College Board has recently announced that it is changing its SAT exam structure. The new Math format will resemble ACT in its pure math content, only that there will be more Math steps involved before getting to the final answer. The Math section will consist of 57 questions (compared to 54 on the previous exam version) that are divided into grid-in and multiple-choice subsections. Multiple-choice subsection will have four answer choices (compared to 5 previously). This will make it easier to answer the question correctly if the student does not know the answer. Grid-in subsection will usually require one to find a single number or quantity (not an algebraic expression). The score for the Math section is 800 as before. Also, each question out of 57 will be given more time (about 20 more seconds on average) compared to the previous exam version. This makes sense, because even though the content is more Math-related, the actual knowledge of Math will require one to perform at least three steps before arriving at the solution.
No one knows exactly what the exam will be like (especially Math), but College Board already posted sample Math problems that will reflect the topics a student may see in March of 2016.
From the sample problems provided one can see that word problems will be given special attention. Word problems require one to transform words into corresponding mathematical expressions. This is tremendously important, as real-life problems typically show similarities with this topic.
Example word problem: Rita is 8 years older than John was 3 years ago. Tom will be twice the current age of John in 4 years time. How old is Tom now if Rita is 25?
Solution: let r be Rita’s age now, j John’s age now, and t Tom’s age now. Then we have r = j – 3 + 8 (we got this from sentence “Rita is 8 years older than John was 3 years ago.”), t + 4 = 2j (from “Tom will be twice the current age of John in 4 years time.”). Since r = 25, we have 25 = j – 3 + 8, which means that j = 25 – 5 = 20, and t = 2(20) – 4 = 40 – 4 = 36. Thus Tom is 36 years old.
Additional topics included in the New SAT Math section are Geometry, Trigonometry, Algebra, Probability, and Data & Graphical Analysis, to name a few.
An interesting algebra-sequence problem:
Suppose that an arithmetic sequence is of the form x,… , -11, -7, -3,… , where the terms (integers) are shown in increasing order.
What integer could NOT be a possible term?
Notice that the constant distance between the terms is 4. This means that valid terms will show up in this sequence for every multiple of 4. Multiples of 4 are 4, 8, 12, 16,… , 100, etc. Going negatively from -11, we know that -111 is also a term, because -111 – (-11) = -100. This makes -115 also valid. Since -3 + 4 = 1 is also valid, 101 is also valid. This makes 99 false. Choice C is valid, because 109 is 4(2) = 8 away from 101. Since 60 is a multiple of 4, the term 1 + 60 = 61 is also valid, which makes 69 valid. Thus the correct choice is (B).