Core 4 flashcards

Question	Answer
Define an impartial fraction	A fraction whose degree of numerator is equal to, or larger than, the degree of the denominator.
ʃ y dx of a set of parametric equations can be found using what formula?	ʃ y x $\frac{dx}{dt}$ dt
ʃ y² dx of a set of parametric equations can be found using what formula?	ʃ y² x $\frac{dx}{dt}$ dt
What what values of x is this binomial expansion valid? √(1-3x)	I-3xI<1 I3xI<1 IxI< $\frac{1}{3}$
What is the differentiation formula for parametric equations?	Image: 9a84bfcd-57f3-4ac4-89f6-101194db69cc (image/png)
What is the implicit differentiation formula?	f(x).g(y) f(x).g'(y) (dy/dx) + g(y).f'(x)
What is the differential of $a^x$ ?	$a^x$ lna
If a rate is proportional to x then it can be said that the rate expression = ...	kx
A vector quantity has both....	magnitude and direction
What is a scalar?	A single number with only magnitude/size but no direction.
What is the triangle law?	A law for adding vectors
Adding the vectors PQ and QP gives...	0
The modulus of a vector gives its...	Magnitude
How do you find the unit vector of a vector a?	a ---- I a I
If $\ambda$ a + $\mu$ b = $\alpha$ a + $\beta$ b and the non-zero vectors a+b are not parallel...	$\ambda$ = $\alpha$ $\mu$ = $\beta$
The distance from the origin to point (x, y, z) is...	√x²+y²+z²
THe distance between 2 points: ₂₃₁ (x₁, y₁, z₁) and (x₂, y₂, z₂) is...	√[ (x₁-x₂)² + (y₁-y₂)² + (z₁-z₂)² ]
What is a.b called?	The scalar product
What is the formula for the scalar product of 2 vectors?	a.b = I a I I b I cos $\theta$
If two vectors are perpendicular then a.b = ...	a.b = 0
If 2 vectors are parallel a.b = ...	a.b = I a I I b I
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What is the sec²x identity?	Image: 54a2188a-c06b-4ba1-bbfe-5fbd4668c711 (image/png)
What is the Cot²x identity?	Image: 4f70c497-e4f8-47a7-ab62-08d121adff57 (image/png)
What is the sine double angle identity?	Image: 72ba0b6b-765d-4eee-b92c-ce77b374fe6d (image/png)
What are the 2 forms of the cosine double angle identity? Image: 8df7703c-f18d-4315-a449-939f49aae93e (image/png)	Image: 42c0c46c-de49-4bc6-8d47-55c5219cffe0 (image/png)
What is the integration by recognition formula for a fraction?	Image: 47e95925-ee08-46a7-8401-4114dcd09664 (image/png)
What is the integration by recognition formula for functions with powers?	Image: c441b02b-8556-4b24-a180-fb69d0103a8c (image/png)
What is the integration by parts formula?	Image: 70b772db-b65f-4ff9-90c1-faa8e4d3cd78 (image/png)
What is the trapezium rule?	Image: 461626ff-3934-4b50-8351-b5710f138530 (image/png)
What is the formula for calculating h in the trapezium rule?	Image: 0a3b9d87-11b4-40c6-a47c-a0ca907871dd (image/png)
What is the formula for solids of revolution 360 degrees of f(x)?	Image: 3942ab79-0973-4061-9e31-a36a1845a8e0 (image/png)
Which method can you use to solve this and what is its formula? Image: e0715771-99ee-4a8e-80c8-15c4758fc310 (image/png)	Separating of variables Image: a1b4b050-cd67-4f5f-902a-5bdb6efad50d (image/png)
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