7th Grade Hard Mode

Probability

100

P(green or orange) when randomly selecting a marble from a bag containing 4 red, 6 orange, 12 green, and 2 purple.

18/24 or 3/4

200

P(not a warm color) when randomly selecting a marble from a bag containing 4 red, 6 orange, 12 green, and 2 purple.

14/24 or 7/12

300

If the probability of getting a Straight in poker is around 1/20, how many Straights would you expect to get if you played 280 hands?

14 Straights

400

A raffle has ping-pong balls numbered 1-25 in a bucket. Any number 20 or above win a prize. The 3 people in front of you grab a ball, sigh disappointedly, and do not put the ball back. What is your chance of winning a prize?

Was 6/25 and is now 6/22 or 3/11

500

A raffle has ping-pong balls numbered 1-25 in a bucket. Any number 20 or above win a prize. You draw 2 balls. What is your probability of winning on both draws?

6/25 times 5/24 = 30/600 or 1/20 or 5%

Equations

100

5x - 2 = -x + 1

x = 1/2

200

4y - 14 = 2(7+2y)

No Solution

300

3(x-4) = -6 +3x -6

All Solutions

400

1/8x + 3/4 = 1/4x - 2

x = 22

500

(4(2x+1/8))/2 = 3x-1

x=-1.25

Proportions

100

x/27 = 4/9

x = 12

200

3/x = 36/84

x = 7

300

What 2 features can you look for in a proportional relationship?

Constant rate or straight line or doubling

and

(0,0) or origin

400

Out of two similar triangles, one has a hypotenuse of 54 and one leg of 21. The smaller triangle has a hypotenuse of 9. What is the measure of the corresponding leg of the smaller triangle?

Scale factor of 1/6 so leg = 21/6 = 3.5

500

If your car can travel 256 miles on 16 gallons of gas, how many gallons will you use if you travel 416 miles?

16 miles per gallon. 416/16 = 26 gallons

Geometry

100

Find the area of a circle that has a radius of 7 dm. Label appropriately.

49pi or 153.86 dm²

200

What is the area of a trapezoid with bases of 4 and 12, and a height of 3? Label appropriately. 

24 un²

300

Find the surface area of a rectangular prism that has edge lengths of 6, 5, and 3. Label appropriately. 

126 un²

400

Find the volume of a triangular prism whose triangular bases have heights of 4.5 and base lengths of 4, and that has a height of 10. Label appropriately. 

180 un³

500

Find the radius of a circle that has a circumference of 18 miles. Round to the nearest hundredth. Label appropriately. 

2.87 miles

Integers

100

-23 - (-44) = ?

21

200

-a(-b)(-b) = ? 

Simplify as much as possible.

-ab²

300

A Magellanic Penguin digs down 22 cm to make a burrow for its eggs. It the decides to tunnel 4 cm further down. Write an equation to represent this situation. 

-22 - 4 = -26 or -22 + -4 = -26

400

Simplify the expression fully. 

-4(-2+8) - (-5)(-2)

-34

500

(-6)² + 4 - 3(-6 + 14)

16