End of the Year Diagnostic Questions

Name________________________Class___________
Date____________
End of the Year Diagnostic
Directions:​ Please complete as many questions as possible. If you do not remember a topic, please try
your best. ​Be sure to show all work!
1. Evaluate the following expression where ​a​ = – 5, ​b​ = 1, and ​c​ = – 4
4√2a2 −b
2
2. Simplify the following expression.
24 − 8 ÷ 2 · 4 − ||3 − 23 ||
+c
3. Solve for x.
2
3 (x
+ 5) = 4
4. Solve for x.
5. Solve for n.
2(x − 4) + 35 > − 5(x − 1) + 1
6. Simplify the following expression.
2
a6 b c8
7
a2 b c8
n−15
2
=
n+3
10
−3
7. Simplify the following expression.
(4k 3 + 3k 2 ) − (3k 3 − 4k + k 2 ) + (5k 2 + 5k)
8. Simplify the following expression.
2
(x − 3)(7×2 + 8x − 1)
(3x − 7)
10. Divide and simplify.
4
8
9. Simplify the following expression.
11. Factor the polynomial.
6
2
(2x + 32x + 8x ) ÷ 8x
20m7 + 28m3 − 12m2
12. What is the percent increase from 625 to 875?
13. Circle the letters of the table(s) below that do not show an example of a proportional relationship
between x and y. For each table below that does exhibit a proportional relationship, give the constant of
proportionality, k.
a.
b.
c.
d.
x
y
x
y
x
y
x
y
3
4
-4
20
2
24
1
½
6
10
-3
15
4
12
2
1
9
16
-2
10
6
8
3
1½
12
22
-1
5
8
6
4
2
k = _________
k = _________
k = _________
k = _________
14. There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
This must be done algebraically.
15. A tennis player asks the referee a question. The sound of the player’s voice travels only 30 feet. Can
the referee hear the question? Explain.
16. Find the area of the shaded region.