In music theory, it is very important to have the fundamentals down before learning more, simply because it builds upon those fundamentals. Just to make sure that the fundamentals have been established, I would ask a question like "What does the bottom number in the time signature indicate?"
To answer this question, the student would need to know what a time signature is, the purpose of the time signature, and a general knowledge on rhythm and notes. The bottom number indicates the type of note that gets the beat. So with a time signature of 4/4, the bottom 4 indicates that the quarter note gets the beat. And as a bonus answer and for clarification, the top number is the number of notes in a measure. So there would be 4 quarter notes in a 4/4 measure.
The main components of English, depending on the level, are grammar and vocabulary. As a tutor I would expect to review essays looking for grammatical or spelling errors or to teach the basis of sentence structure such as different tenses and verb-subject agreement. A great tool for any form of language acquisition is repetition. So although I am asking one question, I would realistically ask multiple questions of the same structure. An example question would be as follows: Choose the best conjunction to combine the two sentences in order to make one sentence. My friend likes to sing _____(and/but) she likes to dance.
I would start answering by making sure that the student understands what a conjunction does. Conjunctions are used to combine sentences or clauses and can determine the relation between those sentences. For the example, there are 2 options for the conjunctions: one that means that the two sentences are similar and one that means that the sentences dissimilar or conflicting. Because both sentences are stating what the speakers friend likes, they are similar in that regard. So the conjunction to use would be “and".
The two main topics covered in algebra are equations and the relation these equations have on graphs. A problem addressing the former would be to solve the equation: 4(5x - 2) - (2x - 6) = -4(3x + 5) + 24
The first step to solving an equation is to consider the order of operations, or PEMDAS. P-parentheses, which we do have. So the first step would be to multiply the factors that precede the parentheses: 20x-8-2x+6=-12x-20+24 E-exponent, we don't have any M-multiplication, none D-division, none A-addition and S-subtraction. So the next step in solving this equation is to group like terms. So terms that are integers and those that have the 'x' variable. So we would have 18x-2=-12x+4 With each side of the equation simplified, we now want to get the 'x' variable onto one side, which can be done by adding 12x to the left side. With the variable on one side, we now want the integers on the other. So we would add 2 to the right side. Now we have 30x=6 The goal is to have a statement where the variable equals a number, or x=?. So to get x by itself, we would divide each side by 30 giving us x=6/30. Further simplifying, x=1/5