Questions covered in Hard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The solution set of the inequality $\frac{x-2}{x+5} > 2$ is
2. The solution set of $1 \le |x-2| \le 3$ is
3. If $|x+2| \le 9$, then $x$ belongs to
4. The inequality representing the region containing the origin for the line $3x + 4y = 12$ is
5. If $|x| > 5$, then
6. Solve for $x$: $\frac{2x-1}{3} \ge \frac{3x-2}{4} - \frac{2-x}{5}$.
7. Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
8. Solve the inequality $|x-1| + |x-2| \ge 4$.
9. Solve the following system of inequalities graphically: $x + 2y \le 10, x + y \ge 1, x - y \le 0, x \ge 0, y \ge 0$.
10. A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?
11. Solve the system of inequalities graphically: $3x + 2y \le 150, x + 4y \le 80, x \le 15, y \ge 0, x \ge 0$. Find the coordinates of the vertices of the feasible region.
12. Case Study: A company produces a product with a fixed cost of Rs 20,000 and a variable cost of Rs 100 per unit. The selling price is Rs 300 per unit.
    (i) Write the inequality to ensure the company makes a profit.
    (ii) Find the minimum number of units the company must sell to avoid a loss.
    (iii) If the selling price is reduced to Rs 200, what is the new break-even point?