Jan. SAT Math

Test Preparation SAT Preparation
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<p>I am currently working through some of the math questions I missed on the January SAT I administration by way of an awesome service known as QAS. With time, I figured out a majority of the mistakes I made on the math portion on the test and duly rectified them. However, I still can't figure out a few of them, and I really wish to improve on my dysmal 590 Math score from January, so help on these questions would be much appreciated. I've included a few questions missed on the test or that I just did not understand, and it would be great if someone could answer and then provide justification for it. For my sake, a how-to-solve step by step explanation for Dummies would be great as well. </p>

<p>Sec. 3 Q. 16 (Grid-in)</p>

<p>Let the function h be defined by h(x) = 3x - 5 for all values of x. If h(5) = t, what is the value of h(t)?</p>

<p>Sec. 5 Q. 13</p>

<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>Sec. 8 Q. 12 </p>

<p>If 2(x +5)(x - 5) = a, what does x^2 - 25 equal in terms of a? (answered correctly but I had no rationale behind my choice..)</p>

<p>A. a^2
B. sq. rt. a
C. 2a
D. a
E. a/2</p>

<p>Sec. 8 Q. 16</p>

<p>6x + 3 >_ a >_ means greater than or equal to</p>

<p>If the inequality above is true for the constant a, which of the following could be a value of x?</p>

<p>A. a/6
B. a/6 - 1
C. a/6 - 3
D. a - 4/6
E. a - 5/6</p>

2

<p>I can answer the first three for you but the last one looks strange to me… perhaps I am just misreading it. </p>

<p>Sec 3 Q.16 (Grid in)</p>

<p>First, plug in the function h(5) into the equation to find t.
h(5)=3(5)-5
= 10</p>

<p>Therefore t must equal 10. Now plug in h(t) a.k.a h(10)
h(10)=3(10)-5
= 25</p>

<p>Therefore your grid in answer will be 25.</p>

<p>Sec 5. Q. 13</p>

<p>Oh, this one is tricky :D. So there are two ways which 1,2,3 can be found in that order, either in 1234 or 4123. And to find the number of possibilities of 4 digit numbers you must multiply 4 by 3 by 2 by 1 which ends up giving you 24. Therefore, you are left with 2/24 which reduces to 1/12 which is A!!!</p>

<p>Sec 8. Q12.</p>

<p>You must recognize that x^2-25 is equivalent to (x+5)(x-5) when it is expanded. As a result, you see that (x+5)(x-5) is being multiplied by 2. If x^2-25 is represented by “a”, then the relation between the two expressions is answer C, “2a”</p>

3

<p>Thanks for the response cdn, but the answer to sec. 8 q. 12 was E, a/2. I dont know why (that’s what I’d like to know). It’s wishful thinking that the collegeboard would give complete answer explanations for there…but thanks for assistance on the first couple questions!</p>

4

<p>Let the function h be defined by h(x) = 3x - 5 for all values of x. If h(5) = t, what is the value of h(t)?</p>

<p>lets start here.</p>

<p>Ok, h(x)= 3x-5. h(5)= 3(5)-5=t so…h(5)=15-5=10, so t=10. Follow?
plug in h(t)=h(10)
h(10)=3(10)-5=…25</p>

<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>First, figure out how many options there are.
4 spots
Spot 1: 4 possibilities (1,2,3,4)
Spot 2: 3 possibilities
Spot 3: 2 possibilities
Spot 4: 1 possibility
multiply</p>

<p>There are 24 (4x3x2x1) different combinations of 1,2,3,4.
Now, think of all the ways 1,2,3 could be next to each other.
1234
4123</p>

<p>2 possibilities</p>

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

<p>so A.</p>

<p>If 2(x +5)(x - 5) = a, what does x^2 - 25 equal in terms of a? (answered correctly but I had no rationale behind my choice…)</p>

<p>A. a^2
B. sq. rt. a
C. 2a
D. a
E. a/2</p>

<p>This one is pretty easy. 2(x-5)(x+5) in terms of a. Well, try to get common factors.</p>

<p>2(x+5)(x-5)=a…but also equals 2(x^2-25)=a…right?
so, if 2(x^2-25)=a, then x^-25 should equal a/2.</p>

<p>6x + 3 >_ a >_ means greater than or equal to</p>

<p>If the inequality above is true for the constant a, which of the following could be a value of x?</p>

<p>A. a/6
B. a/6 - 1
C. a/6 - 3
D. a - 4/6
E. a - 5/6 </p>

<p>Plug in the numbers and use a random number (we’ll say 5) for a.</p>

<p>A. 6(5/6)+3 ><em>5…5+3></em>5…check!
B. 6(5/6-1)+3 ><em>…(5-6)+3></em>nope
C. if a-1 was too small, then a -3 will almost certainly be
D. 6(5/6-4/6)+3><em>…5-4+3></em>5…nope
E. If -4/6 was too small, then -5/6 will almost certainly be.</p>

<p>I hope this helps. Make sure you double check your work. I took the SAT for the first time in March, and left thinking I had an 800 in math for sure (but I missed 5 and got a 690 :frowning: )</p>

<p>So, take your time, pace yourself, and double check (and, if like me you have extra time, triple and quadruple check)</p>

5

<p>^ Above poster; you are erroneous in your last answer: The question was “If 2(x +5)(x - 5) = a, what does x^2 - 25 equal in terms of a?”…They aren’t asking what the relation is between the two, and even if they did you would have gotten it wrong. We split up x^2-25 into (x+5) (x-5) and thus, when comparing the two equations, one can infer that the former is double the latter. If the former is a, this must mean that the latter (x^2-25), is half of a. Hence, the answer would be “E”, which is a/2, or 1/2a. Lol, I’m in 9th grade and they explain this in depth for integrated algebra.</p>

6

<p>I meant the first poster was wrong about his last answer. Sorry for the misinterpretation.</p>

7

<p>Sec. 8 Q. 16</p>

<p>6x + 3 >_ a >_ means greater than or equal to</p>

<p>If the inequality above is true for the constant a, which of the following could be a value of x?</p>

<p>A. a/6
B. a/6 - 1
C. a/6 - 3
D. a - 4/6
E. a - 5/6</p>

<p>6x + 3 >_ a
6x >_ a - 3
x >_ (a-3)/6</p>

<p>from here we can see that a/6 is greater than (a-3)/6 The answer is A.
or…if you didn’t notice that you can choose a convenient value for a such as 0.
so… x >_ -3/6
now look for an answer choice that fits this condition.
Try choice A.
0/6 >_ -3/6 correct!!</p>