<p>I am going through Barron's and I am trying to deal with every question using only a scientific calculator..
I came across some questions like : </p>
<p>Solve x^5 - 3x^3 + 2x^2 - 3 > 0 (PG 56)</p>
<p>Solve 2Sinx + Cos2x = 2Sin^2x - 1 for x<= 0 <= 2pi</p>
<p>Find values of x on interval [0,pi] for which cosx < sin2x (PG 75)</p>
<p>This is probably the only place where I can ask a question like this.. Is it even possible to get a good score without graphing calculator ?</p>
<p>1st question: There are 2 ways to do this: 1. Hit and trial, 2nd Sketch the graph (I don’t know if you know this or not, but this is pretty easy. You’ve to follow a few steps- I learnt it at my IIT coaching classes). For exams, I’d recommend going with hit and trial. Just put in the values of the options. For example =, if option A is [2, 4], put in 3 and check if the inequality holds. Repeat for all other options.</p>
<p>2nd question (i’m assuming that in RHS it’s 2 times (Sinx)^2): Just put cos2x as 1-2(sinx)^2. The resulting equation is quadratic in sinx. Put sinx=t and solve the quadratic. answer is t=-1/2 or 1. Put t= sinx and find the values of x.</p>
<p>3rd question: Put sin2x= 2sinx.cosx. The equation would become cosx.(1-2sinx)<0. Split the interval in [0,pi/2], and [pi/2, pi]. For first interval, cosx is positive , so won’t change the sign and hence can be ignored. Therfore you gotta solve 1-2sinx<0 which means solving for sinx>1/2 which is [pi/6, pi/2]. For interval pi/2 to pi. cosx is negative. You can remove cosx but after reversing the inequality sign. It means solving for sinx<1/2 in interval pi/2 to pi. That gives us interval [5pi/6, pi]. That’s the answer. Please check if the equality holds for 0, pi/6, pi/2, 5pi/6, and pi. I’m running short of time.
Hope I’ve not made any stupid mistakes!
Yes. it’s possible to get a good score w/o a graphing calculator. I got an 800 w/o any calculator in Math Level-II.</p>
<p>Great! I was seriously wishing for you to comment here and ignite my fire back! </p>
<p>Now I solved the 2nd one, got to the point where sin x = -1/2 and sinx = 1 - Where to go now ? I’ve hit the wall. Book says the intersection points are 1.57, 3.67, 5.76. It has chosen Ymin = -4 and Ymax = 4
Hmmm 
</p>
<p>Dude I think you need to do trigonometry again thoroughly. Since the question asks for values in (0, 2pi) plot the graph of sinx b/w 0 and 2pi. Just see where the value of graph is 1 and -0.5. The values are pi/2, 7pi/6, and 11pi/6. Put pi=3.14. Those are the answers. I’m not sure what Y is…</p>
<p>I am going through Trigonometry again; it’s just a bit discouraging when a prep book says “Put the equation 1 in left side and 2nd on right of your calculator, get the points, those are your solutions” =w=
Anyways thanks, I was missing on that bit. </p>