Half Term 2

Question 1

What is the equation for a circle centred at the origin?

Answer 1

x^2 + y^2 = r^2

Question 2

What is the equation of a circle with centre (a,b)?

Answer 2

(x-a)^2 + (y-b)^2 = r^2

Question 3

What is the tangent perpendicular to?

Answer 3

The radius

Question 4

T/F: Any perpendicular bisector to the chord passes through the centre

Answer 4

True

Question 5

What does it mean when a circle is circumscribing a triangle?

Answer 5

The circle surrounds the triangle with the vertices of the triangle all touching the circumference of the circle

Question 6

What is the circle that circumscribes a triangle called?

Answer 6

The circumcircle

Question 7

What is the centre of a circumcircle called?

Answer 7

The circumcentre

Question 8

What is the hypotenuse of an inscribed triangle also?

Answer 8

The diameter of the circle

Question 9

What is the differential equation of a function?

Answer 9

f’(x) = (f(x+h) - f(x)) / h

Question 10

If y = ax^n then dy/dx = ?

Answer 10

anx^(n-1)

Question 11

n! = ?

Answer 11

n x (n-1) x (n-2) x … x 2 x 1

Question 12

What is the factorial of n?

Answer 12

The number of ways of arranging n things in a line

Question 13

nCr = ?

Answer 13

(n!) / r!(n-r)!

Question 14

What is nCr?

Answer 14

The number of ways of choosing r things from a selection of n things when order doesn’t matter

Question 15

What is the sine rule?

Answer 15

sinA / a = sinB / b = sinC / c
a / sinA = b / sinB = c / sinC

Question 16

What is the cosine rule?

Answer 16

a^2 = b^2 + c^2 - 2(bc) x cosA
A = 1/2 x a x b x sinC

Question 17

What do you use cos, sin or tan of 45?

Answer 17

Use a right-angled isosceles triangle

Question 18

What do you use to find cos, sin or tan or 30 or 60?

Answer 18

Use an equilateral triangle split down the middle

Question 19

What is a cast diagram?

Answer 19

Split into four quadrants which dictate what values are positive or negative

Question 20

What are the two main trigonometric functions?

Answer 20

sinx/cosx = tanx
sin^2x + cos^2x = 1

Question 21

What is the relationship between sin and cos angles?

Answer 21

sin(x) = cos(90-x)

Question 22

How do you find other solutions to sin, cos and tan equations?

Answer 22

sin(x) = sin(180 - x)
cos(x) = cos(360 - x)
tan(x) = tan(180 + x)

Question 23

If y = ax^n then dy/dx = ?

Answer 23

anx^(n - 1)

Question 24

What does it mean if f’(x) > 0?

Answer 24

The function is increasing for the interval of [a,b]

Question 25

What does it mean if f’(x) < 0?

Answer 25

The function if decreasing for an interval of [a,b]

Question 26

What is the notation for second order differentiation?

Answer 26

(d^2 x y) / (d x x^2) or f’’(x)

Question 27

How can you tell if a stationary point is a min, max or point of inflection?

Answer 27

If f’‘(x) > 0 it is a minimum
If f’‘(x) < 0 it is a maximum
If f’‘(x) = 0 it could be a min, max or point of inflection

Question 28

What are the rules for mapping the gradient function of an equation?
1. Max/min – > ?
2. Point of inflection –> ?
3. Positive gradient –> ?
4. Negative gradient –> ?
5. Vertical asymptote –> ?
6. Horizontal asymptote –> ?

Answer 28

1. Cuts the x-axis
2. Touches the x-axis
3. Above the x-axis
4. Below the x-axis
5. Vertical asymptote
6. Horizontal asymptote at y = 0