A Level Pure Maths Lent and Trinity Term*

What would be the next step in converting 2cos^2x + 9sinx = 3 sin^2x to 5sin^2x - 9sinx - 2?

2(1 - sin^2x) + 9sinx = sin^2x

Where does y = 0 on a cos graph?

90, 270

Even + Even =

Even

Even + Odd =

Odd

When sketching the graph y =2sinx, what would happen?

Y coordinated would be multiplied by 2

Give the two trig identities

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

Label a cast diagram in the range -360 < x < 0 from the north line at the top going clockwise.

-270, -360/0, -90, -180

How do you write an even number using algebra?

2n

The midpoint of a diameter, is the same as the....

Centre of a circle

Even x Even =

Even

Even x Odd =

Even

Cos(50 + 2x) = -1. X= 180, 540, how would you find the answers for x?

Rearrange so that X/2 - 50 = x

When tan45 = 1, what can you do?

Sub into a right-angled triangle with two 45 degree angles and base and height of 1 unit

If you know cos60 = 1/2, what can you do?

Sub into right-angled triangle with angles of 60 degrees and 30 degrees And base of 1 and hypot of 2

When sketching the graph of y = sin2x, what would happen?

x coordinates would be divided by 2

What is the centre of a circle with the equation x^2 + y^2 + 2fx + 2gy + c = 0

(-f, -g)

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

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

When tanx = 0, what are the solutions for x, in the interval -180<x<180?

-180 degrees, 0 degrees, 180 degrees

Where does y = 0 on a sin graph?

0, 180 and 360

Where does y = 0 on a tan graph?

0, 180 and 360

For a right-angled triangle with two 45 degree angles, what is the base and height?

1 unit

In a right-angled triangle with angles of 30 degrees and 60 degrees, what are the side lengths for hypot and base?

2 for the hypotenuse and 1 for the base

How do you write an odd number using algebra?

2n + 1

How do you write three consecutive odd numbers using algebra?

2n+1, 2n+3, 2n+5

How do you write three consecutive even numbers using algebra?

2n, 2n+2, 2n+4

If the gradient of the radius of a circle is -3/4, what is the gradient of the tangent to the point where the radius meets the edge of the circle?

4/3

When y = f(x) has a positive gradient, where is y = f'(x)?

Above the x-axis

What do you with the interval when sin(x + 60)?

Add 60 to both numbers in the interval

What are inverse trig functions also called?

Arccos, arcsin, arctan

When y = f(x) has a negative gradient, where is y= f'(x)?

Below the x-axis

How do you work out whether a quadratic is a minimum or maximum?

Differentiate twice and see whether the answer is bigger than zero, so a minimum or smaller than zero, so a maximum

How do you write three consecutive numbers using algebra?

n, n+1, n+2

When y = f(x) is a point of inflection, what is y = f'(x)?

A turning point

When drawing a quadratic what must it not do?

Curve inwards

What are the three steps in finding the greatest or least value of a function?

Find f'(x), set to =0 and find the corresponding value f(x)

Odd x Odd =

Odd

What is a unit circle?

A circle with a radius of 1 unit

Name the segments of a cast diagram going from the 0/360 degree point ant-clockwise in the range 0 < 360

A, S, T, C

What does a tan graph look like?

Comes from below the x axis to above the x-axis

What does squaring both sides of 2cosx = 3sinx do?

Creates extra solutions

Odd + Odd =

Even

What would happen with a graph that was transformed by: y = sin(x +60)?

Everything would be shifted by -60 degrees

When y =f(x) has horizontal asymptotes, what does y = f'(x) have?

Horizontal asymptotes at the x-axis

When y = f(x) is a minimum or maximum point, what does y = f'(x) do?

It cuts the axis

Ambiguous case triangle: A side of 12cm is the longest side, and you work out that the angle opposite appears to be 53 degrees, the smallest angle, what do you?

It must have the largest angle so you minus 53 from 180

There is a graph of sin that models sand dunes, why wouldn't the graph be a good model to use?

It shows the sand dunes as all being the same height when they may not be

2cosx = 3sinx, what would squaring both sides do?

It would create extra solutions

When sketching the graph of y = tan(x + 45), what would happen?

It would move left by 45 degrees

When sketching the graph of y = cos(x - 90), what would happen?

It would move right by 90 degrees

When you're solving something that is bigger than zero what should you not do whilst solving it?

Make it equal zero

What must the value of x in xi in a vector be, if the direction is less than 90 degrees?

Positive

What are the four steps in solving a quadratic inequality?

Rearrange, Solve, Sketch graph and Find required set of values

How would you rearrange the equation 3sinx = cosx, to get tanx = 1/3?

Sinx/cosx = 1/3

How can you work out if a line doesn't meet a circle?

Sub into the equation of the circle and then its discriminant will be less than 0 if it doesn't cross the circle

If you know sin30 = 1/2, what can you do?

Sub it into a right-angled triangle with angles of 60 degrees and 30 degrees and base of 1 and hypot of 2

How you find out the coordinates of the points where the line y = x + 5 meets the circle x^2 + (y - 2)^2 = 29?

Sub y = x + 5 into x^2 + (y - 2)^2 = 29

If you know that x is a reflex angle which part of the cast diagram would it be in?

The T or C quadrants

What will the perpendicular bisector of chord go through?

The centre of the circle

When a question asks you to find the set of possible values of k, and k>1 or k<3 what do you also need to write down?

The critical values, so k=1 or k=3

What can you use to discover if an equation has no solutions?

The discriminant

Where is an acute angle always drawn from in a CAST diagram?

The horizontal

What is the radius of a circle with the equation x^2 + y^2 + 2fx + 2gy + c = 0?

The square root of f^2 + g^2 - c

What is a perpendicular bisector of a line segment AB?

The straight line that is perpendicular to AB and passes through the midpoint of AB

What is the relationship between the tangent to a circle and the radius?

They are perpendicular at the point of intersection

Ambiguous case triangle: AB = 4, AC = 3, angle ABC = 44 degrees. How would you work out the two possible values of angle ACB?

Use the sine rule, then minus the acute angle from 180 degrees to get the second answer

When y = f(x) has vertical asymptotes, what does y = f'(x) have?

Vertical asymptotes

What is the equation of a circle with centre(0,0) and radius?

X^2 + y^2 = r^2

When solving cos3x = 0.766, in the interval 0<x<360 what do you do first?

You have to convert the interval so that each number is multiplied by three