Studied by 1 personWhat is proof by contradiction?
Assuming that the opposite of the statement is correct, and using logical steps to prove this is wrong.
How is a rational number written?
a/b
Laws of indices can only used when you have…
the same base
What is the domain of a function?
the set of possible inputs, the x values
What is the range of a function?
The set of possible outputs, the y values.
The roots of the functions are the values when…
f(x)=0
When a quadratic is in this form; a(x+p)² +q, what are the coordinates of the turning point?
(-p, q)
b²-4ac > 0
Two real and different roots
b²-4ac = 0
Two real and equal roots
b^”-4ac <0
No real roots
y=k/x has asymptotes at?
y=0 x=0
y=k/x² has asymptotes at ?
y=0 x=0
A tangent of a circle is…
Perpendicular to the radius
A perpendicular bisector of a chord will go through….
the centre of the circle
The angle made by the diameter is….
a right angle
How do you find the centre of the circle with three points?
Find 2 equations of perpendicular bisectors of 2 different chords
Find the coordinates of intersection of the perpendicular bisectors
What is proof by deduction?
Starting from known truths or facts and using logical steps to get to the answer
What is proof by eshaustion?
Trying all the possible answers to the statement.
What is prrof by counter example?
Finding a case when the statement is incorrect.
Which row of pascals triangle gives the coefficients of the expansion (a+b)^n ?
the (n+1)th row
What is n! called?
N factorial
N! =
n x (n-1) x…..x 2 × 1
What is the cosine rule?
C² = A² +B² - 2AB Cos c
What is the sine rule?
a/sin A = b/sin B = c/Sin C
sin a=
sin (180-a)
What is the area of a triangle?
½ ab sin C
The graphs of cosine, sine and tan are?
Periodic
sin 30
½
cos 30
3^1/2 /2
tan 30
1/ 3^1/2
sin 45
1/2^1/2
cos 45
2^1/2 / 2
tan 45
1
sin 60
3^1/2 / 2
cos 60
1/2
tan 60
3 ^1/2
sin² a + cos² a
1
tan a
cos a / sin a
What is a unit vector of a ?
a/ magnitude
What is a mapping?
A function that every output has a distinct input.
In a arithmetic sequence what is the difference between terms?
The constant d
What is the nth term of an arithmetic sequence?
a + (n-1)d
What is the difference between terms in a geometric sequence?
The common ratio r
What is the nth term of a geometric sequence?
ar^n-1
2 pi radians
360
pi radians
180
1 radian
180/pi
pi/6 rad
30
pi/ 4 rad
45
pi/3 rad
60
pi/2 rad
90
What is the arc length?
ra a is the angle in rad
What is the area of a sector?
½ r² a
when a is small sin a
a
when a is small cos a
1- a²/2
When a is small tan a
a
sin 2A
2 sin A cos A
cos 2A
cos² A - sin² A
tan 2 A
2 tan A / 1- tan² A
Note
Flashcard