Question 1
How do you find the
equation of a
perpendicular
bisector of a line ?
1.1
Answer to Question 1
(i)
(ii)
(iii)
(iv)
find the midpoint of the line
find the gradient of the line
find the gradient
perpendicular to the given
line
Use midpoint and gradient in
y-b = m(x-a)
M(a,b)
Question 2
How do you find the
midpoint of a line
joining two points ?
1.1
Answer to Question 2
Add the coordinates
and divide by two
x+x , y+y
1
2
1
2
(
2
2
)
(x1,y1)
y
(x2,y2)
x
Question 3
How do you find the
altitude AN of
ΔABC ?
1.1
Answer to Question 3
(i) find the gradient of BC
(ii) find the gradient of AN,
perpendicular to BC
(iii)use y-b=m(x-a), Ausing A as
(a,b)
B
N
C
Question 4
How do you show
that x-1 is a factor
of the function
3
f(x)=x -3x+2 ?
2.1
Answer to Question 4
(i)
rewrite the function as
3
2
f(x)=x +0x -3x+2
(ii) use synthetic division
with 1 on the outside
(iii) show that
remainder = 0
Question 5
For what values is this
function undefined ?
x
f(x) =
(x+2)(x-3)
1.2
Answer to Question 5
-2 and 3
Question 6
How do you draw
the graph of 2f(x)
given the graph of
f(x) ?
1.2
Answer to Question 6
Double the
y-coordinates
Question 7
How do you find the
exact value of
sin (α-β),
4
given that sinα = /5
12
and cosβ = /13 ?
2.3
Answer to Question 7
(i) draw triangles
for α and β
(ii) work out
cosα and sinβ
(iii) expand
formula for sin(α-β)
(iv) insert exact values
α
5
4
13
12
β
Question 8
What is the turning
point of
2
y=2(x-a) +b ?
Max or min ?
2.1
Answer to Question 8
(i) (a,b)
minimum
(a,b)
Question 9
How do you draw
the graph of f(-x)
given the graph of
f(x) ?
1.2
Answer to Question 9
Reflect the graph in
the y-axis
Question 10
How do you draw a
graph of the form
y = cos(x+a)
or y = sin(x+a) ?
1.2
Answer to Question 10
Move the graph of
y=cosx or y=sinx
a units to the LEFT
Question 11
Name the steps you
take in order to
differentiate
functions like
2+ 3x + 1
x
f(x) =
√x
1.3
Answer to Question 11
(i)
Change roots to
powers
(ii) split up into 3
fractions
(iii) simplify each term
(iv) differentiate
Question 12
If f(t) is the
distance travelled in
a certain time t
seconds, then what
’
does f (t) represent ?
1.3
Answer to Question 12
Speed (velocity)
Question 13
Given f’(x) and a
point on the curve,
how do you find
f(x) ?
2.2
Answer to Question 13
(i) integrate
(ii) substitute in a
given point to
work out value
of C
Question 14
What do you know
about the gradients
of two parallel
lines?
1.1
Answer to Question 14
They are the same
Question 15
How do you find the
equation of a tangent
to a curve at the point
when x = a ?
1.1
Answer to Question 15
(i)
(ii)
Differentiate
’
fit a into f (x) to get
the gradient (m)
(iii) fit a into f(x) to get
the tangent point (a,b)
(iv) use y-b=m(x-a)
Question 16
How do you find the
rate of change of a
function at a
particular point ?
1.3
Answer to Question 16
(i) differentiate
(ii) fit in given x
value
Question 17
If y is the equation
of a curve, what is
represented by
dy/dx ?
1.3
Answer to Question 17
The gradient
Question 18
How do you find
where a curve is
increasing ?
1.3
Answer to Question 18
(i)
(ii)
(iii)
(iv)
(v)
differentiate
let f’(x) = 0
solve to find stationary
points
draw nature table
read values for which
graph is increasing
Question 19
How would you find
the maximum or
minimum value of a
function given its
equation?
1.3
Answer to Question 19
(i) differentiate
(ii) let f’(x) = 0
(iii) solve to find the
stationary points
(iv) draw the nature table
(v) read off max or min
Question 20
Given a rec. relation in
the form un+1 = aun + b
and 3 consecutive
terms, how do you find
the values of a and b?
1.4
Answer to Question 20
(i) fit 1st term into un and
nd
2 term into un+1
(ii) fit 2nd term into un and
rd
the 3 term into un+1
(iii) solve simultaneous
equations
Question 21
How do you find the value of
a in the polynomial
x3+ax2+4x+3 given either a
factor of the polynomial, or
the remainder when the
polynomial is divided by a
number ?
2.1
Answer to Question 21
(i) do synthetic division
(ii) let the expression
= 0 or the remainder
(iii) solve the equation
Question 22
How do you find
n
∫ (ax + b) dx ?
3.2
Answer to Question 22
(i)
(ii)
(iii)
i.e.
increase power by 1
divide by new power
divide by the
derivative of
the bracket
n+1
(ax+b)
a(n+1)
+ C
Question 23
How do you solve
equations of the form
o
sin2x = 0.5 ?
(0≤x≤360)
2.3
Answer to Question 23
(i) decide on the
2 quadrants (sin is +ve)
(ii) press INV sin to get
angle
(iii) work out your 2 angles
(iv) divide each by 2
Question 24
How do you solve
equations like
o
o
cos2x -5sinx = 0 ?
(0≤x≤360)
2.3
Answer to Question 24
o
2
1-2sin x
o
(i) fit in
for cos2x
(ii) factorise
(iii) solve equation
Question 25
How do you find a
unit vector parallel
to a given vector ?
3.1
Answer to Question 25
(i) find the length of
the given vector
(ii) divide all the
components by
this length
Question 26
How do you prove that
a line is a tangent to a
circle ?
2.4
Answer to Question 26
Rearrange line to make
y = or x =
Substitute line into circle
Prove it has equal roots
2
using b -4ac = 0 or repeated
roots
Question 27
How do you find the
angle between two
vectors ?
3.1
Answer to Question 27
a.b
cosq =
ab
a
q
b
Question 28
What is a unit
vector ?
3.1
Answer to Question 28
A vector of length 1
unit
Question 29
What vector is equal to
AB + CD + BC ?
3.1
Answer to Question 29
AD
Question 30
If u = ai+bj+ck
then what is u in
component form ?
3.1
Answer to Question 30
U=
a
b
c
Question 31
How do you
integrate sin ax ?
3.2
Answer to Question 31
1
-/
a
cos ax + C
Question 32
How would you
differentiate a
function like
3
y = sin x ?
3.2
Answer to Question 32
3
x)
(i) write as (sin
(ii) multiply by the power
(iii) decrease power by one
(iv) multiply by the derivative of
the bracket
2
i.e. 3 sin x cosx
Question 33
Given experimental
data, how do you
find an equation in
x
the form y=ab or
b
y=ax ?
3.3
Answer to Question 33
(i) take logs of both sides
(ii) rearrange to get a
straight line equation
(iii) determine type
(iv) Equate and solve for a
and b
Question 34
How do you differentiate
an expression like
2 x  3
4
without multiplying it out ?
3.2
Answer to Question 34
(i) multiply by the power
(ii) decrease power by 1
(iii) multiply by
derivative of bracket
Question 35
Given an equation
-3k
like m = moe and
an amount by which
it has been decayed,
how do you find k ?
3.3
Answer to Question 35
(i) fit in m and mo
-3k
(ii) rearrange to get e =
(iii) take logs to get -3k =
(iv) solve for k
Question 36
What is
loga x + loga y equal
to ?
3.3
Answer to Question 36
Loga xy
Question 37
How do you solve
equations of the
form
x
3 = 0.155 ?
3.3
Answer to Question 37
(i) take logs of both sides
(ii) bring x down to front
(iii) solve the equation
Question 38
What is loga
to ?
3.3
n
x
equal
Answer to Question 38
nloga x
Question 39
If y =
1
2x
How should you
rewrite y so it is ready
to differentiate?
1.3
Answer to Question 39
1 1
x
2
Question 40
How do you find the
maximum or
minimum values of
acosx + bsinx + c ?
3.4
Answer to Question 40
(i) change
acosx+bsinx into
Rcos(x-a)
(ii) max is R+c