"This session we reviewed all of the math topics that the student got incorrect on the previous two math sections that he took. I gave him representative problems of each type, and he completed them with some coaching.
Some problems that he did involved more combinations, using numbers that would be impossible to count out all of the ways to do something. He needed to learn that he is multiplying the number of choices together, not finding the probability of one choice. After he realized this, he got the rest of the questions of that type correct.
Another type of problem that he did was the calculation of inequalities especially with absolute values. He needed to remember that inequalities are solved like normal equations, but when you multiply or divide both sides by a negative number, you have to switch the inequality direction. We talked about how to solve absolute value problems. If you have that the absolute value of x minus 1 is less than three, then you solve two equations: x minus one is less than three and negative x plus one is less than three. After you solve this, you find that x can rage from being larger than negative four to being less than two.
Another problem type that we went over again was the area of a shaded region this time involving fractions of areas, not whole ones. I drew a square whose vertex was at the center of a circle, and the shaded area was the portion of the square that wasn't in the circle. To find the area of the shaded region, the student had to subtract one quarter the area of the circle from the area of the square.
We did several other problems before deciding to do another practice math section, this time from the practice book that he had for the placement exam. The practice section was a bit easier, and he did quite well on it."