KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
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QUESTION 16  KCSE 2023  3d geometry  PAPER 2  FORM 3 LEVELP, Q and R are points on a level ground. Q is 4.5 m south of P. R is to the east of P and 5.3 m from Q. A vertical post at P is supported by a cable of length 3.5 m. The cable joins the top T of the post to point R.
Calculate the angle between the cable and the level ground correct to 2 decimal places. (3 marks)
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QUESTION 9  KCSE 2023  THREE DIMENSIONAL GEOMETRY  PAPER 1  FORM 4 LEVELIn the following figure, triangle ABC is a uniform cross section of a solid ABCDEF. Given that BE is one of the edges of the solid, complete the sketch showing hidden edges with broken lines. (3 marks)
QUESTION 7  KCSE 2021  Three Dimensional Geometry  PAPER 2  FORM 4 LEVELThe figure below represents a prism ABCDEFGH of length 6 cm. The cross section BCFG of the prism is a trapezium in which GF = 11 cm, BC = 8 cm, BG = 5 cm and GFC = BCF = 90°. Calculate correct to 1 decimal place the angle between the line FA and the plane GFEH. (3 marks)
Form 4 MathematicsForm 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 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; Form 4 MathematicsForm 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. Form 4 MathematicsForm 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. 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 Form 4 MathematicsForm 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. Form 4 MathematicsForm 4 MathematicsForm 4 MathematicsForm 4 MathematicsFree 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2 
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