New SAT on your horizon, are you ready for math?
The College Board recently announced that it will change the structure of its SAT test. The new math format will resemble ACT in its pure math content, only there will be more math steps before arriving at the final answer. The Mathematics section will consist of 57 questions (compared to 54 on the previous version of the exam) that are divided into grid and multiple-choice subsections. The multiple choice subsection will have four answer options (compared to the previous five). This will make it easier to answer the question correctly if the student doesn’t know the answer. The Grid-in 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 question out of 57 will be given more time (about 20 seconds more 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 go through at least three steps before arriving at the solution.
Nobody knows exactly what the test will be like (especially Mathematics), but the College Board has already published sample Mathematics problems that will reflect the topics a student may see in March 2016.
From the sample problems provided, it can be seen that word problems will be given special attention. Word problems require one to transform the words into the 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 current age, j be John’s current age, and t be Tom’s current age. So we have r = j – 3 + 8 (we got this 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 time of 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. Therefore, Tom is 36 years old.
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Additional topics included in the New SAT Math section are geometry, trigonometry, algebra, probability, and data and graph analysis, to name a few.
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an interesting algebra-sequence problem:
Suppose an arithmetic sequence is of the form x,… , -11, -7, -3,… , where the (integer) terms are shown in increasing order.
What integer could NOT be a possible term?
R.-115
B.99
C.109
D.69
Notice that the constant distance between the terms is 4. This means that valid terms will appear in this sequence for every multiple of 4. The multiples of 4 are 4, 8, 12, 16,…, 100, etc. Going negative of -11, we know that -111 is also a term, because -111 – (-11) = -100. This makes -115 valid as well. 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 away from 101. Since 60 is a multiple of 4, the term 1 + 60 = 61 is also valid, making 69 valid. Therefore, the correct option is (B).