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ACP Honors Math 7
Semester 2 Final Review
Name:
Probability
A bag contains 25 apples; 8 are red, 10 are golden, and the rest are green.
1. One apple is taken from the bag. What is the probability that it is not green?
2. If two red apples have been taken from the bag and not replaced, what is the probability that the
next apple taken will be red?
3. Are the events below dependent or independent?
a. Event 1: The first apple is golden and not replaced.
b. Event 2: the second apple taken is green.
4. Make a tree diagram for the following, then list the outcomes.
An ice cream shop offers three flavors: vanilla, chocolate, and strawberry. It also has a choice
of three toppings: berries, candy, or fudge.
5. The following letters are placed in a bag: P R O B A B I L I T Y. You select a letter at random.
Without replacing the letter, you draw a second letter. Find the probability of each.
a. P(B, then T)
b. P(R or I, then B)
6. You pick a marble from a bag containing 4 green marbles, 1 red marble, 3 yellow marbles and
2 black marbles. You replace the first then select a second. Find each probability.
a. P(red, yellow)
b. P(yellow, not black)
7. A test consists of 5 true/false questions. How many outcomes are there? What is the probability
that you will answer all 5 correctly?
8. You flip a quarter and roll a die. How many outcomes are there?
9. A uniform at Cool School consists of a choice of 3 pants, 4 shirts, 2 sweaters, and 5 pairs of
socks. How many different uniforms are possible if each student must wear a pair of pants, a
shirt, a sweater, and a pair of socks?
10. You roll 2 dice. Which of the following events are certain?
a. rolling a 1 or a 3
b. the sum of the 2 numbers is greater than 1
c. rolling two of the same number
d. the sum of the 2 numbers rolled is less than 12
11. A fair number cube is rolled.
a. What is the theoretical probability of rolling an even number?
b. What is the theoretical probability of rolling a 6?
c. What is the theoretical probability of rolling a 1 or a number greater than 4?
12. An experiment is done in which a coin if flipped 60 times. It lands on heads 20 times and on
tails 40 times. What is the experimental probability of the coin landing on heads? If you flipped
the coin another 120 times, estimate the number of times it would land on heads.
13. In your last 25 soccer games, you attempted 150 goals and made 125. What is the experimental
probability of you making a goal in your next game? What is the probability of make a goal in
each of your next 3 games?
14. You randomly draw one card from a standard deck of cards. What is the probability that you
draw either a king or a heart?
15. A spinner has 4 equal sections labeled 1 through 4. The chart shows the results of spinning the
spinner 41 times.
Landed on 1 Landed on 2 Landed on 3 Landed on 4
9
13
13
6
a.
b.
c.
d.
What is the probability of the spinner landing on the number 2?
What is the experimental probability of the spinner landing on an odd number?
What is the experimental probability of the spinner landing on 4?
If you spun the spinner another 150 times, estimate the number of times it would land on 1.
Permutations
16. You and 7 friends go to a concert. How many ways can you arrange your seating?
17. How many arrangements are possible for watching 4 movies?
18. In how many ways can 9 people be seated at a counter with 6 stools?
19. Five people are running a race. How many arrangements of a winner, second place, and third
place are possible?
20. How many four-letter words can you make from 6 letters?
21. How many ways can a winner and a runner-up be chosen from 8 dogs at a dog show?
22. In how many ways can a president, vice-president, secretary and treasurer be chosen from a
club of 12 members?
23. Seven students are running for class president. In how many different orders can the candidates
make their campaign speech?
24. In how many different ways can a coach name the first three batters in a nine-batter softball
team?
25. In how many ways can the gold, silver, and bronze medals be awarded to 10 swimmers?
Combinations
26. There are 11 different marbles in a jar. How many different sets could you get by randomly
picking 6 of them from the jar?
27. A painter was carrying 8 pails of different colored paint and dropped 4 of them, making a big
mess. How many combinations of colors could he have spilled?
28. How many different 6-person teams can be created from a class of 12 students?
29. Jenna asked the pet store owner for any 4 baby mice from a cage containing 9. How many
possible combinations of mice could be picked?
30. 5 names will be picked from a jar to win prizes. There are a total of 11 names in the jar. How
many different combinations of names can be picked?
Conversions
31. How many square feet are there in 288 square inches?
32. Horseshoe Falls has an average water flow of 600,000 gallons per second. What is the average
water flow of Horseshoe Falls in gallons per minute?
33. The length of Ann's bedroom is 5
yards. What is the length, in feet, of her bedroom?
34. What is the number of 750 mL bottles that can be filled from 600 L of water?
35. 16 km equals how many meters?
36. A square has an area of 1 square foot. How many square inches is this?
37. A square has an area of 576 square inches. How many square feet is this?
38. 432 mm equals how many centimeters?
Rotations
Directions: Rotate the following figures about the origin according to the instructions.
1) 90 clockwise
2) 45 counterclockwise
3) 180 clockwise
4) 90 counterclockwise
5) 270 clockwise
6) 90 counterclockwise
7) 180 clockwise
8) 90 counterclockwise
9) 45 clockwise
10) 270 clockwise
11) 90 counterclockwise
12) 180 counterclockwise
Pythagorean Theorem Problems
1. Use the Pythagorean Theorem to find the missing side of the triangle if the hypotenuse is 68 and the
other side is 32.
2. A construction company is pouring a concrete foundation. The measures of two sides that meet in a
corner are 33 ft and 56 ft. For the corner to be square (a right angle), what would the length of the
diagonal have to be?
3. A right triangle has legs of length 6x m and 8x m and hypotenuse of length 90 m. Find the lengths of
the legs of the triangle.
Find the missing length for each right triangle.
4. a = 3, b = 6, c = ?
5. a = ?, b = 24, c = 25
6. a = 30, b = 72, c = ?
7. a = 20, b = ?, c = 46
8. a = ?, b = 53, c = 70
9. a = 65, b = ?, c = 97
9. A right triangle is formed between a telephone pole, a guide wire, and the ground. The guide wire
forms the hypotenuse. The height of the pole is 28 ft, and the length of the wire is 35 ft. Find the
distance between the pole and where the guide wire touches the ground.
10. A rectangular field has sidewalks that come together to make a square corner. One sidewalk is 45
ft. The other is 21 ft. About how far would I walk if I cut across the field diagonally?
Finding the Midpoint of Two Points on a Coordinate Plane
Use the Midpoint Formula to find the midpoint of the line segment connecting each pair of
 x1  x 2 y1  y 2 
,

2
2 

points. 
1. (–6, 12), (2, 8) ____________
3. (1, 8), (7, 2) ____________
5. (1, 2), (3, 4) ___________
2. (– 4, –6), (–2, –12) ____________
4. (–1, 1), (1, –1) ___________
6. (0, 0), (–5, 6) ___________
Similar Figures 1
1. Triangle RST~ BCA. Find x.
2. Trapezoid ABCD is similar to OPMN. Find x.
3. ABCD~EFGH. Find the value of x.
4. If ABC is similar to DEF, what must also be true?
A.
AB DE

AC EF
B.
AB AC

DF EF
C.
AB DE

BC DF
D.
AB AC

DE DF
Find the surface area of each shape below. Sketch each shape and label its dimensions.
Use either a net or the formula SA  2B  Ph .
1. a rect prism with a length of 12 cm, a width of 9 cm, and height of 15 cm.
2. a prism with a square base of 6 ft by 6 ft and a height of 15 ft.
3. a cube with a length, width, and height of 12 m.
Find the surface area of the cylinders. Use the net or the formula SA  2r  2rh . Use 3.14
for π.
2
1.
2.
3.
Find the surface are of each figure to the nearest tenth. Use the net or the formula SA  2B  Ph .
1.
3.
2.
4.
Find the volume to the nearest tenth of a unit.
1.
2.
3.
4.
Volume of Cylinders
Find the volume of each cylinder to the nearest hundredth. Use 3.14 for .
1.
16.5 m
r = 17 m
2. Grain is stored in cylindrical structures called silos. What is the volume of a silo with diameter 15
feet and height 25 feet?
3.
r = 4 in
24 in
4.
Volume of Triangular Prisms
Find the volume.
1.
2.
3.
4.
Use the Fundamental Counting Principle to solve the following.
License plates in a certain state contain 2 letters followed by 3 digits. All license plates are equally
likely.
4. find the number of possible license plates.
5. if license plates can not have any repeat of letter or numbers, find the number of possible
license plates.
6. what is the probability of receiving a license plate with all odd numbers?
Employee identification codes at a company contain 2 letters followed by 2 numbers.
7. find the number of possible identification codes.
8. find the probability of being assigned the code MT49.
9. find the probability that an ID code does not contain the number 7.
Equations with Variables on Both Sides
Solve. Show your work and check your answer.
1. 12x  7  8  3x  12
3.  8x  2  20  6x  6
2. 7 y  4  3 y  11
4. 6  7a  3  4a  9
Solve and check each equation.
1. 10(4  y )  2 y
3.
1
(12n  2)  14  10n
2
5.  7  11g  9  5 g
7.
12x  7  3x  8
2.  4( x  3)   x
4.  12q  4  8q  6
6. 18h  13  12h  25
8. 5( x  3)  9 x  2( x  17)
Solve the proportions. Check your answer.
1.
7
5

x 1 x  3
2.
3
9

x 2( x  2)
3.
7 9 x

10
x
4.
3
2

x  5 x 1