### Diagnostic Math Drill #1 - GET SOME.

I spent some time today putting together a diagnostic math drill for you to try, if you're so inclined. It's 20 (pretty hard) questions, formatted more nicely than I usually bother to do on this blog and completely printable. It's not meant to be done in 25 minutes like an SAT section; it's meant to help you identify some weaknesses so that you can start to fix them.

Whether you're just starting your SAT journey or you've been at it for a while, my hope is that this will be a great jolt to your math prep.

--OR--

All done with this one and want more? Try the more difficult Diagnostic Drill #2!

1. Hi,

Where did you get these questions from? Are they from the college board (real SAT questions)?

2. I wrote them, based on what I've seen in real College Board tests.

3. I've recently stumbled across your website in my attempts to find some hard math problems to help me improve my chances at an 800. After taking the first diagnostic test I got #'s 10 and 14 wrong,  Could you possibly provide a detailed explanation for #14 and I believe your answer key is wrong for number 10.

4. I'm glad you found the site, and thanks for taking the time to comment! The answer key is definitely not wrong for #10. That parabola has a positive y-intercept and opens upwards, so its equation will have a positive coefficient for the x^2 and a positive constant term. Choice A is the only one that accomplishes that. I encourage you to graph all the choices to prove it to yourself.

As a general rule, I like to solve shaded region questions like #14 by finding the area of the whole shape (in this case it's 80 because the length of the rectangle is 8 and the width is 10), and subtracting the area of the unshaded region(s). In this case, there are 4 unshaded right triangles, and each one has one leg that's 4, and one that's 5. So each unshaded triangle has an area of ½(4)(5), or 10. The whole rectangle is 80, and there are 4 unshaded triangles with area 10, so the shaded region must be 80 - 4(10) = 40.

5. Ohhhh I was thinking the +9 referred to the  location of the vertex of the parabola. Thank  you for explaining that and for number 14. I just realized that I got number 18 wrong as well and cant seem to figure it out either. These questions are definitely helping me figure out what I need to work on. Thanks for your time :D

6. I'm glad the drill is helping you isolate weak areas. That's exactly my intention! :)

For #18, I think an image might help explain it better than just me writing words, so I've attached a screencap from the solutions section of my book. Click it to make it bigger. Hope that helps!

7. Shouldn't the answer be E for #4?  Even using the formula for the nth term of geometric sequence I get 1 as the ones digit.  an=a1(r)^n-1 so a96=1(7)^95 = 1.92x10^80

8. Your calculator isn't going to help you on that question. The huge number you got is rounded well before it gets to the units digit. See the attached image for the solution to this I put in the Math Guide.

9. how do you do number 1? I tried it many times but still didn't get it.

10. You're very welcome!

11. Here's an image of the solution that's in my book. A general rule for questions like this: first figure out what f(2) is, then substitute. Don't try to write one really long expression.

12. Hi, can you please explain number 13? I keep on getting C. Since A = Ï€r^2 - A should = Ï€(7Ï€)^2. I'm not sure where the 14 comes in.

13. You've got all the math for 13 figured out...you just need to read the question more carefully! It asks you for diameter, not radius.

19 is a backsolve problem. Start by assuming the right answer is (C), and 192 people were at the concert before people started leaving. 1/3 of them, or 64, leave. Then 20 leave. Then half as many as left at first (half of 64 is 32) leave. 192 - 64 - 20 - 32 = 76, so 192 is the right answer!

15. For #17, there are 2 things you know about line l: it's perpendicular to a line with a slope of -1/2, and it has a y-intercept of 0 (it goes through the origin). Since perpendicular lines have negative reciprocal slopes, you know line l has a slope of 2. So we have enough information to write the equation of line l in slope-intercept form: y = 2x.

Now you can substitute the point (a, a + 2) into that equation to solve for a:

y = 2x
a + 2 = 2a
2 = a

#18 is too hard to explain without pictures, so click the scan below of the explanation from my book.

16. Can you please explain #2?

17. To get #2 right, you need to understand the concept of percent change. Calculate the amount of change for each answer choice, and then put it over the STARTING value for the month. For example, from January to February, there's a \$700 change. Since January comes first, your starting value is the January value, \$2500. 700/2500 = 0.28, so your percent change from January to February is 28%.

18. Thanks Mike for these great questions!

19. :) you're welcome!

20. I got 44 for #1. Not sure where I made a mistake! What I got is 48 - 9 + 5 = 44

21. To solve #1, first find f(2):

f(2) = 8(2) + 2 = 18

Then use that to evaluate 3f(2) + 1:

3(18) + 1 = 55