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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.
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 the 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, a subject for which I am certified and have tutored over 100 hours since joining Wyzant.
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.
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.
here is a sample of my writing......In 1988 Larry Brown won the National Championship as coach of the Kansas Jayhawks. Danny Manning was on that team and given the content of my last article "The Culture Of Losing", I now have so much to talk about with Larry Brown accepting the coaching position at SMU. SMU stands for Southern Methodist University. Let's get that out of the way first because I know many of you out there have never heard of the place. But there are some of us who were alive in the 80's who might remember that 1988 was also the last time the Mustangs(yes i had to answer that one too) won an NCAA Tournament game. I couldn't tell you, however, the name of anyone on that team or any SMU team since. So SMU goes with Larry Brown to try and attract first rate recruits to Dallas(admit it some of you were still asking "Where is SMU?"). The last time Larry Brown was relevant in coaching was in 2005 when he coached the Detroit Pistons to the NBA finals. The high school players he will be trying to recruit were 11 years old or younger at that time and many of them living in Texas or surrounding states. I think it's safe to say that not one of them was aware who the coach of the Pistons was in 2005. The point being that the name Larry Brown no longer has the appeal it once did long ago in the college game, ESPECIALLY at a school which has been so bad at basketball for so long.