Form 4 Mathematics
The figure ABCDEFGH represents a box.
The top lid of the box is opened such that the height OT is 35cm. Calculate the:
(a ) angle the top lid makes with the plane FGHE; (b) length BE, correct to 2 decimal places.
answers
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Form 4 Mathematics
The figure below is a right pyramid VEFGHI with a square base of 8cm and a slant edge of 20cm Points A B C and D lie on the slant edges or the pyramid such that VA = VB = VC = VD = 10 cm and plane ABCD is paralell to the base EFGH.
(a) Find the length of AB.
(b) Calculate to 2 decimal places (i) The length of AC (ii) The perpendicular height of the pyramid VABCD (c) The pyramid VABCD was cut off. Find the volume of the frustum ABCDEFGH correct to 2 decimal places
answers
Form 4 Mathematics
The figure below is a model of a watch tower with a square base of side 10 cm. Height PU is 15 cm and slanting edges UV = TV = SV = RV = 13 cm.
Giving the answer correct to two decimal places, calculate: 
(a) length MP;
(b) the angle between MU and plane MNPQ; (c) Length of VO; (d) The angle between planes VST and RSTU;
answers
Form 4 Mathematics
The figure below represents a wedge ABCDEF. EF 10 cm, angle FBE 45° and the angle between the planes ABFE and ABCD is 20°.
Calculate length BC, correct to l decimal place.
answer
Form 4 Mathematics
The figure below represents a cuboid ABCDEFGH in which AB = 16 cm, BC = 12 cm and CF = 6 cm.
(a) Name the projection of the line BE on the plane ABCD.
Calculate correct to 1 decimal place: (i) the size of the angle between AD and BF; (ii) the angle between line BE and the plane ABCD; (iii) the angle between planes HBCE and BCFG. (c) Point N is the midpoint of EF. Calculate the length BN, correct to 1 decimal place.
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Form 4 Mathematics
In the figure below (not drawn to scale), AB 11cm, BC = 8cm, AD = 3 cm, AC 5cm and angle DAC is a right angle.
Calculate, correct to one decimal place:
(a) the length DC; (b) the size of angle ADC; (c) the size of angle ACB; (d) the area of the quadrilateral ABCD
answers
Form 4 Mathematics
The figure ABCDEF below represents a roof of a house AB= DC = 12m, BC=AD = 6 m, AE=BF = CF = DE = 5 m and EF= 8m
a) Calculate correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD
b) Calculate the angle between i)The planes ADE and ABCD ii)The line AE and the plane ABCD, correct to 1 decimal place iii)The planes ABFE and DCFE, correct to 1 decimal place.
answers
Form 4 Mathematics
The figure below represents a cuboid EFGHJKLM in which EF = 40cm, FG=9cm and GM=30 cm. N is the midpoint of LM.
Calculate correct to 4 significant figures
a)The length of GL: b)The length of FJ c)The angle between EM and the plane EFGH; d)The angle between eh planes EFGH and ENH; e)the angle between the lines EH and GL
answers
Form 4 Mathematics
The figure below represents a cuboid PQRSTUVW. PQ = 60cm, QR = 11 cm and RW - 10cm.
Calculate the angle between line PW and plane PQRS, correct to 2 decimal places.
answer
Form 4 Mathematics
The figure ABCDEF below represents a roof of a house. AB=DC=12 m, BC = AD = 6m, AE = BF = CF= DE = 5m and EF = 8m
(a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD.
(b) calculate the angle between : (I) the planes ADE and ABCD (II) The line AE and the plane ABCD, correct to 1 decimal place; (III) The planes ABFE and DEFE, correct to 1 decimal place.
ANSWERS
Form 4 Mathematics
In the figure below, VABCD is a right pyramid on a rectangular base. Point O is vertically below the vertex V AB = 24cm, BC= 10cm and CV = 26cm.
Calculate the angle between the edge CV and the base ABCD.
answer
Form 4 Mathematics
The figure below represents a rectangular based pyramid VABCD. AB = 12 cm and AD = 16 cm. Point O is vertically below V and VA = 26 cm.
Calculate:
(a) the height, VO, of the pyramid; (b) the angle between the edge VA and the plane ABCD; (c) the angle between the planes VAB and ABCD.
answers
Form 4 Mathematics
Calculate:
a) The length of AC; b) The angle between the line AG and the plane ABCD; c) The vertical height of point V from the plane ABCD; d) The angle between the planes EFV and ABCD.
answers
Form 4 Mathematics
The figure below represents a triangular prism. The faces ABCD, ADEF and CBFE are rectangles.
AB=8cm, BC=14cm, BF=7cm and AF=7cm. 
Calculate the angle between faces BCEF and ABCD.
answer
Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2
The triangular prism shown below has sides AB= DC = EF = 12 cm. The ends are equilateral triangle of sides 10cm. The point N is the midpoint FC.
ANSWERS
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