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Sat Math - SAT Math Subject Tests: Level 1 and Level 2

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Over the years I’ve had a lot of queries about the SAT Math Subject Test. Here are some of the most common questions asked by parents and students along with my replies.


Why are there two levels? Is one easier?

The Math Subject Test level 1 is much easier than the level 2. You should take level 1 if you’re doing geometry (US system) or GCSE ( UK system ). If you are doing US system Advanced Algebra Honors or Pre-calculus, UK A levels or the IB then you should take the level 2. You can take level 1 but it is nowhere near as impressive as taking level 2. To be honest, I’d only recommend the level 1 to younger students who want a ‘warm-up’. Level 2 is where the action is and all the replies below are based on this fact.


Why take the SAT Subject test?

If you are intending to go to a US tertiary institution to study physics, engineering, or math, then you really need a good SAT Subject Level 2 score ( How good? See below. ) Other science and business courses also look very favorably on the SAT Level 2 as evidence of solid math ability.


What’s the test format?

Unlike the SAT Reasoning Test, the SAT math subject tests have a very straightforward structure. You have one hour to complete 50 questions, all of them multiple choice with 5 choices each. Each question is worth the same: 1 mark. The questions are graded in difficulty order so Q1 is going to be easy but Q50 will be much more of a challenge. However, these are not Math Olympic questions. Even the last few questions are definitely doable by non-genius students. Another difference compared to the SAT Reasoning test is that this is a 100% calculator allowed test. In fact you’ll need a calculator to answer about half the questions. A fancy graphing calculator gives a slight edge in terms of speed for a few questions, but a standard scientific model is perfectly fine.

However, unlike on the Reasoning test, there is a penalty for getting a question wrong. Every incorrect response will result in a -1/4 mark loss. If you omit a question then there is no penalty ( and obviously no mark either! )


What’s the grading?

Lowest raw score is about -10 ( truly awful ) which scales to 300. The highest raw score is 50 ( all correct ) which equates to 800. Here’s the good news – you can score 800 and still get about 4-5 wrong with a few omits ( the exact number varies from paper to paper ). This is totally different to the Reasoning test; just a few wrong there and your score starts to dive.


What’s a good score?

This depends on what you need the subject test for. If you’re shooting for a top 10 college intending to major in the sciences then you need 800 or close to it. If you are applying to a mid-level liberal arts college then 600 would be a good score. Generally, though, 700 is considered well above average. For this you need around 35 questions correct with the remaining about equally split between incorrects and omits.


What do I need to know? What do they test?

Importantly, you do not need to know any calculus except for finding simple limits. You do need to be confident with intermediate algebra, trigonometry, coordinate geometry, and some basic ideas from probability and statistics. I’ll go over the exact topics next month.


What are the questions like?

Why not try some?: Below are three questions which are representative of those you’d find at about question 5, 25, and 45 positions on a typical test.


Example ( i )

The expression will be equal to 0 when x equals which of the following?





E. 3


( The answers with solutions to all this month’s problems are at the end of the article. )

Example ( ii )

The diagram below is a sector of a circle with radius 1. Express the shaded area in terms of in radian measure.

Figure not drawn to scale






E. cos‒ sin


Example ( iii )

There are 12 teams in a competition. In how many ways can they be divided into 2 groups of 6 teams?


A. 360

B. 720

C. 462

D. 924

E. 1140


Solutions to questions


Solution ( i ): The answer is D.


Solution ( ii ): The answer is B.

The shaded area is (the area of the sector) ‒ (the area of the triangle) =


Area of a sector

If is in radian measure, area of the sector


Area of a triangle (two sides and an included angle)


Solution ( iii ): The answer is C.

This question concerns combinations. But it has a twist at the end, so we need to be careful! For 12 teams to be divided into 2 groups of 6 teams, since order does not matter, we should use to compute the number of combinations. But, every time we choose a team of 6 people from 12, we are also choosing another 6 (the 6 left behind). This means when we use , we count each team twice. So we need to divide by 2 to get the final answer, that is .


The number of ways (combinations) of selecting r items from n distinct items:


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