are integers. Use the set: { $-9$ , $0$ , $\sqrt{36}$ }. Select every correct number.

a)

$-9$

b)

$0$

c)

$\sqrt{36}$

9.

List all numbers from the given set that are rational numbers. Use the set: { $-9$ , $0$ , $\sqrt{36}$ }. Select every correct number.

a)

$-9$

b)

$0$

c)

$\sqrt{36}$

10.

The chart gives altitudes (in feet) for Mountains A–E are as shown:

List the mountains in order, starting with the lowest and ending with the highest. Choose the correct sequence.

a)

Mountain B, Mountain D, Mountain C, Mountain E, Mountain A

b)

Mountain E, Mountain A, Mountain D, Mountain C, Mountain B

c)

Mountain C, Mountain D, Mountain B, Mountain E, Mountain A

d)

Mountain A, Mountain C, Mountain B, Mountain D, Mountain E

11.

Fill in the blanks with the correct values: The opposite of −17 is ____, while the absolute value of −17 is ____. The additive inverse of −17 is ____, while the additive inverse of the absolute value of −17 is ____. Choose the set that correctly completes all statements in the given order (opposite, absolute value, additive inverse, additive inverse of the absolute value).

a)

17, 17, 17, −17

b)

−17, 17, −17, 17

c)

17, −17, 17, 17

d)

−17, −17, −17, 17

12.

Select the smaller of the two numbers: $|−12|$ , $|−13|$ . Choose the smaller number.

a)

$|−12|$

b)

$|−13|$

13.

Perform the indicated operations, using the order of operations as necessary: $−4 + 12 + 5$ .

a)

13

b)

17

c)

−1

d)

The expression is undefined

14.

Perform the indicated operation: $(−3)(−9)$ .

a)

27

b)

−27

c)

12

d)

The expression is undefined

15.

Find the following quotient, or, if applicable, state that the expression is undefined: $\dfrac{−35}{−5}$ .

a)

7

b)

−7

c)

0

d)

The expression is undefined

16.

Perform the indicated operations, using the order of operations as necessary: $−5[4 + (3 − 6)]$ .

a)

−5

b)

5

c)

−15

d)

0

17.

Perform the indicated operations, using the order of operations as necessary: $−8(−2) − \big[(6^2) + (7 − 4)\big]$ .

a)

−23

b)

23

c)

−19

d)

19

18.

Perform the indicated operations, using the order of operations as necessary: $\dfrac{(−6 + 4)(−6)}{−5 − 1} − \dfrac{(−8 + 5)(−3)}{−5 + 4}$ .

a)

7

b)

−7

c)

2

d)

−2

19.

Which of the following expressions are undefined? Choose the correct expressions below.

a)

$(2-2)/(5-5)$

b)

$8/(7-7)$

c)

$9/0$

d)

$0/(-2)$

20.

Solve the equation $6x + 7 = 19$ . What is the solution set?

a)

{ $2$ }

b)

All real numbers

c)

∅

21.

Solve the equation $4(x - 9) = 8(x + 5)$ . What is the solution set?

a)

{ $-19$ }

b)

All real numbers

c)

∅

22.

Solve the equation $-5x + 5 - 6(x - 1) = -(4x - 4) - 6x + 6$ . What is the solution set?

a)

{ $1$ }

b)

All real numbers

c)

∅

23.

For the equation $-14x + 4(x - 3) + 9x = 6x - 68$ , is it a conditional equation, an identity, or a contradiction?

a)

A contradiction

b)

An identity

c)

A conditional

24.

For the equation $-14x + 4(x - 3) + 9x = 6x - 68$ , what is the solution set?

a)

{ $8$ }

b)

All real numbers

c)

∅

25.

For the equation $10[5 - (4 - 2x)] + 7x = 3(9x + 5) - 5$ , determine whether it is a conditional, an identity, or a contradiction.

a)

A contradiction

b)

A conditional

c)

An identity

26.

For the equation $10[5 - (4 - 2x)] + 7x = 3(9x + 5) - 5$ , what is the solution set?

a)

A single number

b)

All real numbers

c)

∅

27.

Solve the formula $r = \dfrac{wC}{119}$ for $C$ . Enter the simplified expression for $C$ .

(a)

28.

Solve the formula for r. m = u + c + 1/6 r. State r in terms of m, u, and c. Simplify your answer.

(a)

29.

Solve for t in the equation C = tn. State t in terms of C and n.

(a)

30.

Fill in the blank with the correct response. The coordinates of the midpoint of the segment having endpoints (−8, 10) and (6, 4) are (a) . Type an ordered pair.

31.

Fill in the blank with the correct response. The equation of the circle with center (5, 8) and radius 5 is (a) .

32.

For the circle with equation $(x - 4)^2 + (y + 2)^2 = 49$ , determine the center. Type the location of the center as an ordered pair.

(a)

33.

For the circle with equation (x − 4)^2 + (y + 2)^2 = 49, determine the radius.

(a)

34.

When plotting the point (−1, 0) on the coordinate axes, where does the point lie?

a)

On the negative x-axis

b)

On the positive x-axis

c)

On the negative y-axis

d)

In Quadrant II

35.

Observe the figure with points P(−3, 4) and Q(3, 6) on a coordinate grid joined by a segment. Find the distance between P and Q. Simplify your answer, using radicals as needed.

(a)

36.

Observe the figure with points P(−3, 4) and Q(3, 6) on a coordinate grid joined by a segment. Find the coordinates of the midpoint of the segment joining P and Q. Type an ordered pair.

(a)

37.

Write an equation of the circle with the given center and radius: center (−8, 8) and r = 3. The equation is (a) .

38.

Graph the circle. For the circle given by $(x + 5)^2 + (y + 3)^2 = 4$ , which choice correctly identifies its center and radius.

a)

Center $(-5,-3)$ , radius $2$

b)

Center $(5,3)$ , radius $2$

c)

Center $(-5,3)$ , radius $4$

d)

Center $(5,-3)$ , radius $4$

39.

The pitch of a roof is its slope. Find the pitch of the roof shown.

a)

$\dfrac{5}{8}$

b)

$\dfrac{8}{5}$

c)

$\dfrac{10}{16}$

d)

$\dfrac{16}{10}$

40.

For the graph on the right, determine if the slope is positive, negative, zero or undefined. What is the slope?

a)

Negative

b)

Positive

c)

Zero

d)

Undefined

41.

What is the slope of this line $6x - y = 7$ . Remember to put the equation in slope intercept form first then solve for y. The slope of the line is

(a)

42.

For the equation 5x + 3y = 5, give the x-intercept as an ordered pair.

(a)

43.

For the equation 5x + 3y = 5, give the y-intercept as an ordered pair.

(a)

44.

Choose the correct segment whose endpoints are G and H.

a)

A ray starting at G and pointing right toward H

b)

A ray starting at H and pointing left toward G

c)

A line segment between G and H with no arrows

d)

A full line with arrows on both ends through G and H

45.

Choose an appropriate name for a segment whose endpoints are G and H.

a)

Ray GH

b)

Line GH

c)

Segment GH

d)

Ray HG

46.

Choose the correct ray whose endpoint is H.

a)

A ray with endpoint G pointing left toward H

b)

A segment GH with no arrows

c)

A ray starting at H and pointing right through G

d)

A ray starting at G and pointing right through H

47.

Choose an appropriate name for a ray whose endpoint is H and that passes through G.

a)

Ray HG

b)

Ray GH

c)

Line GH

48.

Find the measure of the complement of a 60° angle.

(a)

49.

Find the measure of the marked angles shown where two lines intersect, with vertical angles labeled (3x + 37)° and (7x + 5)°.

Enter the measure of the angles in degrees.

(a)

50.

Lines L1 and L2 are parallel.

Two slanted transversals intersect between them forming an X, creating angles labeled 1 through 12 around the intersections.

Determine m∠7 in degrees.

(a)

51.

Lines L1 and L2 are parallel.

Two slanted transversals intersect between them forming an X, creating angles labeled 1 through 12 around the intersections.

Determine m∠1 in degrees.

(a)

52.

Lines L1 and L2 are parallel.

Two slanted transversals intersect between them forming an X, creating angles labeled 1 through 12 around the intersections.

Determine m∠2 in degrees.

(a)

53.