(a) On the grid opposite, draw the graph of the line with equation

(b) Show, by shading on the grid, the region $\displaystyle R$ defined by the inequalities

For all points in $\displaystyle R$, with coordinates $\displaystyle (x, y)$

(c) find the least value of $\displaystyle P$

Only use this grid if you need to redraw your graph.

(a) On the grid opposite, draw the line with equation

(i) $\displaystyle 3x - 4y = 12$

(ii) $\displaystyle y + 6 + 3x = 0$

(iii) $\displaystyle 3y = 18 - x$

(b) Show, by shading on the grid, the region $\displaystyle R$ defined by the inequalities

For all points in $\displaystyle R$, with coordinates $\displaystyle (x, y)$

Using values from your graph,

(c) find the least value of $\displaystyle P$ and the greatest value of $\displaystyle P$

Only use this grid if you need to redraw your graph.

Figure 1 shows a rectangle with width $\displaystyle x$ cm and length $\displaystyle (2x + 3)$ cm.

The perimeter of the rectangle is $\displaystyle P$ cm and the area of the rectangle is $\displaystyle A$$\displaystyle \mathrm{cm}^2$

Find the set of possible values for $\displaystyle x$

Give your answer in the form $\displaystyle a < x < b$ where $\displaystyle a$ and $\displaystyle b$ are rational numbers.

Show clear algebraic working.

Find the set of values for $\displaystyle x$ for which

(a) $\displaystyle 9 - 3x > 11x + 2$

(b) $\displaystyle 10x^2 + 7x < 12$

(c) both $\displaystyle 9 - 3x > 11x + 2$ and $\displaystyle 10x^2 + 7x < 12$

(a) On the grid below, draw the line with equation

(i) $\displaystyle 3x + 4y = 24$      (ii) $\displaystyle 2x - 5y + 10 = 0$

(b) Show, by shading on the grid, the region $\displaystyle R$ defined by the inequalities

Label the region $\displaystyle R$

The length of rectangle $\displaystyle R$ is 2 cm greater than its width.

The area of $\displaystyle R$ is greater than $\displaystyle 8\mathrm{cm}^2$ and the perimeter of $\displaystyle R$ is less than $\displaystyle 30\mathrm{cm}$.

Given that the width of $\displaystyle R$ is $\displaystyle w$ cm,

find the set of possible values of $\displaystyle w$

Give your answer in the form $\displaystyle a < w < b$ where $\displaystyle a$ and $\displaystyle b$ are rational numbers.

(a) On the grid opposite draw the line with equation

(b) Show, by shading, the region $\displaystyle R$ defined by the inequalities

For all points in $\displaystyle R$ with coordinates $\displaystyle (x, y)$

(c) Using your graph, find the least value of $\displaystyle P$

Only use this grid if you need to redraw your graph.

(a) On the axes opposite, draw the line with equation

(b) Show, by shading on your graph, the region $\displaystyle R$ defined by the inequalities

For all points in $\displaystyle R$, with coordinates $\displaystyle (x, y)$

(c) Find

(i) the greatest value of $\displaystyle P$

(ii) the least value of $\displaystyle P$

Only use this grid if you need to redraw your graph.

Find the set of values of $\displaystyle x$ for which

Find the set of values of $\displaystyle x$ for which

(a) $$8x-7<5x+5,$$

(b) $$2x^2-5x-3>0,$$

(c) both $\displaystyle 8x-7<5x+5$ and $\displaystyle 2x^2-5x-3>0$.

(a) Using the axes below, sketch the lines with equations

(i) $\displaystyle y=6$,

(ii) $\displaystyle y+x=10$,

(iii) $\displaystyle y=2x-5$.

Show the coordinates of any point where each line crosses the coordinate axes.

(b) Show, by shading on your sketch, the region $\displaystyle R$ defined by the inequalities

Use algebra to solve the equations

xy $\displaystyle = 36$

xy $\displaystyle + x + 2y = 53$

(a) Using the axes below, sketch the lines with equations

(i) $\displaystyle y+2x=-5$,

(ii) $\displaystyle y=x+4$.

Show the coordinates of the points where each line crosses the coordinate axes.

(b) Show, by shading, the region $\displaystyle R$ defined by the inequalities

(a) On the grid provided, draw the graphs of the lines with equations

(b) Show, by shading on the grid, the region $\displaystyle R$ defined by the inequalities

For all points in $\displaystyle R$, with coordinates $\displaystyle (x,y)$,

(c) Find the greatest value of $\displaystyle F$.