September 2022

Mathematics Alternative A Paper (2/121/2)    

MATHEMATICS ALT. A (121) Mathematics AIternative a Paper 1 (121/1

Mathematics Alternative A Paper 2 (121/2)

4.3.1 Mathematics Alt.A Paper 1 (121/1)    

2016 Mathematics Paper 2 1. 7. The masses in kilograms of 20 bags of maize were: 90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102 and 105. Using an assumed mean of 96 kg, calculate the mean mass, per bag of the maize. (3 marks) 8. The first term of an arithmetic sequence is —7 and the common difference is 3. (a) List the first six terms of the sequence; (1 mark) First six terms -7,-4,-1,2,5,8 (b) Determine the sum of the first 50 terms of the sequence. (2 marks) Sum of the first 50 terms 50/2 = {2 x -7 + 49 x 3} 332.5 9. A bag contains 2 white balls and 3 black balls. A second bag contains 3 white balls and 2 black balls. The balls are identical except for the colours. Two balls are drawn at random, one after the other from the first bag and placed in the second bag. Calculate the probability that the 2 balls are both white. (2 marks) 10. An arc 11 cm long, subtends an angle of 70° at the centre of a circle. Calculate the length, correct to one decimal place, of a chord that subtends an angle of 90° at the centre of the same circle. (4 marks)   Length 12.7cm11. Given that qi + 1/3j + 2/3k is a unit vector, find q. (2 marks) 12. (a) Expand the expression (1 + 1/2 x)5 in ascending powers of x, leaving the coefficients as fractions in their simplest form. (2 marks) (b) Use the first three terms of the expansion in (a) above to estimate the value of (1½o)5. (2 marks) 13. A circle whose equation is (x – 1)2 + (y – k)2 = 10 passes through the point (2,5). Find the value of k. (3 marks) 14. Water and milk are mixed such that the volume of water to that of milk is 4:1. Taking the density of water as 1 gcm3 and that of milk as 1.2g/cm3, find the mass in grams of 2.5 litres of the mixture. (3 marks) 15. A school decided to buy at least 32 bags of maize and beans.The number of bags of beans were to be at least 6. A bag of maize costs Ksh 2 500 and a bag of beans costs Ksh 3 500. The school had Ksh 100 000 to purchase the maize and beans. Write down all the inequalities that satisfy the above information. (4 marks) x + y ≥ 32,x >20,y ≥ 6,5x + 7y ≤ 200 16. Find in radians, the values of x in the interval O’⋜ x 𕲚Πc for which 2 cos2x — sin x = I. (Leave the answer in terms of Π) (4 marks) (b) Calculate the mid-ordinates of 5 strips between x – 1 and x = 6 Use the mid-ordinates rule to approximate, the area under the curve between x-1 ,X = 6 and the x axis.(3 marks) (c) Assuming that the area determined by integration to be the actual area,calculate the percentage error in using the mid-ordinate rule.(4 marks) 17. A garden measures 10 m long and 8 m wide.A path of uniform width is made all round the garden. The total area of the garden and the path is 168 m2. (a) Find the width of the path. (4 marks) Let the width of the path be x ➡ Area =)(10 + 2x )(8 + 2x) = 168 ➡ 80 + 20x + 16x + 4x² = 168 ➡ 4x² + 36x – = 0 ➡ x² + 9x – 22 = 0 ➡(x – 2)( x + 11) = 0 ➡ x = 2 or -11 width of the path = 2m (b) The path is to be covered with square concrete slabs. Each corner of the path is covered with a slab whose side is equal to the width of the path. The rest of the path is covered with slabs of side 50 cm. The cost of making each corner slab is Sh 600 while the cost of making each smaller slab is Sh 50. Calculate: (i) the number of the smaller slabs used. (3 mark) 14/68 x 12 – {10 x 8 + 4 (2 x2 )} No. of slabs = 72/0.5 x 0.5 Ans = 288 (ii) the total cost of the slabs used to cover the whole path. (3 marks) Cost of slabs = Large = 600 x 4 = 2400 Small = 50 x 288 = 14400 Total Cost = 2400 + 14400 = 16,800 18. In the figure below, P, Q, R and S are points on the circle with centre 0. PRI’ and USTV are straight lines. Line USTV is a tangent to the circle at S. L RST = 50° and L RTV = 150°. (a) Calculate the size of(i) L QRS; (2 marks) (ii) L USP; (1 mark) (iii) L PQR. (2 marks) (b) Given that RT = 7cm and ST = 9 cm, calculate to 3 significant figures: ( ) the length of line PR: (2 marks) (ii) the radius of the circle. (3 marks) 19. 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 = 8 m. (a) Calculate, correct to 2 decimal places, the perpendicular distance of EF from the plane ABCD. (4 marks)(b) Calculate the angle between: (i) the planes ADE and ABCD; (2 marks) (ii) the line AE and the plane ABCD, correct to 1 decimal place; (2 marks) (iii) the planes ABFE and DCFE, correct to 1 decimal place. (2 marks)    

Questions and Answers KCSE 2016 Mathematics Paper 1 1. Without using a calculator evaluate, (3 marks) 3. The external length, width and height of an open rectangular container are 41 cm, 21 cm and 15.5 cm respectively. The thickness of the materials making the container is 5mm. If the container has 8 litres of water, calculate the internal height above the water level. (4 marks) Internal Dimensions :40,20, and 15 Volume unoccupied = 40 x 20 x 15 = 8000 = 4000 Height above water level = 4000/40 x 20 = 5cm

KCSE Past Papers 2017 Mathematics Alt B Paper 2 SECTION I (50 marks) Answer all the questions in this section in the spaces provided. 1. Evaluate 190.1 x 30, correct to 3 significant figures. (2 marks) l90.lx30=5703 = 5700 2. Find the sum of the first 10 terms in the Geometric Progression 3, 6, 12, (3 marks) Common Ratio? = 6/3=2 3(210/2-1)/2 -1) 3(1024_1)/1= 3069 3. Given that 5, x, 35 and 84 are in proportion, find the value of x. (3 marks) 5/x=5/34 x=5×84/35 =12 4. The base of a triangle is 3 cm longer than its height and its area is 35 cm. Determine the height and base of the triangle. (4 marks) 1/2(x+3)x=35 x2+3x-70=0 (x+10)(x-7)=0 x=7 0r x=-10 5. The figure below is a map of a piece of land on a grid of l cm squares. Estimate the area of the map in square centimetres. (3 marks) Full square =11 Fractional square = 26 Area estimate = 11+26/2 =24cm2 6. A chord of a circle, radius 5 cm, subtends an angle of 30° at the centre of the circle. Determine the length of the chord, correct to 2 decimal places. (3 marks) 7. The extension (E), in cm, of a rubber band when pulled by a force (F) was found experimentally and recorded as shown in the table below: (a) On the grid provided, draw a graph of extension(E) against force(F). (2 marks) (b) Use the graph to determine the extension when the force is 7 units. (1 mark) – Extensions when forces is 7 units 10.5cm 8. The position of towns M and N are M(0 °, 5 l °W) and N(0 °, 37 °E). Find the distance between the two towns in kilometres, correct to one decimal place. (Take the radius of the earth as 6370km and π = 22/7) (3 marks) 9. The table below shows the values of y = 2sin(6 + 30°) for 0° S 95 360°. (a) On the grid provided below, draw the graph of y = 2sin(0+ 30°) for 0° S 6 5 360 Use l cm for 30° on the x-axis and 2cm for one unit on the y-axis. (3 marks) (b) Use the graph to detemine the value of y when 0 = 162°. (1 mark) When θ = 162°,y=0.4 10. The figure below represents the distance covered by a car within a given period of time Find the average speed of the car in kilometres per hour. (3 marks) 11. Kitonga deposited Ksh50000 in a bank which paid compound interest at the rate of 10% per annum. Find the compound interest accrued by the end of the fourth year. (3 marks) 12. The number of different vehicles allowed through a road block was recorded as follows: Represent the above data in a pie chart. (3 marks) 14. (a) Find a matrix which, when multiplied by matrix M = gives the identity matrix. (2 marks) (b) Given that N =is a singular matrix, find the value of x. (2 marks) 15. A square QRST with vertices Q(l,1), R(3,1), S(3,3) and T(l,3) is transformed by the matrix  Find: (a) the area of square QRST; (2 marks) (b) the area of image Q’R’S’T’. (2 marks) 16. Given that p = 6i + Zj, determine the magnitude of p, correct to 2 decimal places. (2 marks) SECTION II (50 marks) Answer any five questions from this section in the spaces provided. 17. The second term of an arithmetic progressi0n(AP) and fourth tenn of a geometric progression(GP) are each 80. The sixth terms of the AP and GP are each 320. (a) Find: (i) the first term and the common differences of the AP. (2 marks) (ii) the first teirn and the common ratio of the GP. (2 marks) (b) Determine the 20*“ term of the AP. (2 marks) A.P.T20=20+19X60 =1160 (c) Determine the difference between the sum of the first 12 terms of the GP and the sum of the first l2 terms of the AP. (4 marks) G.P.S12=12(1212-1)/2-1 =49149 A.P.S12=12/2{2×12+(12-1)60} =4104 Difference=49140-4104 =45036 18. (a) (i) Complete the table below for the values of y = x2 ex — 6 for -3 5 x S 4. (2 marks) (ii) Find y when x is 1/2= (l mark) (b) On the grid provided, draw a graph of y = xi —x ~ 6 for —3 5 x 5 4. (3 marks) (c) On the same grid, draw line y = 3- x + l and hence solve the equation x2—x~6= ;3x+l. (4marks) Line y = -3/2x+1 =2.4 =-2.8 19. The marked price of a wall unit was Ksh 50 000. The price on hire purchase (HP) terms was 175% of the marked price. (a) A customer bought the wall unit in cash and was offered 10% discount. Find the amount of money the customer paid for the wall unit. (2 marks) 50,000×0.9 =ksh 45000 (b) A second customer decided to purchase a similar wall unit on HP terms. (i) Determine the HP price. (2 marks) 50000×1.75 =87,500 (ii) The customer paid 20% of the HP price as deposit and was to pay the balance in 28 equal monthly instalments. Find the amount of each monthly instalment. (3 marks) Amount to pay in instalments; 87500×0.8 ksh 70,000 Monthley instalments =70000/28 ksh2500 (c) A third customer bought a similar wall unit in cash by taking a loan equal to the marked price. The loan was to be repaid in 15 months and the bank charged interest at the rate of 4% compounded monthly. (i) Find, correct to the nearest shilling, the amount of money the third customer paid the bank. (2 marks) 50,000×1.0415 90047.17528 90047 (ii) Find the amount of money the third customer spent more than the marked price. (l mark) 90047-50000=ksh4007 20. The figure below shows triangle ABC IN which AB=6cm,BC=8cm,BD=4.2cm and AD=5.3cm.Angle CBD=45° Calculate to one decimal place the length of CD; (3 marks) size of angle ABD; (3 marks) size of angle BCD; (2 marks) area

A sales organization performs the following functions: Analysis of markets thoroughly, including products and market research. Adoption of sound and defensible sales-policy. Accurate market or sales forecasting and planning the sales[1]campaign, based on relevant data or information supplied by the marketing research staff. Deciding about prices of the goods and services; terms of sales and pricing policies to be implemented in the potential and existing markets. Labelling, Packaging and packing, for the consumer, who wants a container, which will satisfy his desire for attractive appearance; keeping qualities, utility, quantity, and correct price and many other factors in view. Branding or naming the product(s) and/or services to differentiate them from the competitors and to recognise easily by the customer. Deciding the channels of distribution for easy accessibility and timely delivery of the products and services. Selection, training and control of salesmen, and fixing their remuneration to run the business operations efficiently and effectively. Allocation of territory, and quota setting for effective Selling and to fix the responsibility to the concern person. Sales-programmes and sales-promotion-activities prepared so that every sales activity may be completed in a planned manner Arranging for advertising and publicity to inform the customer about the new products and services and their multiple uses. Order-preparation and office-recording to know the profitability of the business and to evaluate the performance of the employees. Preparation of customer s record-card to the customer loyalty about the products. Scrutiny and recording of reports to compare the other competitors and to compare with the past period. Study of statistical-records and reports for comparative analyses in terms of sales, etc. Maintenance of salesman’s records to know their efficiency and to develop them.   DUTIES AND RESPONSIBILITIES OF SALE MANAGERS  Environmental analysis and marketing research-this usually involves monitoring and adapting to external factors that affect success or failure such as the economy and competition and  collecting data to resolve specific marketing issues. Broadening an organizations/individuals scope-this involves deciding on the emphasis to place as well as the approach to take on societal issues and international marketing. Consumer analysis-this involves examining and evaluating consumer characteristic needs and purchase processes; and selecting the group(s) of consumers at which to aim marketing efforts. Product planning-this includes goods,services,organisations,people,places,and ideas-developing and maintaining products, product assortments(a set o all products and items that a particular seller offers for sale to buyers),product images, brands, packaging and optional features and deleting faltering products. Distribution planning-this involves forming relations with distribution intermediaries, physical distribution, inventory management, warehousing, transportation, the allocation of goods and services, wholesaling and retailing. Promotion planning-this involves communicating with customers, the general public and others through some form of advertising, public relations, personal selling and or sales promotion. Price planning-this involves determining price level and ranges, pricing techniques, terms of purchase, price adjustments and the use of price as an active or passive factor. Marketing management-this involve planning, implementing, and controlling the marketing program(strategy) and individual marketing functions; appraising the risks and benefits in decision making; and focusing on total quality.   DUTIES AND RESPONSIBILITIES OF SALES MANAGER Knowledge of: firm’s long and short-run goals and objectives, production process, consumer behavior, competitors Functional skills: market forecast, design of sales organization, recruiting and selecting salesperson, training, budgeting, compensation, territory and quota design, sales analysis, developing sales approach, customer service, order processing, credit and collection, promotion Administrative ability: planning, organizing, coordination, motivating, evaluation and control, communication Leadership ability

Questions and Answers Mathematics Alt.B Paper 1 (122/1) Section I (50 marks) 1. (a) Express 4732 in terms of its prime factors. (1 mark) 4732=22x7x132 (b) Find the smallest positive nmnber that must be multiplied by 4732 to make it a perfect square. (1 mark) 22x7x132x 7=22x7x132is a perfect square. 2. Three people Juma, Weru and Njeri went round a circular racing track, 3. 12km long. They all started from the same point and moved in the same direction. Juma walked at 48m per minute,Weru ran at 120m per minute while Njeri cycled at 156m per minute. If they started travelling at 0700 h, find the time when they were first together again. (3 marks) 3. Evaluate 4. Without using a calculator evaluate 5. Use logarithms to evaluate 6. The diagram below represents a cube of side 10cm from which a cuboid measuring xcm by xcm by 10cm is removed as shown. Write an expression in terms of x, for the surface area of the remaining solid. (3 marks) 4x10x10+2(10 × 10-x2 7. A cylindrical tank 1.4m in diameter contains 3234 litres of water. Find the depth, in metres, of the water. (Take π =22/7). (3 marks) The figure below represents a quadrilateral ABCD in which angle DAB = 60°, angle BCD = 30° and BC = DC = 40 cm. Side AB = AD.   11. Two employees Njoka and Okoth contributed i and % of their salaries respectively to start a project. The contribution amounted to Ksh 16 000. If Njoka contributed 2 and Okoth % of their salaries, the contribution would have been Ksh 30 O00. Calculate each person‘s salary. (3 marks) 12. Solve x – 8⋜-x⋝ 4 — 3x and represent the integral values of x on a number line. (4 marks) 13. Figure ABCDEF is a regular hexagon. Line AE and BF intersect at G. size of angle F GE. (3 marks) ∠BAF=120°interior angle of a regular hexagon ∠AEF=∠FAE180-120 60/2=30° in triangle EFG∠EFG=120-130=90° FGE=180-(90+30)=60° 14. Using a ruler and a pair of compasses only, construct triangle PQR in which PQ = 8cm, A RPQ = 60° and L PRQ = 75°. Measure PR. (4 marks) 15. The marked price of a _TV set is Ksh 36 000. A dealer sold the set and allowed a 12% discount on the marked price and still made a 25% profit on the cost price. Find the cost price of the set.(3 marks) selling price was ksh 3600×88/100 =31,680 cost price was ksh 31,680×100/125 =ksh 25,324 16. Figure A’B’C’D’ is the image of ABCD under a rotation. By construction, detennine the centre P and the angle of rotation. (3 marks) SECTION II (50 marks) 17. A saleslady earns a monthly salary of Ksh 60 000. She gets a commission of 4% on the value of goods she sells above Ksh 250 O00 but less than Ksh 400 000. On goods sold above Ksh 400 000, she gets a commission of 7.5%. (a) In a certain month, she sold goods worth Ksh 525 O00. Calculate her total earnings that month. (4 marks) (b) In another month, she earned a total of Ksh 94 500. Find the value of goods that she sold that month. (6 marks)   18. Lines y + 2x = 4 and 3x — y = 1 intersect at point T. (a) Find the equation of line L] which passes through point T and (3,—2). (5 marks)   (b) A line L2 passes through (5,4) and is parallel to L]. Find the equation of L, in the form y = mx + c where m and c are constants. (2 marks)   (c) Another line L3 is perpendicular to L1 at T. Find the equation of L3 in the fonn ax + by = c where a, b and c are integers. (3 marks)   19. A car travelled from town A to town B. The car started from rest at A and moved with a constant acceleration for 2 minutes and attained a speed of 1.2 km/minute. lt then maintained this speed for a further 10 minutes before decelerating at a constant rate for another four minutes. The car finally came to rest at B. (a) On the grid provided, draw a speed-time graph for the car. (4 marks) (b) Use the graph to calculate: (i) the distance, in metres, the car travelled during its deceleration; (2 marks)   (ii) the distance, in kilometres, covered by the car in the whole journey; (2 marks)   (iii) the average speed, in km/h, for the whole journey. (2 marks) Average speed=15.6/4/15hrs 58.5km/h 20. The figure below is a square of side x cm. The square is divided into four regions A, B, C and D. Regions A and C are squares. Square C is of side ycm. Regions B and D are rectangles.   (a) Find the total area of the following regions in terms of x and y in factorised form: (i) A and C; (1 mark) Area of A+C=(x-y)(x-y)+y2 (ii) B and D; (2 marks) Area of B+D=y(x-y)+y(x-y) =2y(x-y) (iii)A,B,C and D 2marks (x-y)2+y2+2y(x-y) =(x-y)(x-y)+y2+2yx-2y2 =x2-2yx+y2+y2+2yx-2y2 =x2 (b) Find the total area of B and D in terms of x given that y = 2cm. =2(x-2)+2(x-2) =4x-8 (c) Factorise 25c2– 16 =25c2-16=(5c)2-42 (d) Evaluate Without using mathematical tables: (i) 50242-49762 50242-49762=(5024+4976)(5024-4976) =10000×48 =480000 (ii) 8.962-1.042 8.962 -1.042=(8.96+1.04)(8.96-1.04) =10×7.92 =79.2 21. The figure below represents a right pyramid VEFGH mounted on a cuboid ABCDEFGH. LineAB =6cm,DA= 8cm andAF =BG =CH=DE=3cm. LineVE=VF=VG=VH= 13cm. Calculate, correct to 2 decimal places: (a) the surface area of the rectangular faces; Area of the face of a cuboid =8x6cm2 2 Area of 4 faces of the side of the cuboid =(2x8x3+2x6x3)cm2 =48+36cm=84cm2 Total 48+84=132cm2 (b) the surface area of the triangular faces. (c) the total surface area of the solid. =132+174.86 =306.86 cm2 22. The figure below is a solid which consists of a frustum of a cone, a cylinder and a hemispherical top. The internal radii of the frustum are

INTRODUCTION TO SALES MANAGEMENT – Click to view SALES MANAGEMENT FUNCTION – Click to view SALES FORECASTING AND PLANNING – Click to view RECRUITMENT AND SELECTION OF SALES FORCE – Click to view MOTIVATION AND TRAINING OF SALES FORCE – Click to view SALES ORGANIZATION – Click to view BUDGETING AND EVALUATION – Click to view EMERGING TRENDS IN SALES MANAGEMENT – Click to view   Need these notes in PDF for reading when offline and printing? Clink link below SALES MANAGEMENT NOTES TOPIC ONE INTRODUCTION TO SALES MANAGEMENT NATURE OF SALES MANAGEMENT Originally, the term ‘sales management’ referred to the direction of sales force personnel. But, it has gained a significant position in the today’s world. Now, the sales management meant management of all marketing activities, including advertising, sales promotion, marketing research, physical distribution, pricing, and product merchandising. The American marketers association (AMA’s) definition, takes into consideration a number of these viewpoints. Its definitions runs like: the planning, direction, and control of the personnel, selling activities of a business unit including recruiting, selecting, training, assigning, rating, supervising, paying, motivating, as all these tasks apply to the personnel sales-force. Further, it may be quoted: it is a socio-scientific process, involving’ group-effort’ in the pursuit of common goals or objectives, which are predetermined. Co-ordination is its key, though, no doubt, it is a system of authority, but the emphasis is on harmony and not conflict. Sales-management differs from other fields of management, mainly in different aspects: the selling operation of a business firm does not exist in isolation. Thus, simultaneous with the changes taking place in the business, as well as marketing-orientation, a new concept of sales management has evolved. The business, is now society-oriented, on human-welfare aspects. So, sales-management has to work in a broader and newer environment, in co-existence with the traditional lines. The present emphasis is now on total development of human resources. RELATIONSHIP BETWEEN SALES MANAGEMENT AND MARKETING MANAGEMENT Sales and marketing always have had a close relationship, so close that many people have confused the two being the same. Marketing is a method of bringing customers to a business as well as making others aware of the business product and brand. Sales is selling the product the company offers.it can be achieved through phone, interaction as well as web page. Marketing sells the idea of product and services to everyone whereas sales sells the actual product one on one through personal interaction. Marketing generates interest but sales brings in money. Marketing does everything it can to reach and persuade prospective buyers while sales does everything it can to close the sale and get assigned an agreement/contract. Marketing responsibility is selling the idea while selling has a responsibility of selling the product and can be achieved through sales making. Selling is only a part of firm marketing activities and refers to personal communication of information to persuade a prospective buyer to buy something. Marketing refers to the process of planning, exchanging, the process, concept/idea, pricing, promotion and distribution of goods and services and ideas to satisfy companies or individuals. Sales excludes all this. Marketing has led to the emergence of marketing concepts (philosophies that aim at satisfying customer needs) while selling has led to the emergence of selling concepts (a philosophy that encourage organizations to undertake a large scale selling promotion effect. Sales people usually sells to customers the products while the marketing meets the organization with customers. The major objectives of sales department is responsible for activities like promotion. Marketing ignores all this. IMPORTANCE OF SALES MANAGEMENT TO AN ORGANIZATION To enable the top-management, to devote to more time in policy making for the growth and expansion of business. (ii) To divide and fix authority among the sub-ordinates so that they may shirk work. (iii) To avoid repetition of duties and functions so that there may not be any confusion among them. (iv) To locate responsibility of each and every employee so that they can complete the whole work in stipulated time; if not then the particular person must be responsible. (v) To establish the sales-routine in the business unit. (vi) To stimulate sales-effort. (vii) To enforce proper supervision of sales-force. (viii) To integrate the individual in the organization.

Questions and Answers 2018 Mathematics Paper 2 1. Given that 2 log x2+log = k log x, find the value of k. (2 marks) 2 log x2+log√x=klogx log(x4x1/2 =logxk k=1/2 2. A variable P varies directly as t3 and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3. (4 marks) 3. Asia invested some money in a financial institution. The financial institution offered 6% per annum compound interest in the first year and 7% per annum in the second year. At the end of the second year, Asia had Ksh 170 130 in the financial institution. Determine the amount of money Asia invested. (3 marks) p2=170130 p2=170130/1.07 =Ksh 150000 4. 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.(3 marks) BF = 10 B1 Cos 20‘ BC/10 BC=10 Cos 20º =9.4 cm 5. Simplify √ 54 + ∛ 3/ √ 3 (2 marks)   6. In the figure below, AB is a tangent to the circle, centre O and radius 6 cm. The arc AC subtends an angle of 60° at the centre of the circle. Calculate the area of the shaded region, correct to 1 decimal place. (4 marks) AB=6tan 60º or OB = 6/cos69 Area of triangle OAB =1/2x60x 6tan 60º Area of sector OAC=60/360 x π x 62 Area of shaded part = 31.18 —18.85 — 12.3 cm2   7. Use completing the square method to solve 3×2 + Sx — 6 = 0, correct to 3 significant figures.(3 marks) 8. Three workers, working 8 hours per day can complete a task in 5 days. Each worker is paic Ksh 40 per hour. Calculate the cost of hiring 5 workers if they work for 6 hours per day tc complete the same task. (3 marks) W : H : D 3 : 5 😡 No. of Days = 5x 8/6×3/5 =4days cost=5x6x4x40 =Ksh4800 9. The table below represents a relationship between two variables x and y.   x 1 2 3 4 5 6 y 3.5 4.5 8.0 8.5 11 13 (a) On the grid provided draw the line of best fit.(3 marks) (b) Use the graph to find the value off when x — 0.(1 marks) When = 0, y = 1 10. State the amplitude and the phase angle of the curve y = 2sin x — 30° .(2 marks) Amplitude = 2 Phase angle = 30° 11. The mass, in kilograms, of 9 sheep in a pen were: 13, 8, 16, 17, 19, 20, 15, 14 and 11. Determine the quartile deviation of the data. (3 marks) 12. The position of two points C and D on the earth’s surface are (8°N, l 0OE) and (8°N, 30°E) respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. (3 marks) Longitude difference = 30 — 10 = 20° 600 — 20 x 60 Cos B Cos 8 = 0.5 8 = 60° Latitude = 60°N 13. In the figure below OP — p, OR = r, PQ:QR = 1:2 and PS = 3PR. Express QS in terms of p and r. (4 marks) 14. In a certain firm there are 6 men and 4 women employees. Two employees are chosen at random to attend a seminar. Determine the probability that a man and a woman are chosen. (3 marks) P(MW or WM) =6/10 + 4/9 + 4/10 + 6/9 24/90+24/90 =8/15 15. Triangle OAB is mapped onto triangle OA’B’ with vertices O(0,0), A’(18,0) and B'(18, 6). Find the area of triangle OAB. (3 marks) Section II Answer any 5 questions from this section 17. The 5th and 10th terms of an arithmetic progression are 18 and —2 respectively. (a) Find the common difference and the first term. (4 marks) a + 4d= 18 a + 9d= — 2 5d = —20 a = 34 (b) Determine the least number of terms which must be added together so that the sum of the progression is negative. Hence find the sum. (6 marks) 18.Complete the table below for the equation y=x2-4x+2 (2 marks)   x 0 1 2 3 4 5 y (b) On the grid provided draw the graph y = x2 — 4x + 2 for 0≤ x ≤ 5. Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent 1 unit on the y-axis. (3 marks) (c) Use the graph to solve the equation, x2 — 4x + 2 = 0 (2 marks) x=0.6± 0.05 x=3.4 ± 0.05 (d) By drawing a suitable line, use the graph in (b) to solve the equation A-2 — 5x + 3 = O. (3 marks) (c) Determine the probability that a plant taken at random has a height greater than 40 cm. (2 marks) No. of plants whose height>40 = 4+2=6 p(height>40cm)=6/40=0.15 20. (a) Using a ruler and a pair of compasses only, construct: (i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 600; (3 marks) (ii) the locus of points equidistant from AB and AD; (1 mark)   Angle bisector of (iii) the perpendicular bisector of BC. (1 mark) bisector of BC ✓ drawn (b) (i) Mark the point P that lies on DC and is equidistant from AB and AD. (1 mark) Point P identified and ✓ marked on line DC (ii) Measure BP. (1 mark) BP = 7 ± O. 1 cm (c) Describe the locus that the perpendicular bisector of BC represents. (1 mark) Locus of Points equidistant from B and C (d) Calculate the area of trapezium ABCP. (2 marks) 21. The table below shows some values of the curves y = 2 cos x and y = 3 sin

Questions and Answers 2018 Mathematics Paper 1 1. Without using a calculator, evaluate:(3 marks) 2. Given that 6 2n-3= 7776, find the value of n. (3 marks) 7776 = 65 662n-3 = 65 2n —3 = 5 n = 4 3. The base of a right pyramid is a rectangle of length 80 cm and width 60 cm. Each slant edge of the pyramid is 130 cm. Calculate the volume of the pyramid. (3 marks) Height h = √ 1302 – 502 = l20cm Volume=1/3 x80x 60 x 120 192000cm2 4. In the figure below ABCDEF is a uniform cross section of a solid. Given that FG is one of the visible edges of the solid, complete the sketch showing the hidden edges with broken lines. 5. The lengths of three wires were 30m, 36 m and 84m. Pieces of wire of equal length were cut from the three wires. Calculate the least number of pieces obtained. (4 marks) 30 = 3x 2 x 5 36 = 2 x 2 x 3 x 3 84 = 2 x 2 x 3 x 7 G.C.D. —— 2 x 3 M1 = 6 AI No of pieces obtained 30/6 + 36/6 + 84/6 = 25 6. A two digit number is such that, the sum of its digits is 13. When the digits are interchanged, the original number is increased by 9. Find the original number. (4 marks) x+y=13 (l0y + x) – (l0x + y) = 9 or — x+ y = 1 x+y=13 y-x=1/2y=14 y=7 x=6 7. (a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle. (2 marks) (b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres. (2 marks) RS= (7.8 ± 0.1) cm Actua x 40m = 312 ± 4m 8. Given that OA = (2/3) and OB = (-4/5) Find the mid point M of AB. 9. Two towns R and S are 245 km apart. A bus travelling at an average speed of 60 km/h left tow: R for town S at 8.00 a.m. A truck left town S for town R at 9.00 a.m and met with the bus c 11.00a.m. Determine the average speed of the truck. (4 marks) Distance covered by truck = 245 — 60 x 3 =65km Time taken by the track = 11-9 = 2h Average speed of truck 65/2 35.5km/hr 10. In the parallelogram WXYZ below, WX = 10 cm, XY = 5 cm and WXY = 150°. Calculate the area of the parallelogram. (3 marks) h = 5 sin 30° = 2.5cm Area = 2.5 x 10 =25cm3 11. Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°(3 marks) 12. Use matrix method to solve: 5x + 3J = 35 3x — 4y — —8 (3 marks)   x=4 y=5 13. Expand and simplify. (2x + 1)2 + (x — 1)(x — 3).(2 marks) (2x+1)’ +(x—1)(x—3) = 4×2 + 4x + 1+ x2 -4x + 3 = 52 + 4 14. Use mathematical tables to find the reciprocal of 0.0247, hence evaluate 𢆳.025/0.1247 correct to 2 decimal places.(3 marks)   15. A Kenyan businessman intended to buy goods worth US dollar 20 000 from South Africa Calculate the value of the goods to the nearest South Africa (S.A) Rand given that 1 US dollar = Ksh 101.9378 and 1 S.A Rand = Ksh 7.6326. (3 marks) 20000 dollars = 20000 x 101.9378 = Ksh. 2038756 In S.A. rand 20000 x 101.93.78/7.6326 =267112 rands 16. A photograph print measuring 24cm by 15 cm is enclosed in a frame. A uniform space of width x cm is left in between the edges of the photograph and the frame. If the area of the space is 270cm2, find the value ofx. (3 marks) Area of space = 2x(15 +2x)z + 2×24 x 30a + 4×2 + 48x — 270 4×2 + 78x — 270 = 0 4×2 — 12 + 90 — 270 = 0 4x(x — 3) + 90(z — 3) — 0 4x(x — 3) + 90(x — 3 = 0 (4x + 90)(z — 3) = 0 x =- 22.5 or x = 3 Section II (50 marks) Answer any five questions from this section. 17. A school water tank is in the shape of a frustum of a cone. The height of the tank is 7.2 m and the top and bottom radii are 6m and 12 m respectively. (a) Calculate the area of the curved surface of the tank, correct to 2 decimal places. (4 marks) (b) Find the capacity of the tank, in litres, correct to the nearest litre. (3 marks) Volume = 1/3πR2H – 1/3πr2h 1/3xπx122x14.4-1/3πx62x7.2 = 1900.0 m3 Capacity = 1900 x 1000 litres = 1900000 litres (c) On a certain day, the tank was filled with water. If the school has 500 students and each student uses an average of 40 litres of water per day, determine the number of days that the students would use the water. (3 marks) Amount used by students per day. =40 x 500 =20000 litres =No. of days = 1900000 =20000 = 95 days 18. Two vertices of a triangle ABC are A (3,6) and B (7,12). (a) Find the equation of line AB.(3 marks) (b) Find the equation of the perpendicular bisector of line AB.(4 marks) (c) Given that AC is perpendicular to AB and the equation of line BC is y = -5x + 47, find the co-ordinates of C. (3 marks)   19. The distance covered by a moving particle through point O is given by the equation, s = t3 – 15t2 + 63f — 10. Find: (a) distance covered when f = (2 marks) S(2)= 2 3 – 15(2)2 + 63(2) —10 — 8 — 60 +126 —10 = 64 (b) the distance covered during the 3rd second;(3 marks) S(s) = 33 —15(3)2 + 63(3) —