Meet 3 – Event A 2016-17 Questions are worth 2-2-2-4-4 points respectively.

No calculators allowed

_______________1. Graph the solution set of x on the number line.

2𝑥 + 1 > 7

____________________2. Simplify.

21 − 3.5(𝑎 − 7𝑏 + 0.5) + 14.25𝑎

_______________3. Simplify. Write your answer using only positive exponents.

(𝑎4𝑏4 • −2𝑏3)−2

__________4. Miranda did yard work from 10:35 a.m. until 3:15 p.m. What fraction of a day did Miranda spend doing yard work?

__________5. International Ian is cleaning out his many travel bags. He found some money in each of three suitcases, however the money in each one is of a different currency.

Ian found 10 Euros (EUR) in Suitcase X.

Ian found 8 British Pounds (GBP) in Suitcase Y.

Ian found 910 Indian Rupees (INR) in Suitcase Z. Use the currency exchange chart below to answer the questions.

A. How much money is in Suitcase Z, in terms of British Pounds (GBP)? B. Ian exchanges the money from all three suitcases for US Dollars (USD). How many

US Dollars should he expect to receive?

Currency Exchange Rates

USD (US Dollar)

EUR (Euro)

GBP (British Pound)

INR (Indian Rupee)

USD 1.00 0.91 0.81 66.36 EUR 1.10 1.00 0.89 73.13 GBP 1.24 1.12 1.00 82.16 INR 0.02 0.01 0.01 1.00

Name_______________________________________ School_______________________________________ ©2016 by the Minnesota Junior High School Mathematics League

day

(Use number line)

A.

__________5B. $

GBP

Meet 3 – Event A 2016-17 Answers Questions are worth 2-2-2-4-4 points respectively.

_______________1. .

____________________2. 21 − 3.5𝑎 + 24.5𝑏 − 1.75 + 14.25𝑎 = 𝟏𝟗. 𝟐𝟓 + 𝟏𝟎. 𝟕𝟓𝒂 + 𝟐𝟒. 𝟓𝒃

_______________3. (𝑎4𝑏4 • −2𝑏3)−2 = (−2𝑎4𝑏7)−2 =1

(−2𝑎4𝑏7)2 =𝟏

𝟒𝒂𝟖𝒃𝟏𝟒

__________4. 10:35 3:15 = 4 hours 40 minutes = 14/3 hours 14

3•

1

24=

𝟕

𝟑𝟔

__________5. 910 INR •0.01 GBP

1 INR= 𝟗. 𝟏 𝐆𝐁𝐏

X: 10 EUR •0.89 GBP

1 EUR= 𝟖. 𝟗 𝐆𝐁𝐏

Y: 8 GBP Z: 9.1 GBP

8.9 + 8 + 9.1 = 26 GBP; 26 GBP •1.24 USD

1 GBP= 𝟑𝟐. 𝟐𝟒 𝐔𝐒𝐃

©2016 by the Minnesota Junior High School Mathematics League

1

4𝑎8𝑏14

7

36

10.75𝑎 + 24.5𝑏 + 19.25

*1 point for A

*3 points for B

Note:

Some students may show response a little differently. For full credit, students must:

Show an OPEN circle at 3. Indicate that everything to the RIGHT of 3 is “shaded” or included in the solution set.

(See number line)

day

A.

__________5B. $

GBP

9.1

32.24

*Order of terms does not matter

Meet 3 – Event B 2016-17 Questions are worth 2-2-2-4-4 points respectively.

No calculators allowed

__________1. Evaluate.

(32)4 ÷ 103

__________2. Solve for both values of x.

12

3𝑥2 = 15

__________3. The diagram shows a rectangle that has been partitioned by two line segments.

Find the values of x and y.

__________4. In a library storage closet: Each bookcase has 6 shelves.

Each shelf has 10 boxes.

Each box has 25 books.

There are a total of 30 shelves. What is the ratio of bookcases to books in the library storage closet?

_______________5. The graph shows the solution set of x.

Write an absolute value inequality to represent the graph.

Name_______________________________________ School_______________________________________ ©2016 by the Minnesota Junior High School Mathematics League

x =

y =

x =

x =

Meet 3 – Event B 2016-17 Answers Questions are worth 2-2-2-4-4 points respectively.

__________1. (32)4 ÷ 103 = 38 ÷ 1000 = (81 • 81) ÷ 1000 = 6561 ÷ 1000 = 𝟔. 𝟓𝟔𝟏

__________2. 5

3𝑥2 = 15; 𝑥2 = 9; 𝒙 = −𝟑, 𝟑

__________3. x = 180 – 128 = 52 y = 180 – (180 – (52 + 25)) = 77

__________4. 30 shelves •1 bookcase

6 shelves= 𝟓 𝐛𝐨𝐨𝐤𝐜𝐚𝐬𝐞𝐬

30 shelves •10 boxes

1 shelf•

25 books

1 box= 𝟕𝟓𝟎𝟎 𝐛𝐨𝐨𝐤𝐬

5

7500=

𝟏

𝟏𝟓𝟎𝟎

_______________5.

©2016 by the Minnesota Junior High School Mathematics League

6.561

x = 52

|𝑥 −3

8| >

5

4

1

1500

x = 3

x = -3

*No partial credit.

**Order does not matter.

y = 77

Also accept:

1:1500 1 to 1500

Also accept:

|x – 0.375| > 1.25

*2 points per response

Meet 3 – Team Event 2016-17 Questions are worth 4 points each.

No calculators allowed

_______________1. Simplify.

(𝑎3 • 𝑏4)𝑐 • 𝑎2

__________2. Solve for x.

−4

5(3𝑥 + 1) =

1

5𝑥 − 9

__________3. Brad purchases a 1.5-gallon tub of coleslaw from the deli. He packs the coleslaw into three 1-

quart containers and two 1-pint containers. Then he packs the remaining coleslaw into 1-cup containers until it is all gone. How many 1-cup containers did Brad fill with coleslaw?

__________4. Solve for x.

−12 + 4(−2𝑥 + 5) > 100

__________5. The time on an analog clock is 4:30. What is the measure of the angle formed by the hour hand and the minute hand at 4:30?

_______________6. Divide. Write your answer in scientific notation.

(2.45 × 108) ÷ 50,000

__________7. Simplify. Write your answer using only positive exponents.

2

3(1

4𝑎−3)

2

__________8. Benjamin’s robot travels at a pace of 3.1 feet per second. How many yards does his robot travel in 10 minutes?

__________9. Angles P and Q are complementary. The measure of angle P can be expressed as (5x + 1)°. The measure of angle Q can be expressed as (8x – 2)°. How many times greater is the measure of angle Q than the measure of angle P?

_______________10. Graph the solution set of x on the number line.

𝑥 + 1 ≤ |2𝑥 − 1| ≤ 3

Name_______________________________________ School_______________________________________ ©2016 by the Minnesota Junior High School Mathematics League

x =

yd

(Use number line)

°

Meet 3 – Team Event 2016-17 Answers Questions are worth 2-2-2-4-4 points respectively.

_______________1. (𝑎3 • 𝑏4)𝑐 • 𝑎2 = 𝑎3𝑐𝑏4𝑐𝑎2 = 𝒂𝟑𝒄+𝟐𝒃𝟒𝒄

__________2. −12

5𝑥 −

4

5=

1

5𝑥 − 9; −

13

5𝑥 = −

41

5; 𝑥 =

𝟒𝟏

𝟏𝟑

__________3. 1.5 gallons = 6 quarts; 6 quarts – 3 quarts = 3 quarts 3 quarts = 6 pints; 6 pints – 2 pints = 4 pints 4 pints = 8 cups

__________4. −12 − 8𝑥 + 20 > 100; 8 − 8𝑥 > 100; −8𝑥 > 92; 𝒙 < −𝟏𝟏. 𝟓

__________5.

_______________6. (2.45 × 108) ÷ (5 × 104) = 0.49 × 104 = 𝟒. 𝟗 × 𝟏𝟎𝟑

__________7. 2

3(

1

4𝑎−3)

2

=2

3(

1

16𝑎−6) =

𝟏

𝟐𝟒𝒂𝟔

__________8. 3.1 ft

1 sec•

60 sec

1 min•

1 yd

3 ft=

186 yd

3 min=

62 yd

1 min;

62 yd

1 min• 10 min = 𝟔𝟐𝟎 𝐲𝐚𝐫𝐝𝐬

__________9. (5x + 1) + (8x – 2) = 90; 13x – 1 = 90; 13x = 91; x = 7

P: 5(7) + 1 = 36 Q: 8(7) – 2 = 54 52/36 = 1.5

_______________10. |2x – 1| ≥ x + 1 AND |2x – 1| ≤ 3 2x – 1 ≥ x + 1 OR 2x – 1 ≤ -x – 1 AND 2x – 1 ≤ 3 AND 2x – 1 ≥ -3 x ≥ 2 OR x ≤ 0 AND x ≤ 2 AND x ≥ -1

©2016 by the Minnesota Junior High School Mathematics League

1

24𝑎6

Also accept:

x < -11½, x < -23/2

𝑎3𝑐+2𝑏4𝑐

8

45°

Also accept:

32

13

Also accept:

3/2, 1½

x = 41/13

x < -11.5

620 yd

1.5

Note:

Some students may show response a little differently. For full credit, students must:

Show CLOSED points at -1, 0, and 2. Indicate that everything BETWEEN -1 and 0

is “shaded” or included in the solution set.

(See number line)

Also accept:

315°

4.9 × 103