Coordinate Geometry Grade IX Worksheet with solutions

Self Assessment Test 4 - Solutions

Based on Chapter 4

1. Question: Simplify \(3x + 5x\).

   Solution: \(3x + 5x = 8x\).

2. Question: Solve for \(x\): \(5x - 3 = 12\).

   Solution: \(5x - 3 = 12 \Rightarrow 5x = 12 + 3 \Rightarrow 5x = 15 \Rightarrow x = 3\).

3. Question: Find the area of a rectangle with length 5 units and width 3 units.

   Solution: Area of a rectangle = length × width = 5 × 3 = 15 square units.

4. Question: Simplify: \(\frac{6x^2 + 9x}{3x}\).

   Solution: \(\frac{6x^2 + 9x}{3x} = 2x + 3\).

5. Question: Factorize: \(x^2 - 6x + 9\).

   Solution: \(x^2 - 6x + 9 = (x-3)(x-3) = (x-3)^2\).

6. Question: Find the slope of the line passing through the points (2, 3) and (4, 7).

   Solution: Slope = \(\frac{7-3}{4-2} = \frac{4}{2} = 2\).

7. Question: Solve the system of equations: \(2x + 3y = 8\) and \(x - 4y = -6\).

   Solution: Solving the system, we find that \(x = 2\) and \(y = 2\).

8. Question: Evaluate: \(2^{3} \times 3^{-1}\).

   Solution: \(2^{3} \times 3^{-1} = 8 \times \frac{1}{3} = \frac{8}{3}\).

9. Question: The following table shows the number of books sold by a bookstore over 6 months. Find the average number of books sold per month.

   Month	Jan	Feb	Mar	Apr	May	Jun
   Books Sold	20	24	22	26	25	27

   Solution: Average number of books sold per month = \(\frac{20 + 24 + 22 + 26 + 25 + 27}{6} = \frac{144}{6} = 24\).

10. Question: Find the sum of the infinite geometric series: \(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \ldots\).

    Solution: This is a geometric series with first term \(a = \frac{1}{3}\) and common ratio \(r = \frac{1}{3}\). The sum of an infinite geometric series is \(\frac{a}{1 - r} = \frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{1}{2}\).