SAT 25 MATH Q types

25 hardest/most missed SAT questions based on the YouTube video :)

• The answer is D) -4

• You get this answer through logical reasoning of using the two conditions given to craft minimums and maximums where the function would be correct

• The answer is B) a=bc/(b+c)

• While simple algebra does work, the more elegant method is taking out common factors(16) then combining one both sides to equal one fraction

• Then use the reciprocal rule(reciprocates both sides) so the variable lands on top. This rule only works if there are 2 things

• The solution to this problem is pretty easy. I think all problems on the SAT can be done by hand, it’s just that the Desmos aspect can be an aid. 

• Essentially, once you notice that the denominator is (x²-9) it’s just the difference of squares which matches the denominators on the opposite side

• From then it’s simple algebra: combine fractions and then match denominators :) 

• The answer should be 72

• Just set up an equation that models the two to each other(set them equal) and solve for x

• Convert x to mins and voila, 80 mins is the answer

(got wrong)

• Key point that I was unsure about: A system of equations have infinite # of solutions if and only if they are equal to each other(7x=7x)

• So set them equal to each other and solve for the ratio relating them

• Im pretty sure the ratio was 1.32, but my mistake was I plugged that 1.32 into the wrong side(bottom instead of the top)

• Solve for b/d to get 50/33 or like 1.51515

(got wrong)

• I KNEW something was wrong… I just didn’t know what. This is what: when there are %’s involved, always beware of the more than or less than because 540% more of something is that times 6.4 because 100% makes it exactly that

• So my error was that I set up my equation to equal a=5.4b when it should’ve been a=6.4b

• Once you get that out of the way, also beware that k is given with % symbol… so the answer is 0.128 🙂

(got wrong)

• For the same reason as the problem above. I set up the equation as (2)^t/11 =7 instead of =8 because 700% more than means 800% of the value

• However, the way you solve this is by using the property of logarithms to move the exponent into a coefficient which is exactly what I did to solve with algebra

• t=16.5 which *12(months) becomes 198

• I did this right 🙂

• I don’t have any other explanation other than just use your logical reasoning and knowledge of functions

• The answer is D)

• Laughably easy once you realize that you can set x^9=y then substituting that in to get the equatio: 15x²+kx+24

• Box method optional to visualize, but to get the largest k-value, you always have to multiply the largest factors together so 15×24=360

• There is a 1×1=1 so ans: 361

• Fairly simple

• Distribute everything and correlate it to it’s assigned variable

• Use algebra to solve to check for each conditions legibility

• The correct answer should be D)

(got wrong)

• This one uses a bunch of memorized formulas:

1. Find the x-cord(h) of the vertex using the equation the middle of the two symmetrical points f(-4) and f(8) has x=2

2. Find the b value using the equation h= -b/2a which should get you b=12 which is definitely NOT <0 so ❌

3. Use your b-value to multiply use the equation: x₁+x₂=-b/a which would equal to 4 ✅

4. Substitute your b-value into the vertex form equation and expand. Then match each value to its a b c value(it should match)

5. The final match is c=k-12 so c is definitely <k so ✅

The final answer is C)

You could also just brute force it with desmos

• You can use desmos for this problem

• Just identify that k=200(height of vertex) and it happens at h=3(x-cord of vertex)

• Write out the vertex form in desmos and substitute your known values

• Adjust a so that one of the x-cords is @x=8

• Since you know that the parabola is symmetrical, and 200 was done in 3 seconds and in 5 seconds, the rock was thrown at a height of 2 seconds post the other x-int.

• And that point is 128

(confused, so do again)

• The core concept here is using the discriminant formula: b²-4ac

• It is given that there is 1 real solution so the discriminant has to equal 0

• Plug in values and use general algebra

• The answer should be 26

• I solved this in a very weird way:

• I just scanned the answer choices, and all but one of them had III in their choices

• I plugged in 0 to the equation to get -a²bc which is definitely not >0 since a b and c are positive constants

• That only left one answer: A

However, the other conditions are pretty simple too. If K is sandwiched between 2 positive numbers. It too must be positive.

And then using + and -, you can easily check condition II

(got wrong 😆 for some Englick reason…)

• Erm I ordered from largest to greatest first.

• Pretty straightforward though. Just create a function: 5a>b+c+9 then substitute values(b=2+a and c=4+a) solve for a which should be a>=5. 

• Since its given that the #’s are even, b=8

• Very easy. Set up the equation:

• 108 km/h²

• =108000m/h²

• =108000m/(1/60)²

• =30