A transport company operates three types of trucks whose load capacities are 3.2 tonnes, 8 tonnes and 10 tonnes. Calculate the least possible mass in tonnes that the company can transport with the three trucks.     (3 mks)

    Use tables of square roots and reciprocals only to evaluate                            (3 mks)

A line that passes through the point (-3, 5) makes an angle of 53.13010235⁰ with the x-axis. Find the equation of the line in the form y = mx + c, where m and c are constants.          (3 mks)

A bag of rice costs Ksh 12,500, a bag of beans costs Ksh 15,200 and a bag of maize costs Ksh 8,750. A school buys 20 bags of rice, 30 bags of beans and 45 bags of maize in a term.

Represent

(a) the cost of each bought as a 3×1 matrix                      (1 mk)

(b) the number of bags of each as a 1×3 matrix                  (1 mk)

(c) Hence calculate the total cost that the school spent in buying the items.     (2 mks)

The figure below shows the net of a right cone. The radius of the circular base is 10.5 cm.

Calculate the slant height of the cone.                           (2 mks)

The points M and N have coordinates (2, -1) and (-4, 3) respectively. A point R divides line MN externally in the ratio 3:2. Find the of modulus of OR, correct to four significant figures.          (4 mks)

Fifteen men working for eight hours a day can complete a certain job in exactly 24 days. For how many hours a day must sixteen men work in order to complete the same job in exactly 20 days?   (3 mks)

A measuring cylinder of base diameter of 10 cm contains water whose level reads 5 cm high. A spherical solid marble is immersed in the water and the new level reads 9 cm. Calculate the radius of the marble      (3 mks)

An irregular polygon has n sides. Its interior angles are such that two of them are right angles while the exterior of each of the remaining angles is 30⁰. Find the value of n and hence the sum of the interior angles of the polygon.               (3 mks)

A train moving at 120 km/h approaches a bridge 50 m long which is 120 m away. If the train takes 9 seconds to completely cross the bridge, determine the length of the train in metres.            (3 mks)

Sarah, a saleslady earns a basic salary of Ksh. 25,000 and a commission of 7.5% for the sales in excess of Ksh. 100,000. In May 2023 she earned a total of Ksh. 48,700 in salaries and commissions. Determine the amount of sales that she made in that month.      (3 mks)

The figure below shows part of a circle that touches the side LM externally and tangentially at a point T.

(a) Using a ruler and a pair of compasses only, locate the point T on LM.             (2 mks)

(b) Measure the radius of the circle.                        (1 mk)

Simplify the expression                       (3 mks)

Ruth paid rent which was ¹/₁₀ of her net salary. She used ¹/₃ of the remaining amount to make a down payment for a plot. She gave mother Ksh. 2,500 and did shopping worth Ksh. 7,500 herself. She saved the remainder which was Ksh. 12,500. How much was the down payment that she made?              (3 mks)

A photograph print measures 24 cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left between the edges of the photograph and the frame. If the area of the space is 270 cm², find the value of x.        (4 mks)

Solve for x in the equation                                          (3 mks)

Four schools: Lihanda, Kagito, Bar-Sari and Ndori are such that Lihanda is 6km from Kagilo on a bearing of 158°, Bar-Sauri is to the west of Kagilo and 20km away while Ndori is to the South of Bar-sauri on a bearing of 240° from Lihanda.

(a) Using a scale of 1:400,000 draw a scale diagram showing the relative positions of the four schools    (5mks)

(b) Using your diagram determine the distance and bearing of Ndori from Kagilo. (2 mks)

(c)  A mast is to be erected so that it is equidistant from Kagilo and Bar-sauri and 20km from Ndori. On the same diagram show the position of the mast and find its distance from Lihanda. (3mks)

Three business partners, Bela Joan and Trinity contributed Kshs 112,000, Ksh,128,000 and ksh,210,000 respectively to start a business. They agreed to share their profit as follows:

30% to be shared equally

30% to be shared in the ratio of their contributions

40%  to be retained for running the business.

 If  at the end of the year, the business realized a profit of ksh 1.35 Million. Calculate:

(a) The amount of money retained for the running of the business at the end of the year.     (1mk)

(b) The difference between the amounts received by Trinity and Bela              (6mks)

(c) Express Joan’s share as a percentage of the total amount of money shared between the three partners.   (3mks)

  Complete the table below for the function y = x³ + 6x² + 8x for   -5  x 1     (3mks)               

(a) Draw the graph of the function y = x³ + 6x² + 8x  for  -5  x 1           (3mks)

(use a scale of 1cm to represent 1 unit on the x-axis . 1cm to represent 5 units on the y-axis)

(b) Hence use your graph to estimate the roots of the equation  (4mks)

x3 + 5x²+ 4x = -x² – 3x -1                                                                                        

A bag contains 5 red, 4 white and 3 blue beads . two beads are selected at random one after another.

(a) Draw a tree diagram and show the probability space.                (2mks)

(b) From the tree diagram, find the probability that;

 i. The last bead selected is red      (3mks)

ii. The beads selected were of the same colour                             (2mks)

iii. At least one of the selected beads is blue.                      (3mks)

The table below shows the distribution of mathematics marks of form 4 candindates in Mavoko Secondary school.

Use the above date to calculate:

(a) Mean  using assumed mean of 65            (3mks)

(b) Median                                      (3mks)

(c) Standard deviation                                      (4mks)

The table below shows how income tax was charged on income earned in a certain year.

Mr. Gideon is an employee of a certain  company and earns a salary of  ksh.15,200 per month. He is housed by the company and pays a nominal rent of Ksh. 1050 per month. He is married and is entitled to a family relief of ksh. 450 per month.

(a) Calculate his taxable income in K£ p.a                         (2mks)

(b) Calculate his gross tax per month.                          (4mks)

(c) Calculate his net tax per month                              (2mks)

(d) Calculate his net salary  per month                             (2mks)

Coast bus left Nairobi at 8.00am and travelled towards Mombasa at an average speed of 80Km/hr. At 8.30am, Lamu bus left Mombasa towards Nairobi at an average speed of  120 km per hour. Given that the distance between Nairobi and Mombasa is 400Km.: determine:

(a) The time Lamu bus arrived in Nairobi.                     (2mks)

(b) The time the two buses met.                           (4mks)

(c) The distance from Nairobi to the point where the two buses met.             (2mks)

(d) How far coast bus is from Mombasa when Lamu bus arrives in Nairobi           (3mks)

Three islands P,Q,R and S are on an ocean such that island Q is 400Km on a bearing of 030⁰  from island P. island R is 520Km and a bearing of 120⁰  from island Q. A port S is sighted 750Km due South of island Q.

(a) Taking a scale of 1cm to represent 100Km, give a scale drawing showing the relative positions of P,Q,R and S.     (4mks) 

(b) Use the scale drawing to:

Find the bearing of:

i. Island R from island  P             (1mk)   

ii. Port S from island R                                          (1mk)

(c) Find the distance between island P and R                              (2mks)