Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level25. Linear Inequalitiesx + 81. Plot the graphs of x = 6, y = 10 – x and y = ----------- for values of x from 0 to 6 and values of2y from 0 to 10. Clearly show the area satisfied by the inequalities x ≤ 6, y ≥ 10 – x andx + 8y ≤ ----------- . Write down the integer points within this area.22. Plot the graphs of y = 6, y = 6 – 2x and y = 4x – 2 for values of x from 0 to 4 and values of yfrom –3 to 7. Clearly show the area satisfied by the inequalities y ≤ 6, y ≥ 6 – 2x and y ≥ 4x– 2. Write down the integer points within this area.x3. For values of 0 to 5 on the x axis and 0 to 12 on the y axis, plot the graphs of y + -- = 4,31y = --x + 3 and y = 12 – 3x . On your diagram clearly indicate the area satisfied by the2x 1inequalities y + -- ≥ 4 , y ≤ --x + 3 and y ≤ 12 – 3x . List the integer points lying within3 2this area.14. Plot the graphs of y = x, y = 12 – 3x and y = 7 – --x for values of x from 0 to 6 and2values of y from 0 to 12. Clearly indicate the area satisfied by the inequalities y>x ,1y > 12 – 3x and y < 7 – --x . Write down the integer points lying within this area.2115. Plot the graphs representing the equations x + y = 10, y + --x = 5, y = --x + 4 and22y = 2x – 3 for values of x from 0 to 6 and values of y from –3 to 10. On your diagram1 1shade in the region representing the inequalities x + y< 10 , y + --x > 5 , y ≤ --x + 42 2and y > 2x – 3 . Write down the integer points lying within this region.6. On graph paper draw lines and shade in the area representing the inequalities y ≤ 8–2x ,1y ≥ 6–3x , y ≤ --x – 1 and y≥x – 4 for values of x from 0 to 6 and y from –4 to 8. Write2down the integer points lying within this region.17. Plot lines and shade in the area representing the inequalities y + --x < 1 , y≥x – 3 ,21y < 2x – 2 and y > –-- ( x + 5)for values of x from –5 to 4 and y from –3 to 2. Write down3the integer points lying within this region.8. Plot lines and shade in the area representing the inequalities y + 2x < 8 , y 2 and y > 2x – 2 for values of x from –1 to 5 and values of y from –2 to 8. Write2down the integer points lying within this area.9. Plot lines and shade in the area representing the inequalities y> x + 1 , y + 3x < 7 ,y < 2x + 6 and y > 1 – x for values of x from –3 to 4 and values of y from –3 to 8. Writedown the integer points lying within this area.