Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Page 1 of 67

ALGEBRA
2002 Oct/Nov Exams
1
...


(b)

Given that

= 1, express c in terms of a and b
...

-

in its lowest terms

2003 Oct/Nov Exams
2
...

2004 Oct/Nov Exams

3
...


(b)
(c)

Solve 3(m – 5) = 7 – 2(m – 3)
Factorise completely 4 - 16
...


2005 Oct/Nov Exams
4
...


(d)

Express

(e)

Solve the equation (

(f)

Simplify

-

as a single fraction in its lowest form
...



...


Page 2 of 67

2006 Oct/Nov Exams
5
...


(b)

Simplify

(c)

Express


...

2007 Oct/Nov Exams

6
...


(c)

Express as a single fraction

–


...


2008 Oct/Nov Exams
7
...


(b)

Simplify

(c)

Express


...

2009 Oct/Nov Exams

8
...


(b)

Simplify


...


...
(a)

Factorise completely 5 - 20


...


(d)

Express

+

as a single fraction
...


Page 3 of 67

(c)

Given that d =

, express y in terms of d and p
...


(c)

Simplify


...
(a)

Factorise 3

- 3
...


(c)

Solve the equation

(d)
(e)

Solve the inequation 7 – 2t < 9
Simplify 3x – 4y – 2(x – 4y) – 2y
...


2012 Oct/Nov Exams
11
...


(b)

Simplify


...

Factorise completely 2xy + x – 10y – 5
...


2013 Oct/Nov Exams
12
...


as a single fraction in its lowest terms
...


2014 Oct/Nov Exams
13
...


(b)

Simplify 5(2y – 3) – 2(5 – 2y)
...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

2015 GCE Exams

14
...


(b)

Simplify


...


-

as a single fraction in its simplest form
...
(a)

Factorise completely 5px – 5py + 3qx – 3qy
...


(c)

Express as a single fraction in its simplest form

-


...
(a)

Simplify

(b)

Simplify

(c)

Express


...

-

as a single fraction in its simplest form
...
(a)

Simplify

(b)

Simplify

(c)

Express


...

-

as a single fraction in its simplest form
...
(a)

Simplify

(b)

Simplify


...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

2018 INTERNAL

19
...


...

2018 GCE

1
...
(c)

Express


...


SETS
2003
1
...

5 like all the three subjects
...

6 like Physics and Chemistry only
...

(i)
Illustrate this information on a clearly labeled Venn diagram
...

(b) The number of pupils who do not like any of the three subjects
...
At showground, there were several traditional dances taking place
...

8 people watched all three dances
...


Page 6 of 67

34 people watched Siyomboka and Ngoma but not Kalela
...

24 people watched Kalela and Siyomboka but not Ngoma
...

Y people watched Ngoma only
...

32 people did not watch any of the three dances
...

(ii)
Given that 500 people went to the show ground, calculate:
(a) The value of y
...


2006
3
...
Their responses were as shown below
...

C= (pupils who cycle)
...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(a) Find the value of x
...

(ii) Given also that 43 pupils use vehicles only, find the total number of pupils
at this school
...
A survey was conducted on 60 women concerning the types of Sim cards
used in their Cell phones for the past 2 years
...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(b) How many women have used only two different types of Sim cards?
(c) If a woman is selected at radom from the group, what is the probability
that:
(i)
She has no Cell phone
(ii)
She has used only one type of Sim card
...
In a particular year, 150 candidates applied for training as teachers of
Mathematics, Science and Home Economics at COSETCO
...


(i) Given that 70 candidates applied for Science, find the values of a and b
...


Page 9 of 67

(iv)

How many candidates applied for either Science or Home Economics but
not Mathematics?
(v) If a candidate is selected at random from the group, what is the probability
that the candidate applied for one subject only?
2010
6
...
The results are shown in the Venn diagram
below
...

(ii) Given that G= (Glo), R= (Rodgers) and D= (Du), find;
(a) n(G
,
(b) n(D

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
In a certain month, a survey was conducted on 250 High School pupils to
find out the number of pupils that bought Oranges(O), Mangoes(M), and
Lemons(L)
...


(i)
(ii)
(iii)

Find the value of x
...


Page 11 of 67

2013
8
...


Given that n(
(i)
The value of x
...
Tokozan Sports Club offers Squash(S), Badminton (B) and Tennis (T)
...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(ii) Find the number of members who played Squash or Tennis but not
Badminton
...

2015 OCT/NOV
10
...
100 students took all these three courses
...


Page 13 of 67

(a) Find
(i)
The value of x
...

(iii) n(B
H’
(iv) n(B
H’
(b) If a student is chosen at random, what is the probability that he/she
took;
(i) One course,
(ii) At least two courses
...
Of the 50 villagers who can tune in to Kambani Radio Station, 29 listen to
news, 25 listen to sports, 22 listen to music, 11 listen to both news and
sports, 9 listen to both sports and music, 12 listen to both news and music,
4 listen to all the three programs and 2 do not listen to any program
...

(ii)
How many villagers
(a) Listen to music only
(b) Listen to one type of program only
(c) Listen to two types of programs only
...


Page 14 of 67

2017 OCT/NOV
12
...

(i)
Illustrate this information on a Venn diagram
...

2017 GCE
13
...


(i) Find the value of y if 7 students visited Mambilima Falls only
...


Page 15 of 67

(c) One tourist attraction only?
2018 OCT/NOV
14
...
All those who study
Chemistry also study Mathematics, 3 students study all the three subjects,
4 students study Mathematics only, 8 students study Chemistry and 14
students study Mathematics
...

2018 GCE
15
...
The learners uses either buses(B), cars(C) or walk(W) to school
...

How many learners use

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...


SEQUENCE AND SERIES
2016 OCT/NOV
1
...

Find;
(a) The value of x
(b) The first term
(c) The sum to infinity
...
The first three terms of a geometric progression are 6 + n,10 + n and 15 + n
...

2017 INTERNAL
3
...

2018 GCE
4
...

2018 INTERNAL

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...


Page 17 of 67

5
...

(a) Find the value of k,
(b) List the first three terms of the geometric progression,
(c) Find the sum to infinity
...
(a) Evaluate ∫

dx
...

2018 GCE
2
...


(b) Determine the equation of the normal to the curve y =
2
which passes through (3,7)
...
(a) Find the coordinates of the points on the curve y = 2
where the gradient is zero
...


2017 GCE
4
...


(b) Find the equation of the tangent to the curve y =
as a point where x = 2
...
The equation of the curve is y =


...

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
Given that M =(

) and N =(

(i) MN
1
...
If A =(
(i)

(ii) the values of x for which the determinant of

is 9
...
Given that M=(

), find

(i)

(ii)S
2007 Oct/Nov Exams

4
...
Hence find;
(ii)
(ii) AB
2008 Oct/Nov Exams
5
...
Given that A =(

), evaluate;

), find the

(i) Determinant of A

(ii)

(iii) value of

( )

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
If P =(

) and Q =(

(i) PQ

), find;

(ii) the value of a and b given that PQ = P – Q
2011 Oct/Nov Exams

)
...

(ii) Find the value of x, given that the determinant of A is 5
...
Given that A =(
) and B =( ), find the
8
...
Given that A =(2 2 -1), P =(
(i) 2P

) and Q =(

(ii) determinant of Q

), find;

(iii) AP

2014 Oct/Nov Exams
11
...


12
...

(ii) Find the value of a, given that the determinant of Q is 2
...
Given that Q =(

), find

(i) the value of x, given that the determinant of Q is 2
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
Given that K =(

), find

(i) the determinant of K

(ii)

2017 Oct/Nov Exams
15
...


(i) Find the value of x, for which the determinant of M is 22
...

2018 GCE
16
...

(ii) hence, find the inverse of A
...
Given that A =(

) and B =(

),

(i) find the value of y, given that the determinants of A and B are equal,
(i) hence, find the inverse of B
...
Three villages Lusuntha(L),Pondako(P) and Chomba(C) are linked up by
three straight paths as shown in the diagram below
...


Page 21 of 67

Lusuntha (L)

6km
Chomba (C)

9km

Pondako (P)

Given thatLP =6km, PC = 9km and angle LPC =9
...

(b) What is the area bounded by the three footpaths correct to 1 decimal
place
...
Calculate this distance correct to 1 decimal
place
...
During a soccer training session, the goal keeper (G) was standing at the
centre of the goal posts, a shooting player(S) was 21m from the goal keeper’s
position, the trainer (T) was 19m from the goal keeper and angle TGS = 11 as
shown in the diagram below
...

(b) The trainer T rolls a ball along TS for a shooting player 9(S) to kick to the
mouth
...

(c) The goal keeper (G) is free to intercept the ball at any point along TS before
it reaches the player at S
...

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
Three towns Choma (C), Monze (M) and Namwala (N) are such that the
distance from Monze to Choma is 100km and Monze to Namwala 80km
...

C
N

N

100km

x

80km

(a) Calculate the
(i) Value of x
(ii) Distance from Choma to Namwala correct to 2 decimal places
...

(b) Given that Nikoh (H) is a bus station on the Choma – Namwala route
such that MH is the shortest distance from Monze to Nikoh, calculate this
shortest distance MH correct to 2 decimal places
...

2010 Oct/Nov Exams
3
...
P is 7
...
2km from R
and angle PQR=12
...


Page 23 of 67

Q

7
...
2km

P

R

(a) Calculate
(i) The distance PR
(ii) The area of triangle PQR
(b) Find the shortest distance from Q to PR
...
Calculate his average
speed in km/h
...
A girls’ high school has been built in such a way that the Administration
block (A), dormitories (B) and classes (C) are connected by straight corridors
...
The bearing of B from A is 11 and the
bearing of A from C is 03 as shown in the diagram below
...


Page 24 of 67

(iii) TheAdministration decided to build a tuckshop at point T along BC such
that T is the shortest distance from A
...
75c , calculate AT
...
The diagram below shows Kapenta (K), Bream (B) and Chisense (C) fishing
camps on Lake Manzi
...
4km
...

(b) The area of triangle KBC
...
Calculate the distance between C and N
...
M, T and R are Food Reserve Agency Maize buying points in a given district
...

T
32km
M
27km

R

Calculate;
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(ii) The area of triangle MTR
(ii) RT to the nearest kilometer
...

2014 Oct/Nov Exams
8
...
Chapa is 78km from Kabwela and Muzi is 123km from
Kabwela
...

(ii) Calculate the distance CM
...
Find the total cost of constructing this road, if the company
charges K21 000
...

2015 Oct/Nov Exams
9
...
7m, AB=
1
...


Page 26 of 67

B

1
...
7m

Calculate
(i) The area of triangle AOB correct to 1 decimal place
...

(iii) The shortest distance from A to OB
...
The diagram below shows the locations of three secondary schools ,
namely Mufulira (M), Kantanshi (K) and Ipusukilo (I) in Mufulira district
...

K
3km
5km

M

I

Calculate
(i) MI
(ii) The area of triangle MKI
(iii) The shortest distance from K to MI
...


Page 27 of 67

(b) Solve the equation tan = 0
...


2017 GCE Exams
11
...
5m, angle PQR =3
QPR=

...
5m

Calculate
(i) PQ
(ii) the area of triangle PQR
(iii) the shortest distance from R to PQ
...
(a) The diagram below shows the location of houses for a village Headman
(H), his secretary (S) and a trustee (T)
...
3km from S
...
9km from H and
angle THS = 13
...


Page 28 of 67

H

1
...
3km

S

T
Calculate
(i) the area of triangle THS
(ii) the distance TS
(iii) the shortest distance from H to TS
...


2018 GCE Exams
13
...

A
15km

B
C

Given that AB = 15km, angle ABC = 7

angle ACB = 4

, calculate the

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(iii) Shortest distance from B to AC
(b) Solve the equation cos

for


...
In the diagram below, K, N, B and R are places on horizontal surface
...


K

N
50m
B

R
(a) Calculate
1
...
(ii) the area of triangle KNB
...


, calculate the

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a)

2x + 5 = 10 – 3x

(b)

2x + 3x = 10 – 5

=
cb – a = c

=

cb – c = a

X=1

=
c=

(c)

-

(c)

Answer
3

- 12

3(

- 4)

3(

-

)

3[

2003
2
...


(a)

+
= +

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) =

(b) =

2a = 3a + b

ab = 3a + b

2a – 3a = 2

ab – b = 3a

-a = 2

=

a = -2

b=

-

(d) (

(c)
=

√

=

x+3=

= 64
=

√

8

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) 2x – 6 = 4 – 3(x – 5)
2x – 6 = 4 – 3x + 15
2x + 3x = 4 + 15 + 6
5x = 25
X=5
(b)

-

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) x -

(b) 3x - 12

=8 – (

=3x(1 - 4

=8 – 4

=3x(

=4
(b)

-

)
)
]

=3x[
–

=
=
=
2008
7
...


Page 34 of 67

=
[

=

]

=r(2 –r)
2009
8
...
(a) 5 - 20
=5(1 - 4
=5( =5[

(b) 2(2x – 5) + 2 = x + 7
)

4x – 10 + 2 = x + 7
4x – x =7 + 10 - 2

)
]

=
X=5

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) 3

–3

=3(

–1

=3(

-

=3[

(b)
=
)

=
]

-

(c)

=
3x +6 = 60
3x = 60 - 6

=

=
X = 18

(d) 7 – 2t < 9
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a)

(b)

2x – 4 = 18

(c) 4b – 3 < 6b + 4

=4b – 6b < 4 + 3

2x = 18 + 4

=

=

=

b > -3

X = 11
(d) 2xy + x – 10y – 5
=x(2y +1) – 5(2y + 1)
=(x – 5)(2y + 1)
2013
12
...


Page 37 of 67

]

=3[

2014
13
...
(a) 5px – 5py + 3qx – 3qy

(b)

=5p(x – y) +3q(x – y)

=

=(5p + 3q)(x – y)

=

prod=-10 sum=-3 factors=-5,2

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a)

(b)

(c) 4(1 – 2x)> 32

3(x + 4) = 2(2x – 1)

=

4 – 8x > 32

3x + 12 = 4x – 2

=(h – k)

-8x > 32 - 4

3x – 4x = -2 – 12

>

=

x<

X = 14
2016
3
...


Page 39 of 67

2017 GCE
4
...
(a)

(b)

(c)

=

=

=

=

=

=
=

=

=

[

]

=

=2(x + 2)
2018 GCE
6
...
(a)

(b)

(c)

=

=

=

=

=

=

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...

(i)

(a) 1+ 5 + 10
= 16 pupils
(c) 6 pupils
2005

2
...


Page 41 of 67

(ii)

(a) 84 + 34 + 8 + 24 + 42 + 32+ y + y – 2=500
2y + 222 = 500
2y = 500 – 222
y = 139
(b)84 + 24 + (139 – 2) + 32
= 177 people
2006

3
...
(a) a + 3 + 2 + 4 = 23
a + 9 = 23
a = 23 – 9
a = 14
(b)5 + 3 + 4
= 12 women
(c)(i)

(b) 0 pupils

(e)14 + 5 + 10
(d) )14 + 8

= 29 women

= 22 women
(ii)
=
2009
5
...


Page 42 of 67

a = 70 – 55
a = 15
(ii)5 + 30 +10

b = 150 - 145
b=5
(iii) 35 students

= 45 students
(iv)15 + 30 + 35
= 80 students

(v)
=
=
2010

6
...
(i) 22 + 23 + 51 + x + 13 + 16 + 20 + 60 = 250
x+ 205 = 250
(ii) 16 + 13 + 20 + 60
x = 250 – 205
= 109 pupils
x = 45
(iii)20 + 16 + 22
58 pupils
2013
8
...


Page 43 of 67

2014
9
...
(a) (i) 15 + 15 + 10 + x + 15 + 5 = 100
70 + x = 100
x = 100 – 70
x = 30
(ii)Human resource= 10 + 10 + 15 + 5 = 40
} {
}
(iii)n(B
H’={
= 15
} {
}= 15 + 30 = 45
(iv) n(B
H’={
(b)(i) p(one course) =
=

=

=

(ii)p(at least two courses)=
=

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(i)
(ii)(a)Music only=5
(b) one type of program=5 + 9 + 10 = 24
(c)two types of programs=8 + 7 + 5=20
2017GCE

12
...
(i)2y + 1 = 7
(ii)(a)6 + 2 =8
(b)4 + 1 + 2 = 7
2y = 7 – 1
2y = 6
y=3

(c) 6 + 2(3) + 1 + 8=21

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(i)
(ii)Physics ony = 6 students
(b) two subjects only=2 + 5 = 7
(c)Maths and Physics not Chemistry = 2
2018 Oct/Nov
15
...
(a) To find the common ratio, we use
(c) S∞ =
(x – 3)(x – 3) = (x + 1)(x – 1)

S∞ =

x2 – 3x – 3x + 9 = x2 – x + x – 1

S∞ =

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) will use the same formula we use when calculating the common ratio
...
140625
S6 =180

= or 1
...


Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) r =

(c) Sn =

r=

( )

S8 = =

(b)Tn = arn – 1

S8 =

Tn = 20( )n – 1

S8 =

Tn= 20

S8 =

Tn =

S8 =26
...
(a) Tn = arn – 1

(b) Sn=

T3 = ar3 – 1

S5 =

ar2
A=

( )

S5 =

………equation (i)

T4 = ar4 – 1

S5 = 2
S5 = 2

= ar3………
...
987654321

=
54r = 18

S5 = 2
...


Page 48 of 67

a=
a=

( )

=2

the first term = 2 and the common ratio is
2018 INTERNAL
5
...

(c)S∞ =

,r=

product= -60

sum = -7

factors = 5, -12

=

S∞ =
S∞ =
S∞ =
S∞ = 16
S∞ = 64
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(a) ∫

(b)y = x +

= *

+

= (

)

= (

)

=(

)

(

= (

)

(

=1(

)

(

at x = 4,

)

=1-

=

)

=

)

=

=

gradient of the normal

=

=

=

=

=

=

to find y replace x
value in the original
equation
y=1+ =5
y – y1 = m(x – x1)
y–5=
y–5=
y=

3y = -4x + 31
2018GCE
2
...


Page 50 of 67

*

+
)

=(

(

)

(b)y = 2x2 – 3x - 2

)

=(
=

at x = 3, 4(3)- 3 = 9

=

gradient of the normal

=

=

=-3

y – y1 = m(x – x1)
y–7=

(x – 3)

y–7=

x+

y=
y=
=
9y = -x + 66
2017 INTERNAL
3

2

3
...


Page 51 of 67

y = -84

(b)∫
*

+

]
=[
] [
=[
=(27 – 9) – (-1 – 1)
=18 – (-2)
=18 + 2
= 20

]

2017 GCE
(b)y = x2 – 3x - 4

4
...
(a)y = x3 = 3x2 – 3x
At x = 2,
(2)2 – 3(2)
=6
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(i) MN = (

)(

)
)

=(
MN=(

)(

(ii)NM=(

)
)

=(

)

NM=(

)

2003
2
...


)

Page 53 of 67

=

(

=(
(

Therefore,B

)(

)
)

)
)

=(
)

=(

2005
(

2
...


Page 54 of 67

2006
(

3
...
(i)deter A =21
A =(

(ii)

=

(

)

)

)
(iii) AB =(

)( )

21 = 5x +6

=(

)

21 – 6 = 5x

AB =( )

21= (5

)

) –(3

x=3
2008
)(

5
...
(i) deter A =(3

(ii)

(

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(i) PQ =(

)

(ii) PQ = P- Q
)

=(

(

)

PQ =(

)

(

)

2a = 2 – a

b = 1- b

2a +a =2

b+b =1

a=

b=

2011
)

8
...
(i) deter A =(2
Deter A =10 +3

(ii)

(

(

=
=

(

)
)

=13
Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
(i) 2P =2(

)

2P=(

)

(ii) deter Q=(
deter Q=(
Deter Q=2+4
Deter Q = 6
(

(iii) AP=

)

=
=
=

2014
11
...


Page 57 of 67

(iii) AB =(

)(

)
)

=(
)

=(
)

=(

2015
)

(ii) deter Q = 2

Deter Q =(
Deter Q = -2a – 6

2 = -2a - 6
2a = -6 – 2

12
...
(i) deter Q (3

(ii)
(

2 = 12 +2x

)

2 – 12 = 2x
x = -5
2017 GCE
14
...


)

Page 58 of 67

15
...
(i) deter A =(2x
12 = 2

2018 GCE
(ii)
A= (

–6

12 + 6 = 2

)
)

=(

(

=
=9
√ = √
x=
x=3
2018 Oct/Nov Exams
17
...


)

Page 59 of 67

TRIGONOMETRY
2005

1
...
36061769

A = 23
...
64709433
LC = 10
...
8k

A=
23
...
6
=
h = 4
...
5km
2008
2
...
9320744

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573
...
4686778
A = 187

√

TS = 32
...
33333333
S
...


(a) (i) 36

- 29

X=7
(ii) (

=

A=
-2nc

(
(
(

A=
A=4000

= 10 000 + 6400 - 16000
16400 + 10284
...
177772
A =3064
...
3542217
CN = 163
...


Page 61 of 67

(b) Shortest distance

(c)

=

A = bh

(

=

A=

6400 =

+ 1407
...
7504
√

h = 37
...
D = 37
...
65585326
HN =70
...


(a) (i) (

=

+

- 2p

(

=(

(

= 174
...
76 – 200
...
32

√

)(7
...
22964618
PR = 18
...
D =

A=

S
...
43983425

S
...
769230769

A = 43
...
D = 4
...


Page 62 of 67

(c) Speed =

, 30 minutes= 0
...
8km/h
2011
5
...
911572

√
√
BC =152
...
D =
S
...
D =
S
...
53618421
S
...


(a)
(

=
=

924
...
16 – 656 = -640

(b) A =
A=
A = 160
A = 145
...


Page 63 of 67

A = 145km
= -0
...
D =
S
...
7714694

S
...
D = 14
...


(i) R ̂ = 13

-

R̂T=7

(ii) (

=

- 2rt

(

=

(ii) A =

(

= 1024 + 729 -1728

A=

(

= 1753 – 591
...
37170076
A = 405
...
08796257
RT = 34km

S
...
D =
S
...
D = 23
...
D =24km
2014
8
...
00

A=
A = 4737
...


135

Page 64 of 67

(i) (
(
(
(

=
=
– 2(123)(78)
= 15129 + 6084 -3001
...
664515

=√
√
CM = 134
...


(i) A =

(ii) Shortest distance

A=

S
...
D =

A = 0
...
D =

A = 0
...
D = 0
...
7)(1
...
89 + 1
...
521195045

=√
√
OB = 2
...
4m
(iii) Shortest distance
S
...
D =
S
...
D = 0
...
D = 0
...


Page 65 of 67

2016 Exams
10
...
2606043)
= 34 + 10
...
047694656
A = 7
...
656864368
MI = 6
...
D =
S
...
D =
S
...
120300752
S
...
12km
2017 GCE
11
...
15
A = 538
...
5k
(iii) Shortest distance

r
r=

= 36
...
D =
S
...


Page 66 of 67

r = 50
...
D =

PQ = 50
...
D = 21
...
D = 21
...


(a) (i) A =

(ii) (
(
(
(

(iii) Shortest distance

A=

S
...
D =

A = 0
...
D =

A = 0
...
69 + 3
...
94(-0
...
3 + 3
...
D =0
...
D = 0
...
911249009
TS = 2
...


(a) (i)

(ii) A =
but we need to find angle A first
BAC + 79 + 40 = 180

b=

BAC = 180 - 119

b = 22
...


Page 67 of 67

AC = 22
...
D =

A = 150
...
D =

A = 150
...
D =
S
...
11790393
S
...
1km
2018 INTERNAL
18
...
92016097
KR = 87
...
050808
A = 1732

(b) Shortest distance from R to KN
s
...
d =
s
...
8m

Compiled and solved by Sikaonga Moses/The only way to learn Mathematics is to do
Mathematics//0968555444/0953236573

---