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
Ethan has a box of 24 markers. A fourth of them are black, 5 are blue, and the rest are yellow.
Is he more likely to pick a black, blue, or yellow marker?
Answer: Yellow
black = 24 divided by 4 = 6
blue = 5
5 + 6 = 11
24 -11 = 13 = yellow markers
100
Sam is studying a map of a building that has a scale of 1 in: 200 ft. The distance from the entrance to the emergency exit is 5 inches on the blueprint.
How long is the distance in reality, in feet?
Answer: 1,000 ft
Explanation:
200 x 5 = 1,000
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
Calculate:
(-1) + 1/3
Answer: -2/3
200
A jar has 1,000 candies (orange, lime, cherry). In a sample of 100, there are 30 orange, 20 lime, 50 cherry.
What is the experimental probability P(orange)?
Answer: 3/10 or 0.3
30/100 =0.3 or 3/10
200
What is the base of a parallelogram that has an area of 32 square feet and a height of 8 feet?
Answer: The base is 4 ft
Area = b x h
32 = b x 8
b = 4 ft
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.
0.5 divide (-4/5)
Answer: -5/8
300
Abigail is going out to a pasta dinner. There are 4 types of noodles to choose from and 4 choices of vegetable side. For the appetizer, Abigail has 2 options. Lastly, there are 2 possibilities for the dessert. How many different pasta dinners can Abigail order?
Answer: 64 different dinners
There are 4 noodle choices, 4 vegetable side choices, 2 appetizer choices, and 2 dessert choices. Multiply.
4 × 4 × 2 × 2 = 64
Abigail can order 64 different pasta dinners.
300
If AOD is a straight line, then find the value of x.
Answer: x = 18 degrees
Explanation:(x+16)+ 128 + x = 180
2x + 144 = 180
2x = 36
x = 18
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
Bernie helped design a magician costume for a school play. He used 5.75 feet of ribbon for the magician's wand. He used 11.75 feet of the same ribbon to decorate the magician's robe. If Bernie used $10.50 of ribbon in all, how much did the ribbon cost per foot?
Answer: The ribbon cost $0.60 per foot.
You need to find how much the ribbon cost per foot. Since you know the total cost, start by finding how much ribbon Bernie used in all. 5.75 + 11.75 =17.5 ft
Now divide to find how much the ribbon cost per foot. The total cost was $10.50, and Bernie used 17.5 feet of ribbon.
10.50 ÷ 17.5 = 105.0÷175 =0.6
400
In a school with 200 students, 60 of them play basketball. If you select a student at random, what is the probability that this student does not play basketball? Answer as a percentage.
Answer: 70%
60/200 =0.3 = 30%
100% - 30% =70%
400
Find the surface area of this triangular prism in square feet.
Answer: 54 ft2
SA = (2 × B) + (P × H)
SA = (2 x 6) + (12 x 3.5)
SA = 12 + (42)
SA = 54
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
Carson is saving money to buy a new bike and bike helmet. The cost of the bike is $282.49, and the cost of the helmet is $23.21, both of which include tax. He has saved 2/5 of the total cost so far. Carson earns $10.19 per hour bagging groceries at a local supermarket on Saturday afternoons.
How many more hours does Carson have to work at the supermarket to save enough to buy the bike and helmet?
Answer: 18 hours
$282.49 + $23.21= $ 305.70 = total cost
$305.70 ×2/5 = $122.28 = how much he has saved so far
$305.70 – $122.28 = $183.42 - how much more he needs to save
$183.42 ÷ $10.19=18 - how many hours he would need to work
500
A password consists of four characters, each randomly selected from the letters A, B, C, D, and E. What is the probability of randomly generating the password "ABCD"?
Answer: 1/625
Since each of the four characters in the password can be any of the five letters (A, B, C, D, or E), we use the multiplication principle for independent events. Each position has 5 possible choices: 5 x 5 x 5 x 5 =625
The problem specifies a unique sequence, which is "ABCD". There is only one way to arrange these specific characters in this exact order to satisfy the condition. 1/625
500
The area of a circle is 113.1 feet squared.
What is the radius of this circle, in feet? Use π≈3.14π and round to the nearest whole number.
Answer: 6ft
Area =
2pir^2
113.1 = 3.14 x r2
113.1 divided by 3.14 = r2
36 = r2
6 = r