The College Board recently announced that it is changing the structure of its SAT tests. The new math format will resemble ACT in its pure math content, only there will be more math steps involved before reaching the final answer. The Mathematics section will consist of 57 questions (compared to 54 in the previous exam version) that are divided into grid and multiple-choice subsections. The multiple choice subsection will have four answer options (compared to the previous 5). This will facilitate the correct answer to the question if the student does not know the answer. The grid subsection will generally require one to find a single number or quantity (not an algebraic expression). The math section score is 800 as before. Also, each 57 question will take longer (about 20 seconds longer on average) compared to the previous version of the exam. This makes sense, because although the content is more related to mathematics, actual knowledge of mathematics will require one to take at least three steps before reaching the solution.
Nobody knows exactly what the test will look like (especially math), but the College Board has already released sample math problems that will reflect the topics a student can see in March 2016.
From the sample problems provided, it can be seen that word problems special attention will be paid to it. Word problems require one to transform the words into corresponding mathematical expressions. This is tremendously important, as real life problems often show similarities to this topic.
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Example word problem: Rita is 8 years older than John 3 years ago. Tom will be twice John’s current age in 4 years. How old is Tom now if Rita is 25?
Solution: Let r be Rita’s age now, John’s age now, and Tom’s age now. So we have r = j – 3 + 8 (we got it from the sentence “Rita is 8 years older than John 3 years ago”), T + 4 = 2j (from “Tom will be twice John’s current age in 4 years . “). Since r = 25, we have 25 = j – 3 + 8, which means that j = 25 – 5 = 20, and t = 2 (20) – 4 = 40 – 4 = 36. So Tom is 36 years old.
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Additional topics included in the New SAT Math section are Geometry, Trigonometry, Algebra, Probability, and Graphing and Data Analysis, to name a few.
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An interesting algebra sequence trouble:
Suppose an arithmetic sequence is of the form x, …, -11, -7, -3, …, where the terms (integers) are displayed in increasing order.
What whole number could NOT be a possible term?
A. -115
B. 99
C. 109
D.69
Note that the constant distance between the terms is 4. This means that valid terms will appear in this sequence for each multiple of 4. The multiples of 4 are 4, 8, 12, 16, …, 100, and so on. Passing 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. Option C is valid, because 109 is 4 (2) = 8 of 101. Since 60 is a multiple of 4, the term 1 + 60 = 61 is also valid, which makes 69 valid. Therefore, the correct choice is (B).