In the figure below PQ = Q and PR = r QM: MR = 1:2. The point S is the midpoint of PQ.

In the figure below PQ = Q and PR = r QM: MR = 1:2. The point S is the midpoint of PQ. X is the intersection of PM and SR. SX = hSR, pX = kPM where k and h are constants.


Find:
a) QR in terms of q and r.
b) PM in terms of q and r
c) SR in terms of q and r
d) Express SX in two ways in terms of h,r and q and in terms of k,r and q, hence determine the ratio in which x divides SR.

---

---

Wilfykil answered the question on September 12, 2019 at 09:05

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

---

• a) Draw the graph of y= - x² + 2x + 8 (Solved)
  

  a) Draw the graph of y= - x² + 2x + 8 for
  
  b) Use 6 trapezia to estimate the area enclosed by the curve y = -x² + 2x + 8, the line x = -2 and X= 4 and the x - axis
  
  c) Hence find the percentage error in area of (b) above and the exact area.

  Date posted: September 12, 2019 .    Answers (1)

• A company wishes to buy two types of squash machines; Electric and manual. (Solved)
  

  A company wishes to buy two types of squash machines; Electric and manual. A manual machine requires 4 attendants whereas an electric one requires two. An electric machine fills 300 packets per hour; a manual one can fill 200 packets per hour. At least 3000 packets need to be filled per hour and the number of attendants should not exceed 40.
  
  a) Write down inequalities to describe these conditions and graph them.
  
  b) If for every hour it is used, an electric machine brings a profit of shs. 200 and a manual one shs. 500, determine the number of machines of each type that should be installed in order to maximize profit per hour.
  
  c) Find the maximum profit

  Date posted: September 12, 2019 .    Answers (1)

• A cupboard has 7 white cups and 5 brown cups all identical in size and shape. (Solved)
  

  A cupboard has 7 white cups and 5 brown cups all identical in size and shape. There is a blackout in the town and Mrs. Wafula has to select three cups one after the other without replacing the previous ones.
  
  a) Draw a tree diagram for the information.
  
  b) Calculate the probability that she chooses.
  i) Two white cups and one brown cup
  ii) Two brown cups and one white cup.
  iii) At least one white cup.
  iv) Three cups of the same colour

  Date posted: September 12, 2019 .    Answers (1)

• Two grades of tea, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by weight. (Solved)
  

  Two grades of tea, costing sh 100 and 150 per kg respectively are mixed in the ratio 3:5 by weight. The mixture is then sold at sh. 160 per kg. Find the percentage profit on the cost price.

  Date posted: September 12, 2019 .    Answers (1)

• A translation maps a point P(3,2) onto P` ( 5,-4) (Solved)
  

  A translation maps a point P(3,2) onto P` ( 5,-4).
  a) Determine the translation vector.
  b) A point Q` is the image of the point Q ( 2,5) under the same translation. Find the length of P` Q` leaving the answers in surd form.

  Date posted: September 12, 2019 .    Answers (1)

• a) Expand ( 3x - 1/3 y)⁴ fully (Solved)
  

  a) Expand ( 3x - 1/3 y)⁴ fully
  b) By substituting suitable values of x and y in your expansion, obtain the value of (29.5)⁴ to 4 significant figures.

  Date posted: September 12, 2019 .    Answers (1)

• A circle of radius 7 units has it’s centre at the point of intersection between the lines x +2y + 1 = 0 and 2x... (Solved)
  

  A circle of radius 7 units has it’s centre at the point of intersection between the lines x +2y + 1 = 0 and 2x + 3y – 3 = 0
  Find the equation of the circle expressing it in the form x² + y²+ gx +fy +c =0

  Date posted: September 12, 2019 .    Answers (1)

• Make x the subject of the formula. (Solved)
  

  Make x the subject of the formula.
  

  Date posted: September 12, 2019 .    Answers (1)

• Solve the following equation; (Solved)
  

  Solve the following equation;
  

  Date posted: September 12, 2019 .    Answers (1)

• The length and breath of a rectangular card were measured to the nearest millimeter and found to be 14.5 cm and 10.6 cm respectively. (Solved)
  

  The length and breath of a rectangular card were measured to the nearest millimeter and found to be
  14.5 cm and 10.6 cm respectively. Find the percentage error in the perimeter.

  Date posted: September 12, 2019 .    Answers (1)

• A school bus was valued at sh 6,000,000 in January 2000. Each year, its value decreased by 12.5% of its value at the beginning of... (Solved)
  

  A school bus was valued at sh 6,000,000 in January 2000. Each year, its value decreased by 12.5% of its value at the beginning of the year. Find the value of the bus in January 2005, giving your answer correct to 4.s.f

  Date posted: September 12, 2019 .    Answers (1)

• Find the image A` B` of AB where, A ( 2,2) and B ( 5,4), Under the combined transformation YX. (Solved)
  

  The transformations X and Y have the matrices respectively.
  Find the image A` B` of AB where, A ( 2,2) and B ( 5,4), Under the combined transformation YX.

  Date posted: September 12, 2019 .    Answers (1)

• Find the x – coordinates of the points on the curve y = 3x³ + 18x² + 2x + 3 (Solved)
  

  Find the x – coordinates of the points on the curve y = 3x³ + 18x² + 2x + 3 at which the gradient is 2.

  Date posted: September 12, 2019 .    Answers (1)

• The principal of Butere High School, decided to have a charity walk to raise money to build a dormitory. (Solved)
  

  The principal of Butere High School, decided to have a charity walk to raise money to build a dormitory. She will cover 10km on the first day. Thereafter, she will cover 2 km more than the previous day.
  Find:
  a) The distance she will travel on the 13th day
  b) How many days she will require to cover a total of 400km.

  Date posted: September 12, 2019 .    Answers (1)

• Without using tables or calculators evaluate. (Solved)
  

  Without using tables or calculators evaluate.
  

  Date posted: September 12, 2019 .    Answers (1)

• Rationalize the denominator and write the following in the form (Solved)
  

  Rationalize the denominator and write the following in the form where a,b,c,d and e are constants.
  

  Date posted: September 12, 2019 .    Answers (1)

• Use logarithms correct to 4 decimal places, to evaluate (Solved)
  

  Use logarithms correct to 4 decimal places, to evaluate
  

  Date posted: September 12, 2019 .    Answers (1)

• The table below shows the marks scored by eighty Form 4 students in a mathematics test. (Solved)
  

  The table below shows the marks scored by eighty Form 4 students in a mathematics test.
  
  
  a) Calculate
  i) Mean mark.
  ii) Lower quartile
  
  b) On the grid provided draw the cumulative frequency curve to represent the above
  distribution
  
  c) From the graph estimate the
  i) 4th decile
  ii) Range of marks of the middle 70% of the students.

  Date posted: September 12, 2019 .    Answers (1)

• The figure below shows points on the earth’s surface (Solved)
  

  The figure below shows points on the earth’s surface
  
  
  a) State the positions of A, B, C and D in coordinate form
  
  b) An aircraft flies from A to B along latitude 40⁰N, B to C. along longitude 30⁰E, C to D along latitude 40⁰S. Calculate to 4 S.f the total distance it covered .(Take radius of the earth =6371km)
  
  c) If the aircraft leaves A at 8.00am at a speed of 720km/h to B. At what local time is it expected at B?

  Date posted: September 12, 2019 .    Answers (1)

• The table below shows income Tax rates (Solved)
  

  The table below shows income Tax rates
  
  
  Faith earns a monthly basic salary of Ksh 45,000 and she is also given taxable allowances amounting to Ksh 20480 per month.
  a) Calculate Faiths’ gross income tax per month.
  b) Faith is entitled to a personal tax relief of Ksh 1162. Determine her net income per month.
  c) Faith received 50% increase in her total income; calculate the corresponding percentage increase on the net income tax.

  Date posted: September 12, 2019 .    Answers (1)