MATHEMATICS
FORM 2
MID TERM
TERM 1
INSTRUCTIONS
- Answer all the questions
SECTION A
- Evaluate -8÷2+12x9-4x6 [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 co-ordinates 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]
272/3 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/m3. 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
2x-y=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+12x9-4x6 [3 Marks]
56÷7x2
-8÷2+12X9-4x6 = -4+108-24=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 co-ordinates of the (x) and (y) intercepts of the line whose equation is [3 Marks]
2y+3x=1
y=1/2 - 3/2x
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]
272/3 x (81/16)-1/4
(33)2/3 x (34/24)-1/4
32x(24/34)1/4
=32x2/3 = 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=34.5cm2 - 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
3x-2x=24-12
x=12
12x3=36 years - Use logarithm tables to evaluate [4 Marks]
- An artisan has 63Kg of metal of density 7000Kg/m3. 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=0.009m3=9000cm3
Volume = l x w x h= 12x15=180cm2
10x12=120cm2
180cm2-120cm2=60cm2
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=10-2x
y=2 - 2/5x
m1=-2/5
y=mx+c
5=-2/5x-2 +c
5=4/5+c
41/5=c
y-5 =-2
x+2 5
5y-25=-2x-4
5y=-2x-21 - 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
6x-4y=16
6x+9y=3
-13y=13
y=-1
3x-2(-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%
100/90x3150=3500
Marked Price= Ksh.3500 - Express as a fraction in its lowest form [3 Marks]
3.71717171...=r
37.171717....=10r
371.717171..=100r
100r-r=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
=20cm2
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
2x-y=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)=70cm2
Area of walls(7x4)2=56cm2
Area 0f walls(10x4)2=80cm2
Total surface areas= 70+56+80=206cm2 - 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=4200m2
Q=½x80(75+40)=40x15=4600m2
R=½x80x25=100m2
S=½x120x80=4800m2
T=½x60(80+50)=30x130=3900cm2
V=½x100x50=2500m2
Total area=4200+4600+1000+4800+3900+2500=21000m2
=2.1ha
- Draw a sketch diagram from the data in the field book [2 Marks]
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