Revision For Exam#1

Practice
1. The ratio of supplementary angles is 3:7. Find the smaller angle.

2. If two supplementary angles are in the ratio 3:2. Find the smaller angle?
3. Find the diagonal of a rectangle whose sides are 6 cm and 8 cm.
4. Find the length of the diagonal of a rectangle whose sides are 8cm and 15cm
5. If Sam can do a certain job in 3 days, while it would take Fred 6 days to do the same job, how
long would it take them, working together, to complete the job?
6. Tim can finish a certain job in 10 hours. It takes his wife JoAnn only 8 hours to do the same
job. If they work together, how long will it take them to complete the job?
7. One pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the
pipe and the drain open how long will it take the pool to be filled?
8. The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction
becomes 3/4. Find the fraction.
9. A woodcutter took 12 min to make 3 pieces out of a block of wood. How much time would be
needed to make 5 such pieces?
10. A trapezoid has legs 8 cm and 10 cm long. One of the bases is 11 cm long and the perimeter is 34
cm. How long is the other base?
11. Solve each equation
a) 5𝑥−18=3𝑥−6 b) 4(x+7)-11=3x-12 c) 5(x-11)-7=3x-8 d) 7x-13=5x-27
12. Express as a polynomial

13. Simplify
14. Solve each equation

a) b)
15. Find the value of the sum x+y for the given system of equations
16. Simplify the expression
17. O-is a center of the circle. <ABD=700, <AOB=?
18. Simplify:
21. AB=8, BC=6, CD=4, DE=5, find the perimeter of the given figure
22. Evaluate
23. , find the value of
24. If the given equation has infinitely many solution, then find value of b
25. Evaluate
26. Solve:
27. ABCD- is a square, and A(4;1), C(2;-1), D(2;1), find coordinates for vertex B.
28. Aladdin had 120 manat. He spent 30% of his money. How much money did he spend?
P1
29. The perimeters of two similar equilateral triangles is in the ratio =7 , find the ratio of the sides of
P2
these triangles.
30. How many angles does a polygon have, with the number of diagonals equal to the number of sides?
A) 3 B) 4 C) 5 D) 6 E) 9
31. Find the value of the expression A) 0.5 B) 1 C) 1.2 D) 1.5 E) 2
32. Find the diagonal of a rectangle whose sides are 6 cm and 8 cm.
A) 9 cm B) 10 cm C) 11 cm D) 12 cm E) 14 cm
33. If one of the bases of a trapezoid whose mid-segment is 12 cm is 8 cm, find the length of the other base.
A) 22 cm B) 20 cm C) 18 cm D) 16 cm E) 14 cm
34. find the sum of integer solutions that satisfy the given inequality.
35.Find the product xy for the following system of equations
38. What is the degree of the polynomial
A) 9 B) 24 C) 8 D) 7 E) 15
39. If a is divided by 4 and the remainder is 3, Find the remainder of 3𝑎2+5𝑎+5 divided by 4.
40. Find the circumference of a circle whose radius is 6 cm.
A) 3𝜋 cm B) 6𝜋 cm C) 9𝜋 cm D) 12𝜋 cm E) 18𝜋 cm
41. The salary increased from 50 manats to 60 manats. By what percentage did salary increase?
A) 10% B) 15% C) 20% D) 25% E) 30%
42. If two similar triangles with total areas of 120c𝑚2 have a similarity factor of 2, find the area of the
smaller triangle.
43. Knowing that the total surface area of the cube is 54, find the diagonal of the base of the cube.
44. There are 5 white, 9 black and 6 yellow balls in the box. Find the probability that a stone drawn from the
box is white or yellow.
a) Karl can clean a room in 3 hours. If his little sister Kyra helps, they can clean it in 2.4
hours. How long would it take Kyra to do the job alone?
b) Doug takes twice as long as Becky to complete a project. Together they can complete the
project in 10 hours. How long will it take each of them to complete the project alone?
c) Joey can build a large shed in 10 days less than Cosmo can. If they built it together, it
would take them 12 days. How long would it take each of them working alone?
d) Clark can complete a job in one hour less than his apprentice. Together, they do the job in
1 hour and 12 minutes. How long would it take each of them working alone?
e) A sink can be filled by a pipe in 5 minutes, but it takes 7 minutes to drain a full sink. If both
the pipe and the drain are open, how long will it take to fill the sink?
f) If an apprentice can do a piece of work in 24 days, and apprentice and instructor together
can do it in 6 days, how long would it take the instructor to do the work alone?
g) A carpenter and his assistant can do a piece of work in 3.75 days. If the carpenter himself
could do the work alone in 5 days, how long would the assistant take to do the work alone?
h) If Sam can do a certain job in 3 days, while it would take Fred 6 days to do the same job,
how long would it take them, working together, to complete the job?
i) Tim can finish a certain job in 10 hours. It takes his wife JoAnn only 8 hours to do the same
job. If they work together, how long will it take them to complete the job?
j) Two people working together can complete a job in 6 hours. If one of them works twice as
fast as the other, how long would it take the slower person, working alone, to do the job?
k) If two people working together can do a job in 3 hours, how long would it take the faster
person to do the same job if one of them is 3 times as fast as the other?
l) A water tank can be filled by an inlet pipe in 8 hours. It takes twice that long for the outlet
pipe to empty the tank. How long would it take to fill the tank if both pipes were open?
m) A sink can be filled from the faucet in 5 minutes. It takes only 3 minutes to empty the sink
when the drain is open. If the sink is full and both the faucet and the drain are open, how
long will it take to empty the sink?
n) It takes 10 hours to fill a pool with the inlet pipe. It can be emptied in 15 hours with the
outlet pipe. If the pool is half full to begin with, how long will it take to fill it from there if
both pipes are open?
o) A water tank is being filled by two inlet pipes. Pipe A can fill the tank in 4.5 hours, while
both pipes together can fill the tank in 2 hours. How long does it take to fill the tank using
only pipe B?
p) One pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With
the pipe and the drain open how long will it take the pool to be filled?

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Practice

1. The ratio of supplementary angles is 3:7. Find the smaller angle.

12. Express as a polynomial

14. Solve each equation

16. Simplify the expression

17. O-is a center of the circle. <ABD=700, <AOB=?

23. , find the value of

31. Find the value of the expression A) 0.5 B) 1 C) 1.2 D) 1.5 E) 2

35.Find the product xy for the following system of equations

38. What is the degree of the polynomial

40. Find the circumference of a circle whose radius is 6 cm.

A) 10% B) 15% C) 20% D) 25% E) 30%

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