C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?

C

Prelim revision Question 1

•How do you get the gradient of a line with an equation like3x + 2y = 5 ?

Ans to Prelim revision Question 1

•(i) Rearrange into the formy = mx + c

(ii) read offgradient = m

C


•What is the equation of a horizontal line passing through the point (a,b) ?


•y = b

x

y

(a,b)

C


•How do you remember the exact trig ratio values of 30o, 45o and 60o ?


•Draw reference triangles•Use SOH CAH TOA

30o

60o

1 2

√3

45o

45o

1

1 √2

C


•How do you find the length of a line joining two points ?


•√(x2 – x1)2 + (y2 –y1)2

A(x1,y1)

B(x2,y2)

x

y

C


•What are the two formulae used to find the area of a triangle ?


•Area = ½base x height

•Area = ½bcsinAA

BCa

bc

B a s e

height

1.1


•What is a median of a triangle ?


•A line from a vertex to the middle of the opposite side

1.1


•What is the equation of a vertical line passing through (a,b) ?


•x = a

x

y

(a,b)

1.1


•What do you know about the gradient of two perpendicular lines ?


•They multiply together togive -1

i.e. m1xm2 = -1x

y

m1

m2

1.2


•How do you draw the graph of 3-f(x) given the graph of f(x) ?


•Reflect the graph in the x-axis, then move it up 3

1.2


•How do you draw the graph of f(x+1) given the graph of f(x) ?


•Move the graph 1 unit to the left

1.2


•How do you draw the graph of f(x-1) given the graph of f(x) ?


•Move the graph 1 unit to the right

C


•What is the Converse of Pythagoras’

Theorem ?


•If a2 = b2 + c2

then ΔABC isright-angled at A

AB

C

a

c

b

1.2


•How do you change from radians to degrees ?


• Divide by π and multiply by 180

1.2


•How do you find f(g(x)) for given functions f(x) and g(x) ?


•Substitute g(x) into f(x)i.e. each x in f(x) is replaced by the entire function g(x)

1.2


•Which two points does the graphy = ax always pass through ?


•(0,1) and (1,a)

1.2


•How do you draw a graph of the form

• y = cos bx• or y = sin bx ?


•Draw the normal graph but fit in b cycles between 0 and 2 π

•Draw the normal graph but fit in b cycles between 0 and 2 π

1.2


•What is the turning point of y = b-3(x-a)2 ?

• and is it max or min ?


•(a,b)

•Maximum

(a,b)

1.2


•For what values of a function is the function said to be undefined ?


•When you fit in a value of x and you cannot get an answer

•Remember you can’t divide by zero, or square root a negative number.

1.2


•How do you write functions like 2x2 + 12x + 3 ?

in the form a(x+b)2+c


• (i) multiply out a(x+b)2+c

•(ii) compare with given function

•(iii) find a, b and c

1.2


•For what values is the functionf(x) = √(x-a) undefined?


•x < a

1.2


•How do you draw a graph of the form

y = acosxor y = asinx ?


• Draw y = cosx

or y = sinx graph shape

with a maximum of a and a minimum of -a

1.3


•How do you show that a curve is always increasing ?


•(i) Differentiate•(ii) show that f’(x) is

always > 0

2.2


•How do you find x2 + 1√x

∫ dx ?


(i) change root to power

(ii) split up into fractions(iii) simplify each term(iv) integrate each term

(v) REMEMBER +C

1.3


•How do you find where a curve is decreasing ?


(i) differentiate(ii) let f’(x) = 0(iii)solve to find st pts(iv) draw nature table(v) read values where

graph is decreasing

1.4


•How do you find the limit of a recurrence relation from its formula ?


•(i) let un+1 = un = Lgiving L=aL+b

•(ii) solve equationRemember:For un+1=aun+b,a limit only exists if -1<a<1

2.1


•How do you show that the root of a function lies between two given values ?


•substitute in the two values and show that for one, the answer is positive, but for the other the answer is negative

x

+ve

-ve

2.2


•How do you calculate the area between two curves ?


•(i) let equations equal each other

•(ii) solve to find limits•(iii) integrate

(upper - lower) functions

between limits

1.2


•How do you solve equations of the form

sin2xo = 0.25 ?(0≤x≤360)


•(i)rearrange to get sinxo = ± …

•(ii) find answers in all 4 quadrants

2.3


•How do you find exact values of sin2x and cos2x given cosx =3/5 ?


• (i) draw aright-angledtriangle

• (ii) find the missing side

• (iii) expand the double angle formula

• (iv) substitute in values from Δ

A3

5

2.4


•How do you find the equation of the tangent to a circle at a particular point on the circumference ?


(i) find thecentre

(ii) find gradientfrom centreto the point(a,b)

(iii) find perpendicular gradient(iv) use y-b=m(x-a)

x

y

(a,b)

C

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C Prelim revision Question 1 How do you get the gradient of a line with an equation like 3x + 2y = 5 ?