QUESTIONS
SECTION I: Answer all question in this section on the spaces provided
 Without using calculators or mathematical tables, evaluate, leaving your answer in surd form
sin60º × cos30º (3mks)
tan 30º sin30º  The mass in kg of nine sheep in a pen were 13, 8, 16, 17, 19, 20, 15, 14, and 11. Determine the quartile deviation (3mks)
 Find
 The equation of the tangent to the curve y=2x^{2}+ 2 at (2, 8). (3mks)
 The equation of the normal to the curve at the same point. (2mks)
 The figure below is a sketch of a curve whose equation is y=x^{2}+x+5.
It cuts the line y = 11at points P and Q.
Find the area bounded by the curve y=x^{2 }+ x + 5 and the line y = 11 using the trapezium rule with 5 strips  Using a ruler and a pair of compasses only:
 Construct a parallelogram PQRS in which PQ=6 cm, and QR = 4 cm and angle SPQ = 75º (3mks)
 Determine the perpendicular distance between PQ and SR (1mk)
SECTION II (30MKS): Answer any three questions from this section in the spaces provided
 A quadrilateral with vertices at K(1,1), L(4,1), M(2,3), and N(1,3) is transformed by matrix T= [1 3] to quadrilateral K’L’M’N’.
[0 1] Determine the coordinates of the image (3mks)
 On the grid provided, draw the object and the image (2mks)
 Describe fully the transformation which maps KLMN onto K’L’M’N’ (2mks)
 Determine the area of the object (1mk)
 Find the matrix which maps K’L’M’N’ to KLMN (2mks)
 The positions of three ports A, B, and C are (34ºN, 16ºW), (34ºN, 24ºE) and (26ºS, 16ºW) respectively.
 Find the distance in nautical miles between;
 Ports A and B to the nearest nautical mile. (3mks)
 Ports A and C (2mks)
 A ship left port A on Monday at 1330 h and sailed to port B at 40 knots. Calculate:
 The local time at port B when the ship left port A; (2mks)
 The day and the time the ship arrived at port B. (3mks)
 Find the distance in nautical miles between;

 Complete the table below by filling in the blank spaces. (2mks)
X
0^{0}
15^{0}
30^{0}
45^{0}
60^{0}
75^{0}
90^{0}
105^{0}
120^{0}
135^{0}
150^{0}
165^{0}
180^{0}
3cos 2x
2.6
1.5
1.5
2.5
3
2.6
1.5
1.5
2sin(2x+30^{0})
2
1
0
1.7
2
1
 On the grid provided; draw on the same axis; the graph of y = 3 cos 2x and y = 2sin (2x +30º) for 0º ≤ x ≤180º.
(Take the scale: 1cm for 15º on the xaxis and 2cm for 1 unit on the yaxis). (5mks)  Using the graph in part (b) above;
 Estimate the solution to the equation 3cos 2x – 2 sin (2x+30º) = 0 (2mks)
 Estimate the range of values of x for which 3cos 2x ≤ 2 sin (2x + 30º) giving your answer to the nearest degree. (1mk)
 Complete the table below by filling in the blank spaces. (2mks)
 The table below shows the number of goals scored in handball matches during a tournament.
No. of goals
09
1019
2029
3039
4049
No. of matches
2
14
24
12
8
 Draw a cumulative frequency curve on the grid provided (5mks)
 Using the curve drawn in (a) above, determine
 The median (1mk)
 The number of matches in which goals scored were not more than 37 (1mk)
 The interquartile range (3mks)
MARKING SCHEME
SECTION I: Answer all question in this section on the spaces provided
 Without using calculators or mathematical tables, evaluate, leaving your answer in surd form
sin60º × cos30º (3mks)
tan 30º sin30º
^{√3}/_{2} × ^{√3}/_{2} = ^{3}/_{4}
^{1}/_{√3} × ^{1}/_{2} ^{1}/_{2√3}
= 3/4 ÷ 1/2√3
= 3/4 × 2√3
= 3√3/2  The mass in kg of nine sheep in a pen were 13, 8, 16, 17, 19, 20, 15, 14, and 11. Determine the quartile deviation (3mks)
Q_{2} = 8, 11, 13, 15, 16, 17, 19, 20
Q_{1} = 11 + 13 = 12 Q_{3} = 17 + 19 = 18
2 2
Queasrtile deviation = Q3  Q1
2
= 18  12
2
= ^{6}/_{2}
= 3  Find
 The equation of the tangent to the curve y=2x^{2}+ 2 at (2, 8). (3mks)
dy = 4x
dx
dy = 2 × 4
dx
= 8
dy = 8
dx
(2, 8) (x, y)
y  8 = 8
x  2 1
y  8 = 8x  16
y = 8x  8  The equation of the normal to the curve at the same point. (2mks)
(2, 8) (x, y)
y  8 = 1
x  2 8
8y  64 = x + 2
8y = x + 66
y = 1/8x + 66
 The equation of the tangent to the curve y=2x^{2}+ 2 at (2, 8). (3mks)
 The figure below is a sketch of a curve whose equation is y=x^{2}+x+5.
It cuts the line y = 11at points P and Q.x 3 2 1 0 1 2 y 11 7 5 5 7 11
Find the area bounded by the curve y=x^{2 }+ x + 5 and the line y = 11 using the trapezium rule with 5 strips
A = rectangular area  area under curve
= 5 × 11  1/2 [(11 + 11) + 2(7 + 5 + 5 + 7)]
=55  1/2(22 + 48)
= 55  35 = 20 sq. units  Using a ruler and a pair of compasses only:
 Construct a parallelogram PQRS in which PQ=6 cm, and QR = 4 cm and angle SPQ = 75º (3mks)
 Determine the perpendicular distance between PQ and SR (1mk)
3.9 cm
 Construct a parallelogram PQRS in which PQ=6 cm, and QR = 4 cm and angle SPQ = 75º (3mks)
SECTION II (30MKS): Answer any three questions from this section in the spaces provided
 A quadrilateral with vertices at K(1,1), L(4,1), M(2,3), and N(1,3) is transformed by matrix T= [1 3] to quadrilateral K’L’M’N’.
[0 1] Determine the coordinates of the image (3mks)
 On the grid provided, draw the object and the image (2mks)
 Describe fully the transformation which maps KLMN onto K’L’M’N’ (2mks)
is a shear xaxis invariant scale factor 3 Determine the area of the object (1mk)
2 × 1 = 2
1/2 × 2 × 2 = 4 units square
 Determine the area of the object (1mk)
 Find the matrix which maps K’L’M’N’ to KLMN (2mks)
 Determine the coordinates of the image (3mks)
 The positions of three ports A, B, and C are (34ºN, 16ºW), (34ºN, 24ºE) and (26ºS, 16ºW) respectively.
 Find the distance in nautical miles between;
 Ports A and B to the nearest nautical mile. (3mks)
 Ports A and C (2mks)
 A ship left port A on Monday at 1330 h and sailed to port B at 40 knots. Calculate:
 The local time at port B when the ship left port A; (2mks)
 The day and the time the ship arrived at port B. (3mks)
 Find the distance in nautical miles between;

 Complete the table below by filling in the blank spaces. (2mks)
X
0^{0}
15^{0}
30^{0}
45^{0}
60^{0}
75^{0}
90^{0}
105^{0}
120^{0}
135^{0}
150^{0}
165^{0}
180^{0}
3cos 2x
3 2.6
1.5
2.0 1.5
2.5
3
2.6
1.5
0 1.5
2.6 3 2sin(2x+30^{0})
1 1.7 2
1.7 1
0
1 1.7
2
1.7 1
0 1  On the grid provided; draw on the same axis; the graph of y = 3 cos 2x and y = 2sin (2x +30º) for 0º ≤ x ≤180º.
(Take the scale: 1cm for 15º on the xaxis and 2cm for 1 unit on the yaxis). (5mks)  Using the graph in part (b) above;
 Estimate the solution to the equation 3cos 2x – 2 sin (2x+30º) = 0 (2mks)
28.5º, 115.5º  Estimate the range of values of x for which 3cos 2x ≤ 2 sin (2x + 30º) giving your answer to the nearest degree. (1mk)
28.5º ≤ x ≤ 115.5º
 Estimate the solution to the equation 3cos 2x – 2 sin (2x+30º) = 0 (2mks)
 Complete the table below by filling in the blank spaces. (2mks)
 The table below shows the number of goals scored in handball matches during a tournament.
No. of goals
09
1019
2029
3039
4049
No. of matches
2
14
24
12
8
cf 2 16 40 52 60  Draw a cumulative frequency curve on the grid provided (5mks)
row showing cummulative frequency (1 mk)
appropriate scale(both x and y axis) (1 mk)
axis labelling (1 mk) ; xaxis  no of goals
yaxis  cummulative freq.
correct plotting of all 5 points (1 mk)
smooth curve (1 mk)  Using the curve drawn in (a) above, determine
 The median (1mk)
Q2 = 26 goals  The number of matches in which goals scored were not more than 37 (1mk)
goals scored ≤ 37 ⇒ 50 mathces  The interquartile range (3mks)
= Q3  Q1
= 32.5  19.5
= 13 goals
 The median (1mk)
 Draw a cumulative frequency curve on the grid provided (5mks)
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