Download Math 8 1st Semester Name

Math 8 1st Semester
Benchmark Test
Name____________________
Date____________ Period____
STUDY GUIDE
Your test will have 33 multiple choice questions that will be
similar to the questions below. If you turn in this review,
completed and signed by your parent/guardian, on the test day
you may “buy” a test question.
Parent/ Guardian Signature: _________________
1. If A and B are independent events such that P(A)=0.14 and P(B)=0.28, what
is the probability that both A and B will occur? “and” means multiply so
.14(.28) = .0392
2. Your parents are buying a car. There are 8 car choices and 7 color choices.
How many possible outcomes exist for the car and color?
8 x 7 = 56 outcomes
3. A box contains 6 red marbles, 4 blue marbles, and 8 yellow marbles. What
is the P(yellow then red) if a marble is selected and replaced, and then a
second marble is selected? “and” means multiply so 8/18 x 6/18 = 48/324
which simplifies to be 4/27
4. Sarah rolls two 6-sided numbered cubes. What is the probability that the two
numbers added together will equal 4? There are 36 total outcomes and you
could roll 1,3 or 3,1 or 2,2 to get a sum of 4. So your answer would be 3/36
or 1/12.
5. Lynnwood High School requires all staff members to have a 6-character
computer password that contains 2 letters and 4 numbers. Find the number
of possible passwords. 26x 26x10x10x10x10 = 6,760,000
6. How would you write 0.0000006234 in scientific notation? 6.324 x 10-7
7.
A mechanic measured the gap in a spark plug and found it to be
4.5 X 10 2 inches. What is the standard form of 4.5 X 10 2 ? .045
8. What is the product of 60,000 and 700 written in scientific notation?
4.2 x 107
9. A ladder is leaning against a wall. The bottom of the ladder is 5 feet from
the wall and the ladder is 13 feet long. What is the distance from the ground
to the top of the ladder?
a2 + b2 = c 2
ladder
52 + b 2 = 13 2
b
13
25+ b2 = 169
-25
-25
b2 = 144
5
b = 12
10. Use the Pythagorean Theorem to solve for the missing side.
a2 + b2 = c 2
122 + 162 = c 2
144+ 256 = c 2
400= c2
20 = c
12m
16m
11. Bob and his uncle are building a deck in the shape of a right triangle for
his aunt’s house. He has calculated the longest board to be 625 feet.
What are the lengths of the other two sides? Oops..don’t do this one!
12. What are all the solutions of y 2 = 25? ±5
13. Estimate the value of the positive square root: about 8.6
73
14. Solve:
225
15
15. On the number line where you would locate 14 ? Between 3 and 4; a
little closer to 4
__
_____
__
16. Simplify: 6  10 √60 = √4 x 15 = 2√15 “2 times the square root of 15”
17. Give an example of an irrational number that is a decimal. 3.1415926…
18. Simplify the following expression: 103  100  92 1000 10 + 81
3+81
84
19. What is 4(n 4) when n=1
4(1-4)= 4-3= 1 = 1
43 64
20. Simplify: 5-2(53) add exponents 51 = 5
22. Evaluate the exponential expression, and write your answer as a fraction in
simplest form: (½) -2 22 = 4 (negative exponent means take the reciprocal)
23. A quality control inspector at a bolt factory examines random bolts that come
off the assembly line. Any bolt whose diameter differs by more than 0.04mm from
6.5mm is sent back. Solve the equation |d-6.5|=0.04 to find the maximum and
minimum diameters of an acceptable bolt.
d - 6.5 = .04
or
d - 6.5 = -.04
+6.5 +6.5
+6.5
+6.5
d = 6.9
or
d = 6.46
24. What is the solution of x  7  13 ?
x+7=13
-7 -7
X=6
or
x+7 = -13
-7 -7
or
x=-20
25. Solve the equation: |x| +2 = 9
-2 -2
|x|
= 7
So x = 7 or -7
26. Solve xy-5 = k for x.
+5 +5
add 5 to both sides
xy = k + 5 now divide both sides by y
y
y
and
x=k+5
y
27. P=2L +2W is the formula for finding the perimeter of a rectangle. Rewrite
the equation to solving for L.
P=2L +2W
-2W
-2W
subtract 2W from both sides
P – 2W = 2L
2
2
P – 2W = L
2
now divide both sides by 2
28. Solve for h: 7(8 +5 h) = -14 distribute first
56 + 35h = -14
-56
-56
35h = -70
35
35
h=-2
29. Solve. 2x-2 = 4x+6. notice variable on both sides; move one of them!
-2x
-2x
-2 = 2x + 6
-6
-6
-8 = 2x
now divide both sides by 2
2 2
-4=x
30. Keri baby sits on the weekends. She charges $8 for the first hour and $6 for
each additional hour. If she made $26 one evening, how many hours did she
work?
$8 + 6x = 26
-8
-8
6x = 18
X = 3 hours
31. Which inequality best describes the following situation: Sara runs 1 hour
everyday. In the 1 hour workout, she burns 200 calories. If Sara wants to burn
700 calories a week, how many hours will she need to run?
200x ≥ 700 (notice it didn’t say to solve)
32. Which graph best displays the solution to this situation: Bob can spend
$125 at Best Buy. In his cart, he has movies that each cost $17. What is the
number of movies he can buy without exceeding his set amount?
<___________________________●
7
33.Which is not a solution of the inequality 3  x  2 ?
-3
-3
-x < - 1 divide both sides by -1
X>1
SWITCH the sign!!
Solutions would be any number greater than 1 (such as 1.5, 5, 25) and NOT a
solution would be numbers like 1, 0, -12.
34. Write a statement that can be modeled by x  3  12 ?
Kelsey can have no more than 12 girls at her party. She has 3 girls on her
guest list so far. How many more girls can she invite to her party?
35. Businesses with profits less than $10,000 per year will be shut down. Write
an inequality that represents this situation.
X<$10,000
36. Which of the following is a subset of A, if A = {1, 3, 5, 7, 9,12, 13,15, 17, 19}?
An example of a subset would be {1, 7, 12}
37. The universal set includes the letters of the alphabet. Set
C={consonants}. What is C’? {vowels}
38. If set B={even numbers} and set C={2, 5, 8, 11, 14}, what is
B C?
{2, 8, 14}