Dec 28, 2023
Did you also have this Math question on your second Math module of the December 2nd digital SAT test?
The last digital SAT of 2023 was conducted on December 2nd, completing the first year of the digital SAT test in international test centers. The US is set to switch to this digital version of the SAT as of March 2024.
I normally interview my students right after their test to gain some insight into how the test went for them. On the December 2nd digital SAT, common feedback I received was that the Math section was harder. Some claim that because the Math scores in the past few tests were pretty high, the College Board decided to increase the level of difficulty of the Math on the December 2nd test. Now, whether that is really the case remains a mystery, as the full tests are not released or leaked for me to analyze.
One of the math questions that I particularly found “interesting” was something like this:
The points (c, 11) and (2c, 251) are on the equation y=a^x-b. What is the value of b?
Take a moment and try to solve it yourself.
Here is how I solved it:
Substitute each of the points into the equation.
11=a^c - b …… (1)
251=a^{2c} - b ……. (2)
Subtract the first equation from the second.
240 = a^{2c} - a^c
Now, let a^c be P.
240 = P^2 - P
P^2 - P - 240 = 0
Use Desmos calculator to solve that quadratic equation. The solutions are P = -15 and P = 16. Keep in mind that P is the same as a^c.
Now, substitute the values into equation 1:
11= -15 - b, which gives you b = -26
11 = 16 - b, which gives you b = 1
Notice that you could use the second equation as well and that would give a new set of values for b. You pick the one that’s in the options.
Digital SAT Math may appear easier than the paper-and-pencil version, but the fact that there are fewer questions on this test means that there is less room for error. One error could lead to a significant drop in your score, which is why it is absolutely necessary to thoroughly prepare for the test. Feel free to book a FREE consultation with me to discuss how you should plan your digital SAT prep in 2024.
By Javid Reyaz
Director of Test Prep & Exam Prep
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