Math help please!

Test Preparation SAT Preparation
1

<p>The digits 1, 2, 3, and 4 are to be arranged randomly to make a positive four-digit integer. What is the probability that the digits 1, 2, and 3 will be directly next to each other, in that order, from left to right? </p>

<p>A) 1/12
B) 1/8
C) 1/6
D) 1/4
E) 1/3 </p>

<p>The function f is defined by f(x)= x/(x-4)-2 </p>

<p>Note: Those parentheses around x-4 are absolute value bars. I don't know how to make those on the computer lol. </p>

<p>What are all values of x for which f(x) is NOT defined? </p>

<p>A) x=0 and x=2
B) x=0 and x=4
C) x=2 and x=4
D) x=2 and x=6
E) x=4 and x=6 </p>

<p>At North High School, the ski club has 15 members and the debate club has 12 members. If a total of 11 students belong to only one of the two clubs, how many students belong to both clubs? </p>

<p>A) 2
B) 7
C) 8
D) 12
E) 16 </p>

<p>The lengths of the sides of an isosceles triangle are 20, n, and n. If n is an integer, what is the smallest possible perimeter of the triangle? </p>

<p>A) 40
B) 41
C) 42
D) 44
E) 60</p>

2

<p>bump 10char</p>

3

<p>1) The two possibilites are 1,2,3,4 and 4,1,2,3 those are two out of 24 possible combinations</p>

<p>2)The denominator essentially has to equal to zero for it to be not defined
so |x-4| = 2 …x = 6, x = 2</p>

<p>3)
Let x = the number of students who took both debate and skiing
then you know only skiing = 15-x, only debate = 12-x
(12-x) + (15-x) = 11
x = 8</p>

<p>4) you know that if n was to equal 10 then you would have a straight line
to get a triangle all you have to do is add one to each n value
so 10+1 = 11
10,11,11 is the smallest iso and the sides added up = 42</p>

4

<p>1- A bc the poosiblties is 4 times 3 times 2 times 1 which is 24 and two possiblties for numerator so 2/24=1/12
last one is C-42
any 2 sides of triangle addded togetherhave to be bigger than the other side.
so the smallest n can be is 11</p>

5

<ol>
<li>The digits 1, 2, 3, and 4 are to be arranged randomly to make a positive four-digit integer. What is the probability that the digits 1, 2, and 3 will be directly next to each other, in that order, from left to right?</li>
</ol>

<p>Total number of possibilities = 4! = 24</p>

<p>The possibilities that fit are:
1234
4123</p>

<p>2/24 = 1/12</p>

<p>Choice A</p>

<ol>
<li>The function f is defined by f(x)= x/|x-4|-2
You want to see where the denominator is 0 - this is where f(x) is undefined.
In order for the denominator to be 0, x must be 2 or 6:</li>
</ol>

<p>|x-4|-2 = |2-4|-2 = 2-2 = 0
|x-4|-2 = |6-4|-2 = 2-2 = 0</p>

<p>Choice D</p>

<ol>
<li>At North High School, the ski club has 15 members and the debate club has 12 members. If a total of 11 students belong to only one of the two clubs, how many students belong to both clubs?</li>
</ol>

<p>Add the two club’s members:
15+12=27 </p>

<p>Subtract by the number of students in only one club:
27-11=16 </p>

<p>Divide by 2 to get the number of students in both clubs.
16/2 = 8</p>

<p>Choice C</p>

<ol>
<li>The lengths of the sides of an isosceles triangle are 20, n, and n. If n is an integer, what is the smallest possible perimeter of the triangle?</li>
</ol>

<p>I’m gonna go with choice C:
"The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides. "</p>

<p>In order for this to hold true, the smallest value of the other two sides must be 11. Giving you a perimeter of 42.</p>