Equations
Solve: 5x = 35.
x = 7.
If the ratio of apples to oranges is 3:2 and there are 12 apples, how many oranges are there?
Oranges = 8
Name the polygon with 6 sides.
What is a Hexagon?
Which measure of center is found by adding all values and dividing by the number of values?
Mean (average).
Sam has 24 marbles and gives 1/3 to his friend. How many marbles does he give away?
Gives away 8 marbles.
Solve: 3(x+4)=21
3(x+4)=21
⇒x+4=7
⇒x=3
Find the unit rate: 45 miles in 3 hours = ____ miles per hour.
Unit rate = 15 miles per hour.
Find the area of a rectangle with length 9 cm and width 4 cm. (Use formula.)
Area = 9×4=36 cm2
If test scores are 70, 80, 80, 90, 100, what is the median?
Ordered: 70, 80, 80, 90, 100 → median = 80.
A store sells 6 notebooks for $9. How much does one notebook cost?
$9 ÷ 6 = $1.50 per notebook.
Write an expression for “8 less than twice a number n,” then evaluate when n=7.
Expression: 2n−82n−8; when n=7
2(7)−8=6
14−8=6
Solve: If 5 pencils cost $2, how much do 8 pencils cost at the same rate?
Cost per pencil = $0.40;
8 pencils = $3.20.
Find the volume of a right rectangular prism with dimensions 3 cm by 4 cm by 5 cm. (Use formula.)
Volume = 3×4×5=60 cm3
Define a statistical question (brief description).
A statistical question expects variability and can be answered with data (example: “How many minutes do students in my class read per day?”).
Leah ran at a constant speed and covered 15 miles in 3 hours. How far will she run in 8 hours at the same speed?
Speed = 5 miles/hour; in 8 hours = 40 miles.
Solve for x: x/4 + 3=10
x/4+3=10
⇒x/4=7
⇒x=28
Use a proportion to find x: 2/3=x/12
2/3=x/12
⇒x=8
A triangle has base 10 cm and height 6 cm. Find its area = 1/2 x b x h
Area = 1/2×10×6=30 cm2
Given data set: 3, 5, 7, 7, 9 — find the mode and the range.
Mode = 7;
Range = 9 − 3 = 6.
A container holds 2.5 liters. How many containers are needed to store 12.5 liters?
12.5 ÷ 2.5=5 containers.
The perimeter of a rectangle is 36 cm. The length is x cm and the width is x−5 cm. Write and solve an equation to find the length.
Perimeter: 2x+2(x−5)=36
⇒4x−10=36
⇒4x=46
⇒x=11.5 cm (length)
A recipe uses 2.5 cups of flour for every 4 cups of sugar. How much flour is needed for 10 cups of sugar?
Set up: 2.5/4=f/10⇒f=2.5×10/4= 6.25 cups flour.
On the coordinate plane, what is the distance between points (−2, 4) and (−2, −1)?
Distance = 5 units (same x-coordinate: vertical distance
∣4−(−1)∣=5
Explain how to determine whether a question is statistical (one-sentence example).
A question is statistical if answers will vary across individuals (example: “What is each student’s favorite lunch?” is statistical).
A school buys 120 pencils and puts them into boxes of 8 pencils each. How many full boxes can they make and how many pencils are left over?
Full boxes = 120÷8=15 full boxes, remainder 0 (no pencils left).