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(a) Solve the equation \( \frac{3x\:-\:5}{10} = \frac{8\:+\:5x}{5} \)
Solution:
Cross multiply
5(3x – 5) = 10(8 + 5x)
15x – 25 = 80 + 50x
collect like terms
15x – 50x = 80 + 25
-35x = 105
divide both sides by -35
⇒ \( \frac{-35x}{-35} = \frac{105}{-35} \)
∴ x = -3
(b) 342five
1st Step: convert to base 10
342five = 3 × 5² + 4 × 5¹ + 2 × 50
= 3 × 25 + 4 × 5 + 2 × 1
= 75 + 20 + 2
= 97ten
2nd Step: Convert to binary
97ten = 1100001two
∴ 342five = 97ten = 1100001two
(a) Calculate the 4th angle of a quadrilateral whose other three angles are 52º, 120º and 125º
Solution:
Sum of the interior angles of a quadrilateral is 360°
∴ 52º + 120º + 125º + x = 360º
297º + x = 360º
x = 360º – 297º
x = 63º
(b) The table below shows the scores of students in a test
(i) What is the modal score?
Answer: Score with the highest number = Modal score = 25
(ii) How many students took part in the test?
Answer: 15 students
(iii) Find the median score.
We can calculate the median from the cumulative frequency table shown above.
Total number of students = 15
∴ The median is the 8th student
From the table, the cumulative frequency that holds the 8th student is 10, corresponding to a score 0f 24.
∴ The medianscore = 24
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