IB Math SL: Things to
Memorize Exam Questions with
Correct Answers
1. Vector lines correct answer: If perpendicular correct answer:
costheta will be 0 when u do the angle formula If parallel correct
answer: If theta when we do costheta formula is 180
Coincident lines correct answer: They are the same line, they share a point & their direction vectors are
scalar multiples
If the question is talking about movement, then the direction vector tells you the velocity and its magnitude
is the speed
2. If you have a question asking for the equation of the tangent line
at x = 1, for example... correct answer: -Plug in 1 into original equation. The value u get is
the 'y' in the y = ax +b!
-Plug in 1 into first derivative equation. The value u get is the exact slope!
-Don't forget to attach an x to this slope value once u put it into the y = ax + b format!
-Solve for 'b' by plugging in your 'y' value from the first step and your slope (plug in slope into 'a' and
your given x value into the 'x').
-After getting 'b', write the equation in the format y = ax+b!
3. Questions in which they ask you for the x to the power of four
term in a sequence... correct answer: Put it in the binomial theorem format. 'N' is the
exponent on the sequence and 'R' is what value of the term they want (in this case the fourth
term)!
If there's an x multiplying on the outside of the expansion, then consider it as well! In this case, for the 'a'
term, you should think of your 'R' and 'N' subtracting to give a power that will also multiply by the outside
term. This ensures
you get x^4 when you multiply by the outside at the end
4. For limit questions where you have to use the "h --> 0"
equations...I need to plug in (x+h) wherever I see 'x' on the given
equation only, right? correct answer: Yes! But, don't forget to subtract by f(x)
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,after you're done doing that (this is part of the formula) and dividing by 'h'!
5. For limit questions where you have to use the "h --> 0" equations,
I always factor out all the 'h's so that I can cancel it out with the 'h'
on the denominator, right? correct answer: Yes! After that, don't forget to plug in '0'
wherever you see any 'h' as part of the 'h --> 0" thing. Your answer should be the only number or term
left after you finishing plugging it.
6. How do I do factorials without calculator? correct answer: The formula is in
the data booklet. You multiply backwards to 1 on the numerator. On the denominator, you subtract
the 'n' and the 'r' in the factorial from each other and do the factorial of this number * the factorial of
the 'r' term. You'll see that some of the top multiplications should cancel out from the bottom
multiplications. correct answer:)
7. If I have to solve for smth that cannot be negative, I do... correct
answer: The absolute value on the calculator by going on 'Math' then 'Num'
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17
, 8. To get rid of a fractional exponent when solving an equation....
correct answer: Do the reciprocal of the power on both sides
9. Concavity is up when... correct answer: F´´(x) > 0
10. Concavity is down when... correct answer: F´´(x) < 0
11. Inflection point/Graph of f(x) changing direction when... correct
answer: F´´(x) = 0
12. "Particle is at rest" correct answer: Velocity is 0
13. Order of operations correct answer: BEMDAS! Rules everything bro
14. "Find the maximum..." correct answer: Find first derivative, equal it to 0, do sign
diagram to see which x-intercept is max and which is min...
OR
Plug in equation into Y = on your calculator, if it's a paper 2 question, and 2nd-trace-maximum that shit
15. Amplitude correct answer: Max - min /2
16. Vertical shift correct answer: Max+min/2
17. Integral of e correct answer: Still e
18. Derivative of ln correct answer: 1/x
19. Period correct answer: 2 pi/b
20. Phase shift correct answer: See how far it is on the x axis from where the graph should
have started...
21. Typical cosine graph... correct answer: Starts at max or min
22. Typical sine graph... correct answer: Starts at origin
23. If they say a point is 'tangent' to a circle at Point P... correct answer:
It's perpendicular to the circle at Point P
24. Quadrants correct answer: From left to right correct answer: I, II, IV, III.
25. If I have a question where I am to solve a trig function's
zeroes, I should attempt... correct answer: Rewriting it as a regular quadratic equation and
equaling it to 0, then bringing back the sin or cos to solve what the x (or angle) would be for that
specific value. Before you do this, make sure it's in a format like correct answer: sin^2x + sinx +
constant, and vice versa for cosine. But it cannot be sin^2x+cosx+constant...Try using trig identity to get
it all sin or all cos...
26. Area Integration correct answer: Top
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17
Memorize Exam Questions with
Correct Answers
1. Vector lines correct answer: If perpendicular correct answer:
costheta will be 0 when u do the angle formula If parallel correct
answer: If theta when we do costheta formula is 180
Coincident lines correct answer: They are the same line, they share a point & their direction vectors are
scalar multiples
If the question is talking about movement, then the direction vector tells you the velocity and its magnitude
is the speed
2. If you have a question asking for the equation of the tangent line
at x = 1, for example... correct answer: -Plug in 1 into original equation. The value u get is
the 'y' in the y = ax +b!
-Plug in 1 into first derivative equation. The value u get is the exact slope!
-Don't forget to attach an x to this slope value once u put it into the y = ax + b format!
-Solve for 'b' by plugging in your 'y' value from the first step and your slope (plug in slope into 'a' and
your given x value into the 'x').
-After getting 'b', write the equation in the format y = ax+b!
3. Questions in which they ask you for the x to the power of four
term in a sequence... correct answer: Put it in the binomial theorem format. 'N' is the
exponent on the sequence and 'R' is what value of the term they want (in this case the fourth
term)!
If there's an x multiplying on the outside of the expansion, then consider it as well! In this case, for the 'a'
term, you should think of your 'R' and 'N' subtracting to give a power that will also multiply by the outside
term. This ensures
you get x^4 when you multiply by the outside at the end
4. For limit questions where you have to use the "h --> 0"
equations...I need to plug in (x+h) wherever I see 'x' on the given
equation only, right? correct answer: Yes! But, don't forget to subtract by f(x)
1/
17
,after you're done doing that (this is part of the formula) and dividing by 'h'!
5. For limit questions where you have to use the "h --> 0" equations,
I always factor out all the 'h's so that I can cancel it out with the 'h'
on the denominator, right? correct answer: Yes! After that, don't forget to plug in '0'
wherever you see any 'h' as part of the 'h --> 0" thing. Your answer should be the only number or term
left after you finishing plugging it.
6. How do I do factorials without calculator? correct answer: The formula is in
the data booklet. You multiply backwards to 1 on the numerator. On the denominator, you subtract
the 'n' and the 'r' in the factorial from each other and do the factorial of this number * the factorial of
the 'r' term. You'll see that some of the top multiplications should cancel out from the bottom
multiplications. correct answer:)
7. If I have to solve for smth that cannot be negative, I do... correct
answer: The absolute value on the calculator by going on 'Math' then 'Num'
2/
17
, 8. To get rid of a fractional exponent when solving an equation....
correct answer: Do the reciprocal of the power on both sides
9. Concavity is up when... correct answer: F´´(x) > 0
10. Concavity is down when... correct answer: F´´(x) < 0
11. Inflection point/Graph of f(x) changing direction when... correct
answer: F´´(x) = 0
12. "Particle is at rest" correct answer: Velocity is 0
13. Order of operations correct answer: BEMDAS! Rules everything bro
14. "Find the maximum..." correct answer: Find first derivative, equal it to 0, do sign
diagram to see which x-intercept is max and which is min...
OR
Plug in equation into Y = on your calculator, if it's a paper 2 question, and 2nd-trace-maximum that shit
15. Amplitude correct answer: Max - min /2
16. Vertical shift correct answer: Max+min/2
17. Integral of e correct answer: Still e
18. Derivative of ln correct answer: 1/x
19. Period correct answer: 2 pi/b
20. Phase shift correct answer: See how far it is on the x axis from where the graph should
have started...
21. Typical cosine graph... correct answer: Starts at max or min
22. Typical sine graph... correct answer: Starts at origin
23. If they say a point is 'tangent' to a circle at Point P... correct answer:
It's perpendicular to the circle at Point P
24. Quadrants correct answer: From left to right correct answer: I, II, IV, III.
25. If I have a question where I am to solve a trig function's
zeroes, I should attempt... correct answer: Rewriting it as a regular quadratic equation and
equaling it to 0, then bringing back the sin or cos to solve what the x (or angle) would be for that
specific value. Before you do this, make sure it's in a format like correct answer: sin^2x + sinx +
constant, and vice versa for cosine. But it cannot be sin^2x+cosx+constant...Try using trig identity to get
it all sin or all cos...
26. Area Integration correct answer: Top
3/
17
