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Mr. Abas uses a cuboid container of length 80cm and width 50cm to store water at home. If the container...

18. Mr. Abas uses a cuboid container of length 80cm and width 50cm to store water at home.
If the container holds 240,000cm³ of water when full, find its height.
19. What is the supplement of 2k + 30°?
20. In the diagram below, what is the bearing of town K from town Y.
SECTION B (60 MARKS)
The Venn diagram below shows 46 visitors who attended the birthday party. Some ate beef (B) while others ate chicken (C). Study it carefully and answer questions that follow:
n(B∪C) = 46
n(B∩C) = 19
n(C) = 3
(a) Find the value of y. (02marks)
(b) What is the probability of selecting a visitor at random who ate chicken but not beef? (03 marks)
22. Study the number line below and answer the questions that follow:
(a) Write the integer represented by:
(i) 0
(ii) -3
(b) Write the mathematical statement represented on the number line. (2 marks)
(b) Calculate the GCF of 24 and 18 (1 mark)
(c) Calculate the LCM of 18 and 24 (02 marks)
24. The table below shows the marks scored by some pupils, in a test.
If the mean mark is 55, find the value of M. (03marks)
23. Given the Venn diagram below:
PF24 PF18
(a) Find the value of x. (01 mark)
(b) Calculate the median mark. (02marks)

Answer

  1. The volume of the container is given by the formula: Volume = length × width × height. Therefore, 240,000 = 80 × 50 × height. Solving for height gives: height = 240,000 / (80 × 50) = 60 cm.

  2. The supplement of an angle is 180° minus the angle. Therefore, the supplement of 2k + 30° is 180° - (2k + 30°) = 150° - 2k.

  3. The bearing of town K from town Y is 132°.

  4. (a) From the Venn diagram, n(B∪C) = 46, n(B∩C) = 19, n(C) = 3. To find y, use the equation: 2y + 19 + 3 = 46. Solving gives: 2y = 24, so y = 12.

  5. (b) The probability of selecting a visitor who ate chicken but not beef is the number of people who ate only chicken divided by the total number of visitors. This is 3/46.

  6. (a) (i) The integer represented by 0 is 0. (ii) The integer represented by -3 is -3.

  7. (b) The mathematical statement represented on the number line is 7 + 6 = 13.

  8. (b) The GCF of 24 and 18 is 6.

  9. (c) The LCM of 18 and 24 is 72.

  10. The mean mark is given by the formula: Mean = (sum of all marks) / (number of pupils). Given the mean is 55, solve for M: (66 + 60 + 70 + 68 + M) / 5 = 55. Solving gives M = 110.

  11. (a) From the Venn diagram, solve for x: x + 2x + 3 = 24. Solving gives x = 7.

  12. (b) The median mark is the middle value when the marks are arranged in order. Arranging the marks: 60, 65, 66, 68, 70. The median is 66.

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