Let’s closely examine the two sentences you presented (italicizations mine):
(1) “This section covers a breadth of important information that will help you tackle any analytical problem that is thrown at you on the exam.”
(2) “This section covers a breadth of important information that will help you to tackle any analytical problem that is thrown at you on the exam.”
To simplify the analysis, let’s examine Sentence 2 first. In that sentence, the italicized phrase “to tackle any analytical problem that is thrown at you on the exam” is what’s called an infinitive phrase. We will recall that an infinitive phrase is simply an infinitive—a verb in the present tense that’s normally preceded by “to”—together with its modifiers, objects, or complements. In the sentence in question, the infinitive is “to tackle” and its modifier is the phrase “any analytical problem that is thrown at you on the exam.”
Now, in Sentence 1, the italicized phrase “tackle any analytical problem that is thrown at you on the exam” is what’s called a bare infinitive phrase. A bare infinitive phrase is one where the infinitive—“to tackle” in this case—has dropped the “to.” The particular construction of Sentence 1, in which the infinitive “to tackle” works in conjunction with the helping verb “help,” allows the dropping of the “to” in that infinitive with no adverse effect on the grammar and semantics of the sentence. In fact, we will notice that the construction with the bare infinitive reads and sounds better than the one with the full infinitive (“to tackle” spelled out), which is the case in Sentence 2.
So, you ask, what’s the general rule for using the bare infinitive form or the regular infinitive?
There are some sentence constructions where certain infinitive phrases have to drop the “to” for the sentence to work properly or—at the very least—sound right. This happens in two specific instances: (1) when the infinitive phrase works in conjunction with such perception verbs as “see,” “feel,” “hear,” and “watch”; and (2) when the infinitive phrase works in conjunction with such helping verbs as “help,” “let,” and “make.” (Sentence 1, of course, belongs to the second category, and it just so happens that although Sentence 1—the one with the bare infinitive “tackle”—reads and sounds better than Sentence 2, Sentence 2 itself—the construction that uses the full infinitive “to tackle”—also works perfectly.)
But we must keep in mind that there are sentences where only the construction that uses the bare infinitive will do, as in this sentence: “We saw the building collapse like a deck of cards.” The following construction that uses the full infinitive sounds very awkward and should be avoided: “We saw the building to collapse like a deck of cards.”
The bare-infinitive construction is also called for in the following sentence where the infinitive “to rise” works in conjunction with the perception verb “watch”: “They watched the young man rise spectacularly in the organization without making any effort at all.” Now see how awful and stilted that sentence becomes when it uses the full infinitive “to rise” instead: “They watched the young man to rise spectacularly in the organization without making any effort at all.”
Indeed, there aren't any hard-and-fast rules when we are faced with a choice between using a full infinitive and a bare infinitive in a sentence. We ultimately just have to play it by ear.
