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# SECTION THREE — ALGEBRA - Inequalities

1. Two schools are merging and a new school is being built to accommodate all the pupils. There will be 1130 pupils in total in the new school. No class must have more than 32 pupils. Show this information as an inequality. Call the number 1 How many classrooms are needed? - of classrooms x.
2. A couple are planning their wedding. For the reception in a local hotel, they have a budget of £900. If the hotel charges £18 per head, how many guests could be invited? Show this information as an 411 inequality.
3. The shaded region satisfies three inequalities. Write down these inequalities. y 6 II A SOLID LINE means the inequality is S or A DASHED LINE means the inequality is < or >. y= 1
4. Draw a set of axes with the x-axis from —2 to 6 and the y-axis from —1 to 7. Show on a graph the region enclosed by the following three inequalities. y < 6, x y 5 and x<_5
5. Draw and label a number line from —5 to 5 for each of the following inequalities. Represent the inequalities on your number lines. a) x2 < 4 c) x2 9 e) 1 6 g) 9 > b) x2 < 1 d) 25 x2 0 x2 1 h) x2 0 Draw a set of axes with the x-axis from —4 to 5 and the y-axis from —3 to 6. Show on a graph the region enclosed by the following. y 5_ 2x + 4, y < 5 —x and y 3 —1 A company are recruiting new members of staff. All applicants must take two online tests. To get an interview, applicants must score higher than 5 on the first test, at least 7 on the second, and have a total combined score of at least 1 4 . a) Write out three inequalities to represent the three criteria for getting an interview. Use x for the score on the first test and y for the score on the second test. b) The company want to analyse the quality of applicants by plotting their test scores on a graph, and picking out the ones who satisfy the criteria. Using suitable axes, show on a graph the region enclosed by the three inequalities where suitable candidates would be placed.