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**Question 3: 1991 Q8 P2 **Simplify

**Question 6: 1993 Q14 P2 **Simplify

**Question 7: 1994 Q 2 P1 **Simplify

The amount of money contributed by a group of students during a fundraising for a needy student was as shown in the table below.

(a) On the grid provided draw an ogive to represent the data.

(b) Use the graph to estimate:

(i) The median;

(ii) The quartile deviation;

(iii) The percentage number of students who contributed at least Ksh 750.50.

(b) Use the graph to estimate:

(i) The median;

(ii) The quartile deviation;

(iii) The percentage number of students who contributed at least Ksh 750.50.

A workshop makes cupboards and tables using two artisans A and B every cupboard made requires 3 days of work by artisan A and 2 days of work by artisan B. Every table made requires 2 days of work by artisan A and 2 days of work by artisan B.

In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days.

The workshop made x cupboards and y tables in that month.

(a) Write all the inequalities which must be satisfied by x and y.

(b) Represent the inequalities in (a) on the grid provided.

(c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table.

Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.

In one month artisan A worked in less than 24 while artisan B Worked for Not More Than 18 Days.

The workshop made x cupboards and y tables in that month.

(a) Write all the inequalities which must be satisfied by x and y.

(b) Represent the inequalities in (a) on the grid provided.

(c) The workshop makes a profit of Ksh 6 000 on each cupboard and Ksh4 000 on each table.

Find the number of cupboards and the number of tables that must be made for maximum profit and hence determine the maximum profit.

A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)

(a) Calculate the distance between P and R in:

(i) nm;

(ii) km.

(b) Determine the position of point R.

(c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m.

(a) Calculate the distance between P and R in:

(i) nm;

(ii) km.

(b) Determine the position of point R.

(c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m.

The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m

(a) On the figure, construct

(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM.

(ii) the locus of a point Q such that ∠KQL = 90°.

(b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM.

(ii) Find the area of the region R in m². (Take ℼ= 3.142).

(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM.

(ii) the locus of a point Q such that ∠KQL = 90°.

(b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM.

(ii) Find the area of the region R in m². (Take ℼ= 3.142).

Mbaka bought some plots at Ksh 400,000 each. The value of each plot appreciated at the rate of 10% per annum.

(a) Calculate the value of a plot after 2 years.

(b) After some time t, the value of a plot was Ksh 558,400. Find t, to the nearest month.

(c) Mbaka sold all the plots he had bought after 4 years for Ksh2,928,200.

Find the percentage profit Mbaka made, correct to 2 decimal places.

(a) Calculate the value of a plot after 2 years.

(b) After some time t, the value of a plot was Ksh 558,400. Find t, to the nearest month.

(c) Mbaka sold all the plots he had bought after 4 years for Ksh2,928,200.

Find the percentage profit Mbaka made, correct to 2 decimal places.

The first term of an Arithmetic Progression(AP) is equal to the first term of a Geometric Progression (GP). The second team of the AP is equal to the fourth term Of the GP while the tenth term of the AP is equal to the seventh term of the GP.

(a) Given that a is the first term and d is the common difference of the AP while r is the common ratio of the GP, write the two equations connecting the AP and the GP.

(b) Find the value of r that satisfies the progressions.

(c) Given that the tenth term of the GP is 5120, find the values of a and d.

(d) Calculate the sum of the first 20 terms of the AP.

(a) Given that a is the first term and d is the common difference of the AP while r is the common ratio of the GP, write the two equations connecting the AP and the GP.

(b) Find the value of r that satisfies the progressions.

(c) Given that the tenth term of the GP is 5120, find the values of a and d.

(d) Calculate the sum of the first 20 terms of the AP.

Solve for x in log(7x—3) + 2 log 5 = 2 + log(x + 3).

The vertices of a triangle PQR are P(-3, 2), Q(0,-1) and R(2, -1). A transformation matrix maps triangle PQR onto triangle P’Q' R' whose vertices are P'(-7, 2), Q'(2, -1) and R’(4, -1).

Find M^{-1}, the transformation that maps P'Q'R' onto PQR.

Find M