MATHProblems 16-30

I’ll have more problems up this weekend.

16. What is the least common multiple of 70, 60, and 50 ?

F. 60 G. 180 H. 210 J. 2,100K. 210,000

0 50 100 150 200 250

Multiples of 50 eliminate 60, 180, and 210.

What about 2100?

210042

50

210035

60

210030

70

Let’s lay out multiples of 50, to get the feel of the problem:

50, 60, and 70 all evenly go into 2100, 2100 is the least

common multiple.

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

l=45

w=30

h=?V = 81000

V lwh

81000V 45l 30w

81000 45 30 h

81000 1350h

60 h

`

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

To find most volumes …

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

length

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

length

width

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

length

widthbasearea l w

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

length

width

heigth

basearea l w

17. Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

length

width

heigth

basearea l w

l w h basevolume area h

18. Four points, A, B, C, and D, lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

B is 2 units counterclockwise from A.

A

B

2

15

18. Four points, A, B, C, and D, lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

C is 5 units clockwise from A.

A

B

2

5

C15

18. Four points, A, B, C, and D, lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

D is 7 units clockwise from A.

A

B

2

5

C

D

715

18. Four points, A, B, C, and D, lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

D is 8 units counterclockwise from A.

A

B

2

5

C

D

7

8

15

19. A group of cells grows in number as described by the equation y = 16(2)t, where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in the group at the end of the first 5 days?

516 2y

16 32

512

16 2t

y

20. The length of a rectangle is 3 times the length of a smaller rectangle. The 2 rectangles have the same width. The area of the smaller rectangle is A square units. The area of the larger rectangle is kA square units. Which of the following is the value of k ?

l 3×l

w wArea=A Area=kA

Area A lw 3Area lw Area kA

3lw k lw

3 k

`

3lw kA

`

21. (a + 2b + 3c) − (4a + 6b − 5c) is equivalent to:

2 3 4 6 5a b c a b c

2 3 4 6 5a b c a b c

3 4 8a b c

22. The dimensions of the right triangle shown below are given in feet. What is sin θ ?

SOH CAH TOA

sinopposite

hypotenuse

`

sina

c

a

bc

yes

no(neighbor)

23. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball?

yes

start

no(neighbor)

23. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball?

no(person who

passed it)

yes

no(neighbor)

no(neighbor)

23. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball?

no(person who

passed it)

yes

no(neighbor)

no(neighbor)

23. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball?

no(person who

passed it)

yes

no(neighbor)

no(neighbor)

23. In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball?

no(person who

passed it)

yes

no(neighbor)

no(neighbor)

24. Lines p and n lie in the standard (x, y) coordinate plane. An equation for line p is y = 0.12x + 3,000. The slope of line n is 0.1 greater than the slope of line p. What is the slope of line n ?

line p: 0.12 3000y x

line n:

.1

0.22 3000y x

25. The expression −8x3(7x6 − 3x5) is equivalent to:

3 6 58 7 3x x x 3 6 3 58 7 8 3x x x x

9 856 24x x

25. The expression −8x3(7x6 − 3x5) is equivalent to:

Suppose you can't remember whether

3 6 9 18 or ?x x x x

Add exponents

2 3t t tt ttt5t

26. −3 |−6 + 8} = ?

3 6 8

3 2

3 2

6

27. In right triangle ΔACE below, BD is parallel to AE , and BD is perpendicular to EC at D. The length of AC is 20 feet, the length of BD is 3 feet, and the length of CD is 4 feet. What is the length, in feet, of AE ?

These two triangles are similar.

I can use proportions and similar parts of

the triangles.

27. In right triangle ΔACE below, BD is parallel to AE , and BD is perpendicular to EC at D. The length of AC is 20 feet, the length of BD is 3 feet, and the length of CD is 4 feet. What is the length, in feet, of AE ?

12x

20

3 5

x

43

x

5

2 2 23 4 d 29 16 d 225 d

5 d

Oops – I don’t have this. Can I get it?

28a. As part of a lesson on motion, students observed a cart rolling at a constant rate along a straight line. As shown in the chart below, they recorded the distance, y feet, of the cart from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.Which of the following equations represents this data? F. y = t + 14G. y = 5t + 9 H. y = 5t + 14 I. y = 14t + 5 J. y = 19t

0 14 14

5 0 9 9

5 0 14 14

14 0 5 5

19 0 0

f.

g.

h.

i.

j.

t = 0(looking for 14)

t = 1(looking for 19)

1 14 15

5 1 14 19

Sometimes, it helps to start with the answers:

28b. As part of a lesson on motion, students observed a cart rolling at a constant rate along a straight line. As shown in the chart below, they recorded the distance, y feet, of the cart from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.Which of the following equations represents this data? F. y = t + 14G. y = 5t + 9 H. y = 5t + 14 I. y = 14t + 5 J. y = 19t

I could also graph the data quickly and find the line …

5 14y t (0,14)

(5,39)

255

5

risem

run

28c. As part of a lesson on motion, students observed a cart rolling at a constant rate along a straight line. As shown in the chart below, they recorded the distance, y feet, of the cart from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds.Which of the following equations represents this data? F. y = t + 14G. y = 5t + 9 H. y = 5t + 14 I. y = 14t + 5 J. y = 19t

when t increases by 1, y increases

by 5.

at t = 0, y = 14

`

5 14y t

I could also try to analyze the data in the table …

29. The inequality 6(x + 2) > 7(x − 5) is equivalent to which of the following inequalities?

6 12 7 35x x

6 2 7 5x x

12 1 35x 6x 6x

353547 x

30. The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?F. (−4, 0)G. (0, 1)H. (1, −1)J. (4, 1)K. (5, 0)

(2, 0)(-4, 0)

distance = 6

Sometimes, it helps to start with the answers:

The distance is 6. I’m looking for a distance of 3. Wrong answer.

30. The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?F. (−4, 0)G. (0, 1)H. (1, −1)J. (4, 1)K. (5, 0)

(0, 1)

(2, 0)

Wrong answer.

30. The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?F. (−4, 0)G. (0, 1)H. (1, −1)J. (4, 1)K. (5, 0)

(2, 0)

distance = 3

(5, 0)

Right answer!