MATHEMATICS
FORM 2
MID TERM
TERM 1
INSTRUCTIONS
 Answer all the questions
SECTION A
 Evaluate 8÷2+12x94x6 [3 Marks]
56÷7x2  A matatu travelling at 56 Km/h take 2 ½ hours to move from town A to town B.
Find the distance between towns A and B. [2 Marks]  Determine the gradient and the coordinates of the (x) and (y) intercepts of the line whose equation is [3 Marks]
2y+3x=1  Find the correct 3s.f the value of [2 Marks]
^{1}/_{6.43} + ^{2}/_{3.56} + ^{1}/_{8.51}  Without using mathematical tables, evaluate [3 Marks]
27^{2/3}_{ }x (^{81}/_{16})^{1/4}  The diagonals of a rhombus measure 9.2 cm and 7.5 cm respectively. Calculate the area of the rhombus [2 Marks]
 A man is three times as old as his daughter. In twelve years time he will be twice as old as his daughter. Find their present age. [3 Marks]
 Use logarithm tables to evaluate [4 Marks]
 An artisan has 63Kg of metal of density 7000Kg/m^{3}. He intends to use it to make a rectangular pipe with external dimension 12 cm by 15 cm and internal dimension 10 cm by 12 cm. calculate the length of the pipe in metres. [4 Marks]
 Determine the equation of a line that passes through (2,5) and is parallel to the line whose equation is [4 Marks] 5y+2x=10
 Use the elimination method to solve the simultaneous equations[4 Marks]
2x+3y=1
3x=2y+8  A trader sold a wrist watch for sh. 3,150 after giving a 10% discount. Find the marked price of the watch. [2 Marks]
 Express as a fraction in its lowest form [3 Marks]
 Seven people can build five huts in 30 days. Find the number of people working at the same rate that will build nine similar huts in 27 days. [3 Marks]
 The size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon. [3 Marks]
 Line AB below shows a side of triangle ABC. BC= 5cm and angle ABC = 60º
 Using a ruler and compass only, complete the triangle ABC. [2 Marks]
 From C construct a perpendicular to meet line AB at point N. Measure length CN in centimetres [2 Marks]
 Determine the area of triangle ABC [1 Mark]
SECTION B [50 MARKS]

 Complete the tables below for the equations of the lines y^{3}/_{4x}+4 and y=3+2x
x 2 0 2 y 4 x 2 0 2 y 3  using one big square to represent 1 unit on y – axis and 2 big squares to represent 1 unit on – axis, draw the lines + 4 and [5 Marks]
 use your graphs to solve the simultaneous equations[1 Mark]
3x+2y=8
2xy=3
 Complete the tables below for the equations of the lines y^{3}/_{4x}+4 and y=3+2x
 a school hall measure 10m long, 7m wide and 4m high. All its inside walls and ceiling are painted.
Calculate, the total surface area painted
 the cost of painting at 200/= per square metre. [10 Marks]
 a bird flies from tree P to another tree Q which is 50m on a bearing of 030º from P. from Q the bird flies 80m due west to another tree R and finally flies due south to another tree S which is on a bearing of 120º from P.
 using the scale 1cm = 10m, construct an accurate scale drawing showing the positions of P,Q,R, and S [5 Marks]
 by measurement from your scale drawing determine;
 the distance and bearing of R from Q [2 Marks]
 the distance and bearing of S from R [2 Marks]
 the distance of S from P [1 Mark]

 On a Cartesian plane plot and draw the triangle ABC, A(1,2), B (1,6), C (5,5) [2 Marks ]
 Draw the image of triangle ABC after reflection on the line y=x
 Draw A"B"C" the image of ABC after reflection along y – axis [2 Marks]
 Draw A"B"C" the image of A'B'C' after rotation through 180 about the origin [2 Marks]
 Determine the mirror line that makes A'''B"'C"' the image of triangle ABC [2 Marks]
 The table shows recordings from surveyors’ field book.
 Draw a sketch diagram from the data in the field book [2 Marks]
 Given that the recordings are in metres, determine the area of the land in hectares.[8 Marks]
MARKING SCHEME
SECTION A
 Evaluate 8÷2+12x94x6 [3 Marks]
56÷7x2
8÷2+12X94x6 = 4+10824=80
56÷7x2= 8x2=16
^{80}/_{16}=5
 A matatu travelling at 56 Km/h take 2 ½ hours to move from town A to town B.
Find the distance between towns A and B. [2 Marks]
Distance= Speed x time
56 x ^{5}/_{2}=140km/h  Determine the gradient and the coordinates of the (x) and (y) intercepts of the line whose equation is [3 Marks]
2y+3x=1
y=^{1}/_{2 } ^{3}/_{2}x
Gradient= ^{3}/_{2}
when y=0, x=^{1}/_{3}
(0,^{ 1}/_{3})
when x=0, y=^{1}/_{2}(0,^{1}/_{2})  Find the correct 3s.f the value of [2 Marks]
^{1}/_{6.43} + ^{2}/_{3.56} + ^{1}/_{8.51}0.1555+(0.2809x2)+0.1175
0.1555+0.5618+0.1175
0.8348
0.835  Without using mathematical tables, evaluate [3 Marks]
27^{2/3}_{ }x (^{81}/_{16})^{1/4}
(3^{3})^{2/3}_{ }x (^{34}/2^{4})^{1/4 } 3^{2}x(^{24}/3^{4})^{1/4}=3^{2}x^{2}/_{3} = 3x2
=6^{}  The diagonals of a rhombus measure 9.2 cm and 7.5 cm respectively. Calculate the area of the rhombus [2 Marks]
½ x 9.2 x 7.5=34.5cm^{2}  A man is three times as old as his daughter. In twelve years time he will be twice as old as his daughter. Find their present age. [3 Marks]
Daughter's age=x
Man's age =3x
3x+12=2(x+12)
3x+12=2x+24
3x2x=2412
x=12
12x3=36 years  Use logarithm tables to evaluate [4 Marks]
 An artisan has 63Kg of metal of density 7000Kg/m^{3}. He intends to use it to make a rectangular pipe with external dimension 12 cm by 15 cm and internal dimension 10 cm by 12 cm. calculate the length of the pipe in metres. [4 Marks]
Density=m/v
Volume=m/d = ^{63}/_{7000}=0.009m^{3}=9000cm^{3}
Volume = l x w x h= 12x15=180cm^{2}
10x12=120cm^{2}
180cm^{2}120cm^{2}=60cm^{2}
^{9000}/_{60}=150cm=1.5m  Determine the equation of a line that passes through (2,5) and is parallel to the line whose equation is [4 Marks] 5y+2x=10
5y=102x
y=2  ^{2}/_{5}x
m1=2/5
y=mx+c
5=2/5x2 +c
5=4/5+c
41/5=c
y5 =2
x+2 5
5y25=2x4
5y=2x21  Use the elimination method to solve the simultaneous equations[4 Marks]
2x+3y=1
3x=2y+8
(3x 2y=8)x2
(2x+3y=1)x3
6x4y=16
6x+9y=3
13y=13
y=1
3x2(1)=8
3x+2=8
3x=6
x=2  A trader sold a wrist watch for sh. 3,150 after giving a 10% discount. Find the marked price of the watch. [2 Marks]
3150=90%
? =100%
^{100}/_{90}x3150=3500
Marked Price= Ksh.3500  Express as a fraction in its lowest form [3 Marks]
3.71717171...=r
37.171717....=10r
371.717171..=100r
100rr=99r
99r=368
=3 ^{71}/_{99}  Seven people can build five huts in 30 days. Find the number of people working at the same rate that will build nine similar huts in 27 days. [3 Marks]
7 people→ 5 huts →30 days
? → 9 huts →27days
Rater of work is same
^{30}/_{27} x ^{9}/_{5} x7=
2x7=14
14 people
^{}  The size of each interior angle of a regular polygon is five times the size of the exterior angle. Find the number of sides of the polygon. [3 Marks]
interior angle=5x
exterior= x
5x+x=180
6x=180
x=30
360/30=12
12 sides  Line AB below shows a side of triangle ABC. BC= 5cm and angle ABC = 60º
 Using a ruler and compass only, complete the triangle ABC. [2 Marks]
 From C construct a perpendicular to meet line AB at point N. Measure length CN in centimetres [2 Marks]
 Determine the area of triangle ABC [1 Mark]
^{1}/_{2} x 8 x 5
=20cm^{2}
SECTION B [50 MARKS]

 Complete the tables below for the equations of the lines y^{3}/_{4x}+4 and y=3+2x
x 2 0 2 y 7 4 1 x 2 0 2 y 7 3 1  using one big square to represent 1 unit on y – axis and 2 big squares to represent 1 unit on – axis, draw the lines + 4 and [5 Marks]
 use your graphs to solve the simultaneous equations[1 Mark]
3x+2y=8
2xy=3
 Complete the tables below for the equations of the lines y^{3}/_{4x}+4 and y=3+2x
 a school hall measure 10m long, 7m wide and 4m high. All its inside walls and ceiling are painted.
Calculate, the total surface area painted
Area of ceiling(10x7)=70cm^{2}
Area of walls(7x4)2=56cm^{2}
Area 0f walls(10x4)2=80cm^{2}
Total surface areas= 70+56+80=206cm^{2}  the cost of painting at 200/= per square metre. [10 Marks]
cost of painting=206x200=41,200
 the total surface area painted
 a bird flies from tree P to another tree Q which is 50m on a bearing of 030º from P. from Q the bird flies 80m due west to another tree R and finally flies due south to another tree S which is on a bearing of 120º from P.
 using the scale 1cm = 10m, construct an accurate scale drawing showing the positions of P,Q,R, and S [5 Marks]
 by measurement from your scale drawing determine;
 the distance and bearing of R from Q [2 Marks]
11.3 x 10=113m±1  the distance and bearing of S from R [2 Marks]
Bearing 067±1  the distance of S from P [1 Mark]
Bearing 180º
 the distance and bearing of R from Q [2 Marks]
 using the scale 1cm = 10m, construct an accurate scale drawing showing the positions of P,Q,R, and S [5 Marks]

 On a Cartesian plane plot and draw the triangle ABC, A(1,2), B (1,6), C (5,5) [2 Marks ]
 Draw the image of triangle ABC after reflection on the line y=x
 Draw A"B"C" the image of ABC after reflection along y – axis [2 Marks]
 Draw A"B"C" the image of A'B'C' after rotation through 180 about the origin [2 Marks]
 Determine the mirror line that makes A'''B"'C"' the image of triangle ABC [2 Marks]
 The table shows recordings from surveyors’ field book.
 Draw a sketch diagram from the data in the field book [2 Marks]
 Given that the recordings are in metres, determine the area of the land in hectares.[8 Marks]
P=½x120x70=4200m^{2}
Q=½x80(75+40)=40x15=4600m^{2}
R=½x80x25=100m^{2}
S=½x120x80=4800m^{2}
T=½x60(80+50)=30x130=3900cm^{2}
V=½x100x50=2500m^{2}
Total area=4200+4600+1000+4800+3900+2500=21000m^{2}=2.1ha
 Draw a sketch diagram from the data in the field book [2 Marks]
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