Thursday, March 8, 2018

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Wednesday, February 21, 2018

Mathematics Secondary 2. Chapter 1 Congruence and Similarity. Page 4

16. On a map the distance between two places A and B is 15 cm and the area of the Central Business District is 8 cm2. If the scale of the map is 1 : 80000,
(a) Find the actual distance of AB in km,
(b) Find the actual area of the Central Business District in km2.

17. The plans of a building are drawn to a scale of 1 : 150.
(a) Find the actual length, in metres, represented by 42 cm on the plan.
(b) The actual length of the diagonal of a hall is 33 m. Find its lenth, in cm, on the plan.
(c) The area of a meeting room is 450 m2. Find its area, in cm2, on the plan.

18. The diagram shows a triangle ABC where AB = 4 km, AC = 3 km and BC = 5 km. If  triangle ABC is drawn on a map of scale 1 : 50000, find
(a) the length of AB, in cm, on the map,
(b) the area of triangle ABC, in cm2, on the map.


19. A football stadium is represented by a scale of 1 cm to 8 m on paper.
(a) Find the actual length of the field if the length on the drawing is 28 cm.
(b) The actual width of the stadium is 120 m. Find its width on the diagram.
(c) If the area of the seating gallery is 960 m2. Find its area on the drawing.

20. The area scale of a map is 1 : 16000000. The length of two places A and B on the map is 8 cm and the area of a private housing estate is 12 cm2.
(a) Find the linear scale of the map in the form 1 : n.
(b) Find the actual distance of AB in metres.
(c) What is the area of the private housing estate in hectares?

Mathematics Secondary 2. Chapter 1 Congruence and Similarity. Page 3

11. Given that ABC triangle is similar to APQ triangle, calculate the values of x and y.



12. APQ triangle is similar to ABC triangle and AP : PB = 5 : 3. If PQ = 8 cm and QC = 6 cm, calculate the length
(a) BC,
(b) AQ.



13. A model of an apartment block is made to a scale of 1 : 50.
(a) Find the actual height of the apartment bloack if its height on the model is 42 cm.
(b) If the area of the hall of the apartment is 34 m2, find the area of the hall on the model.
(c) If the area of a unit of the apartment is 1200 cm2 on the model, find its actual area in m2.

14. On a map drawn on a scale of 2 cm to represent 300 m, what length on the map will represent a road 2.4 km long? A railway track on the map has a length of 14. 5 cm. Find its actual length in km.

15. A model of a building is made to a scale of 1 cm to 6 m.
(a) How tall is the model if the actual height of the building is 260 m?
(b) The base area of the building is 5400 m2. Find the base area of the building in the model.

Need more practise, go to number 16

Tuesday, February 20, 2018

Mathematics Secondary 2. Chapter 1 Congruence and Similarity. Page 2

6. PQRS is similar to ABCD
(a) Name three pairs of corresponding sides.
(b) Find the values of x and y.




7. The figure shows two similar cones.
(a) find the values of x.
(b) What is the ratio of the base circumference of the smaller cone to that of the big cone?



8. In the figure, BPC is parallel to DQE.
(a) Name three pairs of similar triangles.
(b) If AC = 6 cm, CE = 8 cm, CP = 5 cm, BP = 2 cm and BD = 10 cm, find the values of x, y and z.



9. ABC Triangle is similar to PRQ triangle. Find the values of x and y.



10. Given that PQR triangle is similar to XYZ triangle, calculate the values of x and y.


Need more practise, go to number 11

Wednesday, February 7, 2018

Secondary 2 Mathematics. Chapter 2 Direct and Inverse Proportion page 3

11. A local radio station has been given the exclusive rights to promote a concert in the city’s civic arena, which seats 22 000 persons. The commission $ C for the radio station is $ 5 000 plus $ 0.50 for each of the n tickets sold for the concert.
(a) Write down the formula connecting C and n.
(b) Use the formula to calculate
 (i) the commission for the radio station when 15 000 tickets are sold,
 (ii)the number of tickets sold when the commission for the radio station is $ 11 250,
 (iii)the maximum commission for the radio station.



12. (a) If a is directly proportional to the cube of b and that a = 54 when b = 3, find the equation relating a and b.
      (b) using the equation in (a), find the value of
            (i) a when b = 5, (ii) b when a = 128.



13. In each of following, find the unknown variable without finding the proportionality constant.
(a) If h is directly proportional to the square of k and h = 8 when k = 3, find h when x = 6.
(b) If m is directly proportional to p1/2 and m = 12 when p = 16, find p when m =18.



14. If the height of a cylinder is fixed, its volume is directly proportional to the square of its radius. When the radius of the cylinder is 2 cm, its volume is 81 cm3. Find the radius of the cylinder if the volume is 506.25 cm3.



15. Given that a2is directly proportional to b3 and a = 8(3)1/2whenb = 4,
(a) find the equation connecting a and b,
(b) find the value of a when b = 3.




Tuesday, February 6, 2018

Secondary 2 Mathematics. Chapter 2 Direct and Inverse Proportion page 2

6.Two quantities P and Q are related by the formula  P = A - B/Q2, where A and B are constants. Given that P = 1 when Q = 2 and P = 6 when Q = 3,
(a) write down two equations in A and B,
(b) solve these equations to find the value of A and the value of B,
(c) find the positive value of Q when P = 7 3/4



7. The intensity of illumination, I lumens/m², at a point on a screen is inversely proportional to the square of the distance, d m, of the light source from the point. Given that d = 2.5 m when I = 0.8 lumens/m², find
(a)  I, when d = 1.25 m, 


(b)  d, when I = 0.05 lumens/m².





8. Water flows from a container such that the depth of water x cm at any instant, is inversely proportional to the square root of the time t s, for which the water has been flowing. After 25 s, the depth is 450 cm. Calculate the depth after
(a)  100 s,
(b)  3 min 45 s.




9. The resistance R, to the motion of a car is directly proportional to the speed v of the car. Given that the resistance is 2 688 newtons when the speed is 16 m/s, find
(a)  the resistance when the speed is 28 m/s,
(b)  the speed when the resistance is 16 800 newtons.



10.The total cost, $ c, of owning and operating a car is given by the formula c = a + bx, where x is the distance driven in km and a and b are constants. When the car is driven 2 500 km during it lifetime, the total cost is $ 19 000 and when the car is driven 6 000 km during its lifetime, the total cost is $ 20 400.
(a) Write down two equations in a and b.
(b) Solve these equations to find the value of a and of b.
(c) Find the total cost, if the car is driven a total distance of
(i) 50 000 km, (ii) 100 000 km.


go back to number 1-5

Monday, February 5, 2018

Secondary 2 Mathematics. Chapter 2 Direct and Inverse Proportion page 1

Chapter 2 Direct and Inverse Proportion


1. If q is inversely proportional to p, and q = 120 when p = 2, form an equation connecting p and q and calculate q when p = 5.


2.         If y is inversely proportional to (2x + 1) and y = 5 when x = 3, find
(a)  y when x = 17,                  (b)  x when y = 7.


3. If y is inversely proportional to the square of (3x + 2) and y = 4 when x = 2/3  , find
(a)  y when x = 11 1/3 , (b)  x when y = 16.



4. Given that p is directly proportional to (2q + 1)1/2  and p = 63 when q = 24, find
(a)  p when q = 12, (b)  q when p = 27.



5. Given that d is directly proportional to the square root of t, copy and complete the table below.





Need more practise, go to number 6

Sunday, February 4, 2018

Mathematics Secondary 2. Chapter 1 Congruence and Similarity. Page 1

Chapter 1 Congruence and Similarity.
 
1.  ∆PQR is similar to ∆ABC. Given that PQ = 5 cm, QR = 4 cm and AB = 8 cm, calculate the length of BC.


2.  ABCD is a trapezium where AB is parallel to DC. Name a pair of similar triangles. If
     AM = 5 cm, MC = 7 cm, BM = 6 cm, AB = 8 cm, DC = x cm and MD = y cm, find the
    values of x and y.



3. State, with reasons, whether ABC is similar to PQR and find the value of x.



4.  OAB is similar to OPQ.
(a) Explain clearly why AB is parallel to QP.
(b) If OA = 5 cm, OB = 6 cm, OQ = 8 cm, QP = 5.5 cm, OP = x cm and AB = y cm, find the values of x and y.





5. In Figure, ABC is similar to PQR. Given that AB = 8 cm, AC = 10 cm, PQ = 12 cm, QR = 9cm, BC = x cm and PR = y cm, calculate the values of x and y.




Need more practise, go to number 6