Form 3 MathematicsForm 3 Mathematics
In the figure below, OABC is a trapezium. AB parallel to OC and OC = 5AB. D is a point on OC such that OD: DC = 3:2
a) Given that OA = p and AB = q, express in terms of p and q:
i. OB; ii. AD; iii. CB; b) Lines OB and AD intersect at point X such that AX = kAD and OX = rOB, where k and r are scalars. Determine the values k and r. Form 3 Mathematics
In triangle OPQ below, OP = p, OQ = q. Point M lies on OP such that OM : MP = 2 : 3 and point N lies on OQ such that ON : NQ = 5:1. Line PN
intersects line MQ at X.
(a) Express in terms of p and q:
(i) PM (ii) QM. (c) Given that PX = kPN and QX = rQM, where k and r are scalars: (i) write two different expressions for OX in terms of p, q, k and r; (ii) find the values of k and r; (iii) determine the ratio in which X divides line MQ. Form 3 Mathematics
Give that x = 2i +j – 2k,y =  3i +4j –k and z =  5i +3j +2k and that p = 3x – y +2z. Find the magnitude of vector p to 3 significant figures.
Form 3 MathematicsForm 3 Mathematics
In the figure below OJKL is a parallelogram in which OJ = 3p and OL 2r.
(a) If A ¡s a point on LK such that LA = 1/2 AK and a point B divides the line JK externally in the ratio 3:1, express OB and AJ in terms of p and r.
(b) Line OB intersects AJ at X such that OX = mOB and AX= nAJ. (i) Express OX in terms of p, r and m. (ii) Express OX in terms of p, r and n. (iii) Determine the values of m and n and hence the ratio in which point X divides line AJ. Form 3 MathematicsForm 3 Mathematics
The coordinates of points O,P,Q and R are (0,0)(3,4) (11,6) and (8,2) respectively. A point T is such that vectors OT,QP and QR satisfy the vector equation. OT = QP + ½ QR .Find the coordinates of T.
Form 3 MathematicsForm 3 MathematicsForm 3 MathematicsForm 3 Mathematics
The position vectors of points X and Y are
x = 2i + j – 3k and y = 3i + 2j 2k respectively. Find xy; Form 3 Mathematics
In the figure below, OQ = q and OR = r. Point X divides OQ in the ratio 1: 2 and Y divides OR in the ratio 3: 4 lines XR and YQ intersect at E.
(a) Express in terms of q and r
(i) XR (ii) YQ (b) If XE = m XR and YE = n YQ, express OE in terms of: (i) r, q and m (ii) r, q and n (c) Using the results in (b) above, find the values of m and n. Form 3 Mathematics
In the diagram below, the coordinates of points A and B are ( 1,6) and (15,6) respectively)
Point N is on OB such that 3 ON = 2OB. Line OA is produced to L such that OL = 3 OA
(a) Find vector LN
(b) Given that a point M is on LN such that LM: MN = 3: 4, find the coordinates of M (c) If line OM is produced to T such that OM: MT = 6:1 (i) Find the position vector of T (ii) Show that points L, T and B are collinear Form 4 Mathematics
A translation maps a point P (3,2) onto P’ (95,5)

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AuthorMaurice A Nyamoti is a Mathematics/ Computer Teacher and has passion to assist students improve grades RSS_FEED
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