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4958 Questions  View: All | Solved | Unsolved

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• Given that z varies directly as the square of x and inversely as the square root of y.(Solved)
  

  Given that z varies directly as the square of x and inversely as the square root of y. If x = 2, y = 9 when z = 3, find z when x = 3 and y = 4.

  Date posted: November 8, 2019.  

• Solve for x in the equation log (5x - 15) - log(2x - 3) = 1(Solved)
  

  Solve for x in the equation log (5x - 15) - log(2x - 3) = 1

  Date posted: November 8, 2019.  

• The equation of a curve is given by y=x³ + 4x² - 3x.(Solved)
  

  The equation of a curve is given by y=x³ + 4x² - 3x. a) Find the value of y when x=1 b) Determine the stationary points of the curve. c) Find the equation of the normal to the curve at =1 .

  Date posted: November 8, 2019.  

• (a) The ratio of Juma’s and Akinyi’s earnings was 5:3. Juma’s earnings rose to Ksh 8 400 after an increase of 12%. Calculate the percentage...(Solved)
  

  (a) The ratio of Juma’s and Akinyi’s earnings was 5:3. Juma’s earnings rose to Ksh 8 400 after an increase of 12%. Calculate the percentage increase in Akinyi’s earnings given that the sum of their earnings was Ksh. 14 100. (b) Juma and Akinyi contributed all the new earnings to buy maize at Ksh 1 175 per bag. The maize was then sold at ksh 1 762.50 per bag. The two shared all the money from the sales of the maize in the ratio of their contributions. Calculate the amount that Akinyi got.

  Date posted: November 8, 2019.  

• The figure below represent two neighboring plots with QR as their common boundary. Find to 2 decimal places, i. The length of boundary PQ. ii. The length of...(Solved)
  

  The figure below represent two neighboring plots with QR as their common boundary. Find to 2 decimal places, i. The length of boundary PQ. ii. The length of boundary RS. iii. The angle RQS. iv. Area of triangle QRS.

  Date posted: November 8, 2019.  

• On the grid provided, draw the square whose vertices are A(6, -2), B(7, -2), C(7, -1) and D(6, -1).(Solved)
  

  On the grid provided, draw the square whose vertices are A(6, -2), B(7, -2), C(7, -1) and D(6, -1). On the same grid, draw: (i) A’B’C’D’ the image of ABCD, under an enlargement scale factor 3 centre (9, -4) (ii) A"B”C”D” the image of A’B’C’D’ under a reflection in the line x = 0 (iii) A”’B’”C’”D’” the image of A”B”C”D” under a rotation of +90° about (0,0).

  Date posted: November 8, 2019.  

• Complete the table below for the function y = 3x² - 2x + 5(Solved)
  

  a. Complete the table below for the function y = 3x² - 2x + 5 b. Use the completed table and mid ordinate rule to estimate the area bounded by the curve, the x - axis and the lines x = -3 and x = 5 c. Use calculus to calculate the actual area in part b above. d. Calculate to 3 significant figure the percentage error when mid ordinate rule is used to estimate the area.

  Date posted: November 8, 2019.  

• A line L₁ passes through the points (-2, 3) and (-1, 6) and is perpendicular to L₂ at (-1, 6).(Solved)
  

  A line L₁ passes through the points (-2, 3) and (-1, 6) and is perpendicular to L₂ at (-1, 6). a) Find the equation of L₁. b) Find the equation of L₂ in the form ax + by - c = 0 where a, b and c are constants. c) Given that another line L₃ is parallel to L₁ and passes through point (1,2) , find the x and y intercepts of L₃ . d) Find the point of intersection of L₂ and L₃.

  Date posted: November 8, 2019.  

• The diagram represents a solid frustum with base radius 21cm and top radius 14cm. The frustum is 22.5cm high and is made of a metal whose...(Solved)
  

  The diagram represents a solid frustum with base radius 21cm and top radius 14cm. The frustum is 22.5cm high and is made of a metal whose density is 3 𝑔⁄𝑐𝑚³. (Take 𝜋 = 22/7) a) Calculate (i) The volume of the metal in the frustum. (ii) The mass of the frustum in kg. b) The frustum is melted down and recast into a solid cube. In the process 20% of the metal is lost. Calculate to 2 decimal places the length of each side of the cube.

  Date posted: November 8, 2019.  

• A number m is such that if its reciprocal is added to three times itself the result is 4. Form an equation in m and...(Solved)
  

  A number m is such that if its reciprocal is added to three times itself the result is 4. Form an equation in m and solve it.

  Date posted: November 8, 2019.  

• At the end of his stay in Kenya, a French tourist had 3 420 French francs which he decided to change into Euros. Given the exchange...(Solved)
  

  At the end of his stay in Kenya, a French tourist had 3 420 French francs which he decided to change into Euros. Given the exchange rate was; 1 French franc = Ksh. 11.25 1 Euro = Ksh. 72.50 Calculate the number of Euros he received if the bank charged him 2% commission.

  Date posted: November 8, 2019.  

• Expand and simplify (1 - 4x)⁶ up to the expansion of the term in x³.(Solved)
  

  Expand and simplify (1 - 4x)⁶ up to the expansion of the term in x³.

  Date posted: November 8, 2019.  

• Solve the equations below using matrix method. x + y = 8 2y - 3x = 1(Solved)
  

  Solve the equations below using matrix method. 𝑥 + 𝑦 = 8 2𝑦 − 3𝑥 = 1

  Date posted: November 8, 2019.  

• Find the area of the shaded region in the figure below given that AD = 15 cm, BE = 3 cm, AB = 3 cm, ???????...(Solved)
  

  Find the area of the shaded region in the figure below given that AD = 15 cm, BE = 3 cm, AB = 3 cm, ∠𝐷𝐴𝐵 = ∠𝐸𝐵𝐶 = 90°.

  Date posted: November 8, 2019.  

• A man sets off by bus on a journey of 130 km. after the bus has traveled 119 km at an average speed of 42...(Solved)
  

  A man sets off by bus on a journey of 130 km. after the bus has traveled 119 km at an average speed of 42 𝑘𝑚/ℎ𝑟, it breaks down and he is immediately given a lift by a passing cyclist who takes him to his destination at average speed of 66 km/h. Calculate; a) The time taken for the whole journey. b) His average speed for the whole journey.

  Date posted: November 8, 2019.  

• The position vectors of A and B are respectively. Find the magnitude of the vector AB.(Solved)
  

  The position vectors of A and B are respectively. Find the magnitude of the vector AB.

  Date posted: November 8, 2019.  

• (a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm, angle ABC = 30° and angle ACB = 45°...(Solved)
  

  (a) Using a ruler and a compass only, construct triangle ABC in which BC = 8 cm, angle ABC = 30° and angle ACB = 45° . (b) At A drop a perpendicular to meet BC at D and measure AD.

  Date posted: November 8, 2019.  

• The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed...(Solved)
  

  The distance from A to B is d km and that from B to C is x km. if a bus maintains an average speed of 50 km/h between A and B and 60 km/h between B and C, it takes 3 hours to travel from A to C. If it maintains 60 km/h between A and B and 50 km/h between B and C, the journey takes 8 minutes less. What is the distance from A to C via B?

  Date posted: November 8, 2019.  

• A cylindrical tank of diameter 1.4 m and height 1.2 m is two – thirds full of water. The tank if filled using a cylindrical...(Solved)
  

  A cylindrical tank of diameter 1.4 m and height 1.2 m is two – thirds full of water. The tank if filled using a cylindrical bucket of diameter 35 cm and diameter 20 cm. Find the number of buckets required to fill the tank.

  Date posted: November 8, 2019.  

• Solve for x in the equation 125^-x × 5^2(x-2) = 25^(x+2)(Solved)
  

  Solve for x in the equation 125^-x × 5^2(x-2) = 25^(x+2)

  Date posted: November 8, 2019.  

• a) Complete the table given below by filling the blank spaces. b) On the grid provided draw on the same axes, the graph of y=4 cos²x...(Solved)
  

  a) Complete the table given below by filling the blank spaces. b) On the grid provided draw on the same axes, the graph of y=4 cos²x and y=2 sin (2x +30^o ) for O^O ≤ X ≤180^O . Take the scale 1cm for 15^o on the x –axis and 1cm for 1 unit on the y-axis. c) From your graph i) State the amplitude of y= 4cos 2x. ii) Find the period of y=2sin(2x +30^o ) d) Use your graph to solve 4cos 2x – 2sin (2x + 30^o ) = 0

  Date posted: November 8, 2019.  

• a) The first term of a geometric progression is 36. The sum of the first three terms is 27. Calculate the common ratio and the value...(Solved)
  

  a) The first term of a geometric progression is 36. The sum of the first three terms is 27. Calculate the common ratio and the value of the second term. b) The first term of an AP is 2. The first term of a geometric sequence is also 2 and its common ratio equals the common difference of the arithmetic sequence. The square of the fifth term of arithmetic sequence exceeds the third term of the geometric sequence by 2. Find the common difference and the sum of the first 50 terms of AP.

  Date posted: November 8, 2019.  

• The table below shows the income tax brackets for a certain year. Mr.Bundi earns a monthly salary of ksh.45, 000. He gets a house allowance of...(Solved)
  

  The table below shows the income tax brackets for a certain year. Mr.Bundi earns a monthly salary of ksh.45, 000. He gets a house allowance of ksh.13, 000 and a commuter allowance of ksh.6, 000. He is entitled to a family relief of ksh.1, 166 per month. Find a) Mr.Bundi’s taxable income in ksh per month. b) Total tax payable per month in ksh. by Mr.Bundi. c) Mr.Bundi’s net salary per month if the following deductions are also made monthly. NHIF –ksh. 1500 Wcps 2% of basic salary.

  Date posted: November 8, 2019.  

• Two towns on latitude 30^oS are 3000km apart. Find the longitude different of the two towns(Solved)
  

  (a) Two towns on latitude 30^oS are 3000km apart. Find the longitude different of the two towns (Take and the radius of the earth to be 6370km) (b) The positions of airport P and Q are (60^oN,45^oN) and Q(60^oN,K^oE). It takes a plane 5 hrs to travel due east from P to Q at an average speed of 600 knots (i) Calculate the value of K (ii) The local time at P is 10.45am, what is the local time at Q when the plane reaches where? (c) Calculate the shortest distance between (30^oS,36^oE) and (30^oS,144^oW) in nautical miles

  Date posted: November 8, 2019.  

• The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared...(Solved)
  

  The cash price of a camera is Sh.42,200. Joseph bought the camera on hire purchase (H.P) term by paying a deposit of Sh.7,200 and cleared the balance in 24 equal monthly installments each of Sh.2,250 (a) Find the amount of interest paid under hire purchase plan (b) Ken took a loan from a financial institution and bought the camera with cash. He repaid the loan in two years at 18% interest compound semi-annualy. Find the total interest paid by Ken (c) The cash price is taken as the value of the Camera. If the camera depreciated at a rate of 15% in the first year after buying and at P% p.a for rest of the time, calculate the value of p if the value of the camera after 5 years was Sh.23,534

  Date posted: November 8, 2019.  

• (a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed...(Solved)
  

  (a) A sequence is formed by adding corresponding terms of an A.P and a G.P. The first, second and third terms of the sequence formed after adding the first three terms of the sequences are 14,34 and 78 respectively. Given that the first term of the A.P is a and the first term of the G.P is b, and that the common ratio of the G.P is 3; Find the first term of the AP and G.P and the common difference of the A.P (b)The second and third terms of a geometric progression are 24 and 12(x+1) respectively. Given that the sum of the first three terms of the progression is 76, find the whole number value of x and hence the first term

  Date posted: November 8, 2019.  

• The points A¹B¹ and C¹ are the images of A(4,1), B(0,-2) and C(-2,4)(Solved)
  

  (a) The points A¹B¹ and C¹ are the images of A(4,1), B(0,-2) and C(-2,4) respectively under transformation represented by the matrix M= write down the coordinates of A¹B¹C¹ (b) A¹¹B¹¹C¹¹ are the images of A¹B¹C¹ under another transformation whose matrix is write down the coordinates of A¹¹B¹¹C¹¹ (c) Transformation m followed by N can be represented by a single transformation P. Determine the matrix for P (d) Another transformation has the matrix T = Determine the matrix for transformation m followed by N and T in that order

  Date posted: November 8, 2019.  

• The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR(Solved)
  

  The diagram below shows a square based pyramid V vertices above the middle of the base. PQ=10cm and VR=13cm M is the midpoint of VR Find (a)(i) the length PR (ii) the height of the pyramid (b)(i) the angle between VR and the base PQRS (ii) the angle between PM and the base PQRS (iii) the angle between the planes QVR and PQRS

  Date posted: November 8, 2019.  

• Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.(Solved)
  

  Given that OA= -i +j, OB=3i+5j and OC= 11i+13j. Show that A, B and C are collinear.

  Date posted: November 8, 2019.  

• Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300^o from Y. Calculate...(Solved)
  

  Three towns X,Y and Z are such that Y is 50km South of X and Z is on a bearing of 300^o from Y. Calculate the angle XZY given that XZ is 70km.

  Date posted: November 8, 2019.