Test 5 Section 2 - #17 (page 642)

It's important to note that when the SAT tells you that a line passes through the origin, they're giving you a point on the line: (0,0). So we know line l contains points (0,0) and (t, t+1).

Since we also know that it's perpendicular to the line y = -4x + k, we know line l has a slope of +1/4 (the negative reciprocal of the slope of the line it's perpendicular to).

We can use these two facts to solve for t. Set up the slope equation using the points we know:

1/4 = [t + 1 -0]/[t - 0]

1/4 = [t + 1]/[t]

t/4 = t + 1

t = 4t + 4

-3t = 4

t = -4/3

2010 PSAT - Saturday - Section 2 (Math)

The following are TestTakers' suggestions for solving the problems on the October 16th, 2010 PSAT, Section 2 (a math section). Click "Read More" to view!

Test 1 Section 3 - #15 (page 400)

I love this question because it's susceptible to multiple techniques.  GUESSTIMATE makes the most sense:

You know this slope is negative just from looking at it: it goes down from left to right.  So that leaves us with only (A) and (B) before we even look very closely.  When we do look more closely, we can tell that this slope isn't very steep...its run is bigger than its rise, if you will.  The only answer that really makes sense is (B): -1/2.

Let's confirm that by putting our answer back into the question.  This is the other way we could have solved it, BACKSOLVE (using the slope formula).

Slope is rise over run, or:

We're luck here that our line goes through the origin, so we can replace y₁ and x₁ with 0.  Basically, we're looking, then, for an answer choice in the form of y/x that fits our diagram at point A.  Again, we're basically back to guesstimating here, in that the way we make our decision is that (-2,1) looks more like point A than (-1,2) does.  Either way, our answer is (B).

Test 7 Section 9 - #11 (page 798)

You can use your graphing calculator to help you visualize this (if you use a graphing calculator).  They tell you the slope of the line is -4/5, so you can graph a line with that slope simply by putting "y = (-4/5)x" in your calculator.  You can do the same with all the answer choices, and eyeball pretty easily which one is a true reflection across the x-axis.

Let's assume for a minute that you're doing this question without a graphing calculator, though.  A reflection across the x-axis negates the y-values of your graph.  How will that affect the slope?  Well, let's use the same equation I made up above to see:

2 easy points to find on that graph are (0,0), and (5,-4). If I reflect those two points across the x-axis, what happens?  (0,0) stays the same.  (5,-4) reflects to (5,4), because we're negating the -4, to get +4.  What's the slope of a line that goes through (0,0) and (5,4)?

(B) is our answer.

Test 7 Section 7 - #12 (page 787)

If we're trying to identify the segment with a slope of -1, the first thing I want to do is eliminate the segments that have positive slopes.  We know any of these segments that are going up as we're going from left to right have a positive slope, so we're not even going to consider them.  That eliminates segments OC and OD.

OA, OB, and DC all have negative slopes.  If you've got a good eye for slopes,  you've got a good feeling about (E) right now, because OA looks way too steep, and OB looks way too gradual.  It's a good idea to confirm though, so let's put the points into the slope formula just to be sure.

DC goes between points (1, 3) and (3, 1).  So our slope is:

Yep, (E) is our answer.

Note that we can use this same formula to find the slopes of all the segments for practice, or just for fun (hah!):  Slope of OA = -3, slope of OB = -1/3, slope of OC = 1/3, slope of OD = 3.

Test 2 Section 5 - #6 (page 464)

The key here is recognizing that slope = rise/run (or, in this question, y/x).  According to this question the slope of that ramp is 7/16.  We can actually BACKSOLVE this one, by basically taking our answers and plugging them into rise/run (or, like we said, y/x) to see which one will give us that same fraction.  We know our rise (or y) is 3.5 feet.  With backsolve, always try (C) first:

(C) 3.5/20 = 7/40.  Nope.  Way too long on bottom.  Go smaller.
(B) 3.5/12.5 = 7/25.  Still too long on bottom, but getting warmer...
(A) 3.5/8 = 7/16.  BINGO.