CRCT Prep 7 th grade 2012-2013. Numbers and Operations

CRCT Prep

7th grade2012-2013

Numbers and Operations

Fraction Decimal Percent

½

¾

2/5

¼

2/3

4/5

1/3

Common Equivalents

.5 50%

.75 75%

.4 40%

.25 25%

.66 66 2/3%

.8 80%

.33 33 1/3%

1)

2)

3)

4)

5)

6)

7)

Integers

1) 4 + -92) -4 + -93) -4 - 94) -4 - (-9)5) -32 ÷ 4 6) -8 • -7

-5-13-13

5-856

7)8)9)10)

6-9

-15

Integers

On the same winter morning, the temperature is -28° F in Anchorage, Alaska and 65° F in Miami, Florida. How many degrees warmer was it in Miami than in Anchorage on that morning?

This problem should be looked at by imagining or drawing an outside thermometer. Then, the distance from the negative temperature to 0 and the distance from 0 to 65 can be added together. This will result in the answer of 93 degrees.

Integers

The lowest temperature ever recorded on earth was -89° C in Antarctica. The average temperature on Mars is about -55° C. Which is warmer, the coldest temperature on earth or the average temperature on Mars? Write an inequality to support your answer.

-55 > - 89 so, the average temperature on Mars is warmer.

Integers

A flea is jumping around on the number line. 1.If he starts at 1 and jumps 3 units to the right, then where is he on the number line? 2.How far from zero is he? 3.If he starts at 0 and jumps 5 units away, where might he have landed?4.If the flea jumps 2 units and lands at zero, where might he have started? 5.The absolute value of a number is the distance it is from zero. The absolute value of the flea’s location is 4 and he is to the left of zero. Where is he on the number line?

44 units

Either 5 or – 5

Either 2 or – 2

-4

Order of Operations 

1. -5 – 2(-3) + 2³

2. 12 ÷ 3 - 2 + 1

3. -2(10 - 7) - 4

4. 30 – 6 · -4 + -1³

5. -2(20 - 2) - 4²

6. -2³ + 2(14 – 6) + -2

7. -3 + -2 · 2³

93

-10

53

-52

6

-19

Ordering Rational Numbers

Find and label the numbers 4/3, 5/4, -2/3 and - ¾ on the number line. Then, state which of the following inequalities is true. a)2/3 > - ¾ b)– 2/3 < -3/4

Since –2/3 is to the right of – 3/4, then – 2/3 > - 3/4

Rational Numbers

* Put stocks in order from highest to lowest price after the change.

4

2

10

8

3

6

5

9

7

1

Continued from previous slide.

Use stock prices after the change to answer the following questions.

1

2

$ .02

Percents– A CD costs $16.50. How much will it cost if you are given a 14% discount?

– A customer is buying a portable CD player that costs $65.00 and the state tax is 5%. How much does the customer owe?

– Your sales were $4,500 in July and $4,650 in August. By what percent did your sales increase from July to August?

– Your costs were $4,650 in August and $2,940 in September. By what percent did your costs decrease from August to September?

$14.19

$68.25

36.8 %

1.Determine the original price of the sandals from the chart above.2.A person decides to buy a pair of sandals and a Denim Collection. If she had purchased them before the sale, she would have paid $189.00 before taxes. Using the answer from question one, determine the total price she would have paid for the two items during the sale.3.The original price for printed T-shirts is $5.00 more than the original price for plain T-shirts. Let n represent the price of a plain T-shirt and write an expression for the cost of two printed T-shirts and two plain T-shirts.4.During the sale, the final price for the items in number four comes toapproximately $58.00. What are the original prices and sale prices ofeach type of T-shirt?

$45.00

$146.25

4n+10

Plain original $12.00 Printed original $17.00sale $8.40 $15.30

Properties

Name the property shown.

Commutative

Associative

Distributive

Algebra

• Ali is n years old and Bart is four years older. Write an expression for Bart’s age.

• Ali’s allowance is m amount. Bart’s allowance is twice Ali’s plus another $5. Write an expression for Bart’s allowance.

• Jack is x years old. George is twice as old as Jack. Alex is 3 years younger than George. Write an expression for Alex’s age.

n + 4

2m + 5

2x - 3

Algebraic Expressions

Combine Like Terms 

1. -2(x + y) + x - 4 + 2y - 1

2. -5x + 4x - 7 – x - 2

3. 3m + -8m - 5d – 2d – 4m

4. 3y – -2y + 9 - 5y - 4

5. -8 + -b + 4b - 2 – 3b

6. -5(5 - y) + 2x + 5 – 3y - x

7. -23g – 12 + 8d - 9g + 3d

8. x - 7(4x - 7y) + 3

-x - 5

-2x - 9

-7d – 9m

5-10

x + 2y - 20

11d – 32g - 12

-27x + 49y + 3

The Camping Club is planning a series of camping trips this fall. The club will provide equipment and organize transportation. Participants must bring enough food and water for the trip and be prepared to carry a backpack with all necessary equipment and food. The club would like to develop formulas to provide members an easy way to figure out how much weight they will need to carry for each trip.

– Trips between April 15 and September 15 will use warm-weather gear (lighter tent and sleeping bag), which weighs 21 lbs, including the backpack.

– Trips between October 16 and March 15 will use cold-weather gear (heavier tent and sleeping bag), which weighs 27 lbs, including the backpack.

– Students should plan to bring 1.75 lbs of food per day (water will be filtered along the way).

– Trips longer than 4 days will require an extra 7 lbs of gear (extra fuel for cooking and more cooking gear).

Write equations that would allow members to figure out how much weight they willneed to carry depending on when the trip occurs and how long it lasts.Use your equations to determine how much weight each camper will be carrying at the start of each of the following trips:

– Second week of August—Black Rock Mountain State Park—2-day trip– First week of September—Unicoi State Park—3-day trip– Third week of November—Fort Mountain State Park—4-day trip– First week of December—Vogel State Park—7-day trip

24.5 lbs26.25 lbs34 lbs46.25 lbs

You have invited all your friends to your birthday party, and every friend who is coming will bring 4 cookies. How many cookies will there be at your party if 1 friend comes? How many cookies will there be if 2 friends come?•Make a table for the number of cookies at your party if up to 6 friends attend.

•Using your results in the table, develop a general rule for finding the number of cookies, y, at your party for any number of friends that come, x. •Graph the ordered pairs.

•Does your general rule work with the results on your graph? •What happens to the number of cookies at your party as the number of guests goes up? •Use your rule to write an equation for finding the number of cookies.

Scenario 1

Friends 1 2 3 4 5 6

Cookies 4 8 12 16 20 24

4 times number of friends

yes

The number of cookies increases as well.

y = 4x

You buy a box of 30 cookies for your birthday party and invite all of yourfriends. How many cookies will each person get if there is only 1 guest?How many cookies will each person get if there are 2 guests?

•Make a table for the number of cookies each person gets if the number of guests is 3, 4, 5, 6, 10, and 15.

•Using your results in the table, develop a general rule for finding the number of cookies per person, y, at your party for any number of friends that come, x. •Graph the ordered pairs •What happens to the number of cookies each person can have as the number of guests increases? •Use your rule to write an equation for finding the number of cookies.

Scenario 2

Friends 3 4 5 6 10 15

Cookies 10 7.5 6 5 3 2

30 divided by number of friends

The number of cookies each guest gets decreases.

x = 4 n = -18 x = 6

x = 7 n = -15 6 = n

Equations

n/2 + 17 = 27 n = 20

2n + 15 = 85 n = 35

50 + 2n = 144 n = 47

Write the equation and solve.

Data and Probability

What is the probability of choosing a red shirt in each of the following situations?

1.A drawer has only 1 red shirt.

2.Four red shirts and five white shirts are added to the drawer.

3.Three red shirts and three white shirts are added to the drawer.

4.Three red shirts and no white shirts are added the drawer.

5.No red shirts and 3 white shirts are added to the drawer.

100% or 1

Calculate Probability

2 24

Tree Diagrams

3 39

Tree Diagrams

2 2 28

Mayo Mayo

Tree Diagrams

3 3 327

Tree Diagrams

Calculate the following probabilities using the information above.

6%

2%

16%

Calculate Probability

LE

LQ

UE

Median UQ

71.5

The data is more spread out in that section.

1. Identify the upper and lower extremes, upper and lower quartiles, and the median of the box and whisker plot below.

Mean Absolute Deviation

1)How do you find the mean absolute deviation of a set of data?

2) Find the mean absolute deviation (MAD) of the height of the following basketball players. (Heights are in inches.): 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84, 82, 84, 80, 84

3) What does the MAD tell us about the heights of the basketball players?

1) Find the mean of the data. 2) Find the absolute value of the difference between each data point and the mean. 3) Find the average of those absolute values.

MAD = 2.5

The average distance of each player’s height from the mean height of the players is 2.5 inches. The players are around the same height.

30

8

5.5

5 and 9

28

The mean because the outlier is included in the calculation.

The median because the outlier is crossed off first when finding the median. The mode because the outlier will never be the mode.

Geometry

Find any missing lengths of sides, doors, and Windows using ratios of corresponding sides.

Scale =

2.17

.17

1.5

.9

A farmer buys a new system to water crops that uses a rotating steel arm, which sprays water over a circular area. The arm rotates around a center point of an existing square field. The arm will reach exactly to the edges of the square. The square field measures 100 feet along each edge.

1. What is the length of the arm?2. What is the area watered by the system?3. What area of the square field will NOT be watered?

50 ft7850 ft

2150 ft

Area

Common diameters of bicycle tires are 16 in, 20 in, 24 in, 26 in, and 27 in. Fill in the following chart using this information.

Diameter Radius Circumference DiameterRadius

CircumferenceDiameter

16 8 50.24 2 3.14

20 10 62.8 2 3.14

24 12 75.36 2 3.14

26 13 81.64 2 3.14

27 13.5 84.78 2 3.14

What pattern do you see in the calculation of column 4? What about in column 5?

Diameter is twice radius

Circumference

Angles

68º 45º90 = x – 20

110º

2y + y = 18060º 120º (w – 50) + (w + 50) = 180

90º

Infinite…similar figures can be drawn for any length sides, but the angles would be the same.

No because the two shorter sides must add up to be longer than the longest side.

No because the two shorter sides must add up to be longer than the longest side.

Yes because the two shorter sides do add up to be longer than the longest side.

The two shorter sides must add up to be longer than the longest side.

180º

Similar Figures

p

12.5 cm

cm

cm

1) Find the missing side of the similar triangles below.

n

2. Find the length of the bridge in the drawing of the similar figures above. _____________5 cm

12 ft

Trapezoid Area

A =( )h1 2

Surface AreaRectangle Area = base times height Triangle Area = (base times height) ÷ 2

216 mi³ 58 m³

512 yd³56 km³

VolumeArea of the base times height

Practice Test