Ratios and Proportional Relationships
Expressions and Equations
The Number System and Exponents
Statistics and Probability
Geometry
100
Are the ratios 15:12 and 9:6 equivalent?
No
15:12 simplifies to 5:4
9:6 simplifies to 3:2
100
What is the coefficient of the first term in this expression?
7k+1+10n+6m
Answer: 7
The first term is 7k and 7 is the coefficient.
100
Evaluate:
-3^3
Answer: -27
-3 x -3 = 9
9 x -3 =-27
100
The school collected canned goods for a food drive. What is the mean number of cans collected? Write your answer as a decimal.
Room 1-120 cans
Room 2- 96 cans
Room 3- 115 cans
Room 4- 125 cans
Answer: 114 cans
Explanation:
120 + 96+ 115 +125= 456
456 ÷ 4 = 114
100
The scale on a map shows that 5 centimeters = 2 kilometers. What number of centimeters on the map represents an actual distance of 4 kilometers?
Answer: 10 cm
Explanation:
5cm =2km, then 10cm = 4km
200
There are 32 students in the school play. The ratio of girls to all students in the play is 5 : 8. How many girls are in the play?
Answer: 20 girls are in the play
5/8 =x/32
200
Simplify the expression:
a + 10a -2 + 5
Answer: 11a +3
200
Is 0 (zero) a rational number?
Answer: Yes
Rational numbers can be written as a/b where an and b are integers and b is not zero. When written as decimals, rational numbers terminate or repeat. 0 can be written as 0/1, which is a fraction, so 0 is a rational number.
200
The arrow on this spinner is spun once.
What is the probability that the arrow will land on a section labeled with a number greater than 3? Write your answer as a simplified fraction or percent.
Answer: 1/4 (or 25%)
2 of the 8 numbers are greater than 3
2/8 simplifies to 1/4
200
Determine whether the solids are similar.
Answer: No
Their measurements are not proportional
8/18 does not equal 2/6
300
At soccer practice, Hassan warms up by kicking balls at the goal. Yesterday, Hassan made 24 goals in 3 minutes. Today, he only spent 2 minutes kicking balls at the goal.
If Hassan made goals at the same rate, how many goals did he make today?
Hassan made 16 goals.
24 goals in 3 minutes = 8 goals in 1 minute
So 2 minutes =16 goals
300
Solve for c:
1/10 = c - 4/5
Answer: 9/10
300
Solve and write your answer in lowest terms.
-3/10 + 1/2 =
Answer: 1/5
300
Paul wrote the equation t=2m+40 to represent the temperature, t, in degrees Celsius, after a substance had been heated for m minutes.
Based on Paul's equation, how many minutes does the substance have to be heated to reach a temperature of 100 degrees Celsius?
Answer: 30 minutes
100 = 2m +40
60 = 2m
m = 30
300
Answer: x = 63
Explanation:
(x-12) + 39 = 90
x-12 + 39 - 39 = 90-39
x -12 + 12 = 51 + 12
x = 63
400
Richard went kayaking last weekend. On Saturday, he kayaked for 2 hours and went 7 kilometers. On Sunday, he kayaked on a different river for 3 hours and went 12 kilometers. On which day did Richard kayak at a faster average speed?
Answer: Sunday
Find the unit rate:
Saturday - 7km/ 2hr =3.5 km/h
Sunday - 12km/ 3hr = 4km/hr
4km/hr is the faster rate.
400
The height requirement for the Star Speed roller coaster is 54 inches. Even after growing 3 inches since last summer, Dakota is too short to ride. Write and solve an inequality that describes the problem. Let x represent how tall Dakota was last summer.
Answer:
Inequality: x+3 < 54
Solution: Dakota was less than 51 inches tall last summer.
400
An airplane’s altitude changed −378 feet over 7 minutes. What was the mean change of altitude in feet per minute?
Answer: -54 feet per minute
-378 divided by 7 = -54
400
A student surveyed a random sample of 40 students in the school cafeteria about whether they ate the cafeteria's tomato soup.
14 of the sampled students said they ate the soup.
A total of 840 students eat in the cafeteria each day.
Based on the results of the survey, how many of the 840 students who eat in the cafeteria can be expected to eat the tomato soup?
Answer: 294 students
14/40 = x/840
14 x 840 =11,760
40x = 11760
x = 11760 divided by 40
x = 294
400
A circular mirror has a diameter of 12 inches.
A = pi r^2
Answer: C
36pi
500
In order to keep track of the elephant population in Africa, Adriana catches 65 elephants and marks them. Later, Adriana gets in a helicopter and takes pictures containing 570 elephants. Of the elephants in the pictures, 39 are marked. To the nearest whole number, what is the best estimate for the elephant population?
Answer: 950 elephants
65/x = 39/570
500
Russell has been training for a race. The first week he trained, he ran 5 days and took the same two routes each day. He ran 2 miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of 30 miles.
Write and solve an equation to find how many miles, x, he ran each day after school.
Answer:
The equation 5(x+2)=30 can be used to find how many miles Russell ran each day after school.
Then solve the equation for x.
5(x+2) = 30 or 5(2+x) = 30
divide both sides by 5
x+2 = 6
subtract 2 from both sides
x = 4
Russel ran 4 miles each day after school.
500
A carpenter bought 750 nails. Each nail has a mass of 5.2×10−3 kilogram. What is the total mass, in kilograms, of the nails the carpenter bought? Give your answer as a decimal.
Answer: 3.9 kg
5.2×10−3 = .0052
.0052 x 750 = 3.9
500
Eric planted a seedling in his garden and recorded its height each week. The equation shown can be used to estimate the height, h, in inches, of the seedling by the end of each week, w, after it was planted.
What does the slope of the graph of the equation
h = 3/4w + 9/4
represent?
Answer: The slope represents the increase in the height, in inches, of the seedling each week.
500
Answer: 8/125 in3
L = 4x1/5 =4/5
W = 2 x 1/5 = 2/5
H = 1 x 1/5 = 1/5
Volume = 4/5 x 2/5 x 1/5 =8/125