Practice[+] aims to teach skills beyond those accessible in school, using varied questions that may seem exotic at first. It does not aim to teach basic mathematical concepts; it is assumed you have covered those in school before delving into Practice[+] or the CSAT. If you haven’t covered the required syllabus for a particular question then you can wait until you do, and can skip that question, to avoid getting the wrong impression about difficulty or overlap. The Related Topics section of each question does provide refreshers, which you may undertake on your own if you feel adventurous. However, remember that you have choice in the actual CSAT test! You may still not cover some topics in school by the time of your test, and that’s fine.

Practice[+] is not meant to serve as the only preparation for content such as the CSAT, so at first you might feel that Practice[+] is challenging. Don’t worry, the key is to persist. That said, it’s best to ensure you undergo enough prior-preparation for the more basic concepts first as indicated on the CSAT page.


Each question page from a Practice[+] paper contains a CSAT or CSAT-like question, Related topics, Warm-Up questions, a set of carefully crafted set of progressive Hints, and a full Solution; all of these are detailed below. When you first access a Practice[+] question page, you will notice that most fields are hidden. Click on the [+] links to reveal the content − that’s where the name comes from, by the way.

We strongly encourage you to read the following guide, heed its advice, and employ its steps in the order posted below, so that you make out the most of Practice[+].

The CSAT Question

By default, this is the only content that isn’t hidden. First, attempt it on your own, for at least 30 minutes (Section A) or 60 minutes (Section B) when you have started out with Practice[+]. As you cover more papers you can decrease those times to approach the limits of the actual test. Remember that the primary purpose here is to learn.

It is important that you don’t rush to other sections or hints, or refer to books/internet. The most important part of any learning process is your own struggle. It enables consolidation and sharpens skills. Referring too early to hints or solutions goes against those goals and usually creates only short-lived skills. Take your time and persist.

If you’re willing to push past the above time limits, then we encourage it!

Progressive hints

The 2nd most important part. Designed to go from vague to explicit, they follow the milestones of the thinking process. They teach you how to think by gently pointing in the right direction, instead of revealing even intermediary results. This allows you to make ample progress on your own, which is extremely important. You may discover that the slightest hint gets you a long way! Either way, after a while you will notice you won’t need to open all the hints to figure out the solution. That’s great, as it also offers the satisfaction that you solved the question mostly by yourself!

It’s very important to spend a good amount of time thinking before revealing the next hint! Do your best to understand and translate it into something meaningful towards making progress. Each hint carries new information towards the solution, so ask yourself what that is and see what you can do with it. If you feel you’re really not getting anywhere, reveal the next hint. Continue like this till the end, making sure, once again, that you spend more than sufficient time on each hint.

If you feel some of the hints contain keywords you don’t recognize then it could mean you haven’t covered those concepts in school; and if you feel sufficiently certain about it, then reveal the Related Topics section. This may possibly spoil the fun of the thinking process as the key to the solution may lie in the name of a related topic, but it may be required in some situations.

Warm-up questions

By revealing and attempting the warm-up questions you may discover that they hint more clearly at a useful concept for the CSAT question, allowing you to make more progress with it. Despite the name, the warm-up questions are mostly there to consolidate the raw concepts from the Related Topics.


If all fails, then that’s what the full solution is there for. It’s okay to feel you wouldn’t have thought of that solution. You are learning, and that’s the most important aspect! On to the next question!

It is worth checking the full solution regardless: maybe you discovered an alternative solution, in which case, you can feel rightfully proud (and free to let us know about it). Note that the Related Topics listed pertain to the solution shown, so they may not directly apply to alternative solutions.