Number Sense
Show on a number line why a number and its opposite add to 0. Give a specific example using 7 and −7 and explain in one sentence.
They are the same distance from 0, but on opposites sides. 7 + -7 = 0
A positive and a negative cancel each other out.
Given a table: 2 shirts cost $18, 5 shirts cost how much at the same unit price? Identify the unit rate and compute the total.
$45 for 5 shirts
Unit rate is $9 a shirt
Solve: 3x+5=20. Show steps.
3x=15
x=5
Compute the area of a circle with radius 7.
153.86 square units
From the list of numbers: {3,7,7,9,12} find the mean and median.
Mean is 7.6
Median is 7
Find the sum: -3 1/2 + 2 2/3.
-5/6
A map uses a scale where 1 inch = 12 miles. If two cities are 3.5 inches apart on the map, how many miles apart are they in reality?
42 miles
Solve and interpret: −2(x+4)=10. Find x
x= -9
A scale drawing has scale 1:50. If a wall measures 8 cm on the drawing, what is the actual length in meters?
4 meters
What is mean; median; mode; range; and outlier?
Mean is average
Median is middle number
Mode is the number that appears the most
Range is the largest number - smallest number
Outlier is a number that doesn't fit in the rest of the numbers
What is the distance between -2 1/4 and 3 2/5 on a number line? Show the calculation using absolute value.
5 13/20
A recipe uses 2/3 cup of sugar for 4 servings. Find the unit rate (sugar per serving) and how much sugar is needed for 10 servings.
1/6 cup per serving
10 servings need 1 2/3 cups
Solve the inequality and graph the solution set: 1/2x − 3 ≥ 2.
x ≥ 10
Find the volume of a composite solid made of a right rectangular prism (length 6 cm, width 3 cm, height 4 cm) attached to a cylinder of radius 1.5 cm and height 4 cm. Show the calculations separately then give total volume.
Prism volume is 72 cm cubed. Cylinder volume is 28.26 cm cubed
Total volume is 100.26 cm cubes
Sam and Joe both hiked trails through a park. The probability of Sam hiking at least 5 miles is
78. The probability of Joe hiking at least 5 miles is 14.
Who is more likely to hike at least 5 miles?
A. Sam is more likely to hike at least 5 miles because 78 is closer to one than 14 is.
B. Sam is less likely to hike at least 5 miles because 78 is closer to zero than 14 is.
C. Sam and Joe are equally likely to hike at least 5 miles because 78 and 14 are the same probability.
D. Neither Sam nor Joe are likely to hike at least 5 miles because 78 and 14 are both close to zero.
A
Write two fractions that are equivalent to -(7/8).
-7/8 and 7/-8
Convert the proportional relationship to an equation and graph description: total cost (t) is proportional to number of items (n) with unit price $2.40. Write the equation and state the unit rate.
t=2.40n
Unit rate is $2.40 an item
Given slope m=−3/4 and point (4,5), write the equation of the line in slope‑intercept form and graphically describe the slope.
y=-3/4x + 8
Slopes goes down 3 and over 4
A circle's circumference is measured as 24π. Find the radius and the area of the circle.
Area is 452.16 units squared
A spinner has 8 equal sectors numbered 1–8. Develop the probability model for the event "spinner shows an even number" and compute the theoretical probability. Then predict the approximate relative frequency if spun 80 times.
Even number probability is 4/8 or 1/2
Relative frequency would be 40 out of 80
Solve
(-1 1/2)(0.25)(-3)
1.125
A store increases a price by 15% and then later decreases the new price by 15%. Explain (with calculation) whether the final price returns to the original price and why using proportional reasoning.
Let original price = P.
After 15% increase: P1=P(1+0.15)=1.15P
Decrease by 15%: P2=P1(1−0.15)=1.15P×0.85=0.9775P
0.9775P<P, so final price is lower than original. Reason: percent increase and decrease are applied to different bases.
Use properties of operations to factor and justify each step: write an equivalent expression for 6x−18 and explain why factoring is valid.
6(x-3)
they both have 6 in common so you can factor out a 6
The dimensions of a cylinder are a radius of 3 cm and a height of 9 cm. What is the volume?
254.34 cm cubed
A survey reports that in a town of 1,000 people, a random sample of 200 people, 62 have solar panels. What percent of the whole population would have solar panels? What is the sample? What is the population?
31%
Sample is 200; population is 1,000