ACT English is about understanding grammar, proper sentence structure, and mechanics. If the student does not have a good foundation in this material and starts sentences with, "Me and Billy went to see a show," I will get that corrected.
Besides Pre Algebra, the most covered topic on the ACT is Plane Geometry. Parallel lines are lines with the same slope and perpendicular lines are lines whose slopes are negative reciprocals. The area of a circle is Pi*r^2, the area of a triangle is 1/2*b*h, and the area of a rectangle is l*w. All these formulas constitute Plane Geometry.
You really don't need a strong foundation in science to do well in the Science section. The ACT Science section is really about reading and understanding graphs and charts that pertain to science topics. I will teach the student how to quickly size up a graph and interpret the results.
At the heart of Algebra 1 is the ability to solve linear equations. Equations of the form ax + b = c. There are two steps needed to solve such an equation. First you subtract b from both sides and then you divide both sides by a. It is necessary to understand these two steps before proceeding in algebra.
In Algebra 2 you learn how to solve 2 linear equations with 2 variables. A popular method is to multiply both sides of one equation by a number so that the coefficient on one of the variables is the same in both equations. Then you subtract one equation from the other to eliminate that variable. The problem has then been reduced to a problem from Algebra 1.
Calculus is all about derivatives and integrals. Derivatives are instantaneous rates of change and integrals are areas under curves. It turns out that derivatives and integrals are inverses of each other. That is, the area under the curve of a derivative function is the function itself. Fascinating.
A differential equation is one that contains one or more derivatives of a function. To solve any differential equation involves taking antiderivatives of that function. Taking antiderivaties is one of the foundations of calculus.
Discrete Mathematics has grown in stature over the years to be used in computer science, cryptology, information theory, logic, set theory, combinatory mathematics, graph theory, and doing proofs by induction. This subject is quite complex and can sometimes be quite difficult to learn. However, it is a fascinating and interesting field in the mathematics space.
I am qualified in math by virtue of passing the Elementary Math test with 100%. I certain am qualified to assist in all aspects of elementary subjects although my only real interest would be in the math part.
What is covered is very basic such as addition, subtraction, multiplication, and division. The key to good performance here is memorizing the multiplication table.
How would you prove the area of a circle is Pi*r^2. Well, you could inscribe the circle inside an octagon and form 8 triangles within that octagon. The area of each of those 8 triangles is 1/2*r*s where s is the length of each side of the octagon. So we have an area within the octagon of 8s*1/2*r. This is an approximation of the area of the circle that improves if the polygon (in this case, an octagon) has more sides. In particular, a polygon with many sides will have a perimeter very close to the perimeter of the circle which is 2*Pi*r.
The GRE is mostly calculus and algebra. In addition there are questions about sequences and series. A sequence is a list of numbers and a series is the terms of a sequence added together. An arithmetic sequence is when the each term is obtained from the preceding one by adding a certain amount and a geometric sequence is when each term is obtained from the preceding one by multiplying by a certain amount. For instance, 1/2 + 1/4 + 1/8 + 1/16 + .....is a geometric series with the multiplier being 1/2.
Perhaps the most difficult hurdle in pre-algebra is how to add, subtract, multiply, and divide fractions. Adding and subtracting fractions requires a common denominator. Multiplying fractions does not, and dividing by a fraction is just multiplying by the reciprocal.
One topic covered in pre-calculus is the polar coordinate system. Using the definition of sine and cosine you can express the rectangular coordinates x and y as rcos(theta) and rsin(theta). Then, using the tangent and Pythagorean theorem, you can write polar coordinates in terms of rectangular.
If you draw 5 cards from a 52 card deck there are 52 ways to draw the first card, 51 ways to draw the second card, 50 to draw the third, 49 to draw the fourth, and 48 to draw the fifth. But if we look at the hand 2,3,4,5,6 there are 5 places we could have put the 2 and for each of those 4 places we could have put the 3 and for each of those 3 places we could have put the 4, etc. That means there are 120 repeats. Therefore there are 52*51*50*49*48/120=2598960 possible poker hands
One topic on the SAT includes finding the length of an arc using the Pythagorean Theorem. If the arc is a quarter circle and there is a rectangle inscribed in that quarter circle with the length and width known, then the Pythagorean Theorem will calculate the radius of the quarter circle and from that we use the fact that the arc length is the radius times the angle which in this case is 90 degrees or pi/2 radians.
Statistics has to do with hypothesis testing, trying to determine whether data from an observation is real or a fluke of nature. However, the concepts and terminology are often not well described by the teacher and have to be put into everyday common perspective. That is my role as a tutor.
Trigonometry begins with a right triangle and the Pythagorean theorem. After that we label one of the angles not equal to 90 degrees with the Greek letter theta and we call the sides the opposite, adjacent, and hypotenuse. From that we can define the sine, cosine, and tangent of an angle.