Inequalities

Using the axes below, find the region that satisfies the following inequalities.

Make sure that you clearly indicate the region that represents your answer.

On the graph paper below, draw the region that satisfies all of the following conditions.

Clearly indicate the region that represents your answer.

What is the least possible value of x so that all three conditions are met?

What is the greatest possible value of y so that all three conditions are met?

What is the greatest integer value of n if 2n < 17?

What is the least integer value of n if 2ⁿ > 125?

What is the greatest integer value of n if 2n < 17?

What is the least integer value of n if 2ⁿ > 125?

Complete the following table to give the set of inequalities that describes the shaded region shown above.

One inequality has already been written for you.

Simplify each of the following. Circle your answer in each case.

m⁴ m³

Write down an expression for the nth term of the following sequence.

List all of the integers that satisfy the following inequality.

13 < 2 n < 19

Simplify each of the following. Circle your answer in each case.

m⁴ m³

Write down an expression for the nth term of the following sequence.

List all of the integers that satisfy the following inequality.

13 < 2 n < 19

On Monday morning, Twm picked n apples from a tree. Ceri picked 5 times as many apples as Twm.

On Monday afternoon, Twm picked 19 more apples. Ceri gave 7 of her apples to Twm.

Ceri still had more apples than Twm.

Write down an inequality in terms of n to show the above information. Use your inequality to find the least possible number of apples Twm picked on Monday morning.

You must show all your working.

The rectangle below has: • a length of 3y • a width of y + a • an area of 3y² +12y.

Find the value of a.

You must show all your working.

Another rectangle has a width of 4x 10.

Given that x is a whole number, explain why the value of x cannot be less than 3.

The perimeter of the rectangle is 14x 4.

Find the length of the rectangle in terms of x.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

On Monday morning, Twm picked n apples from a tree. Ceri picked 5 times as many apples as Twm.

On Monday afternoon, Twm picked 19 more apples. Ceri gave 7 of her apples to Twm.

Ceri still had more apples than Twm.

Write down an inequality in terms of n to show the above information. Use your inequality to find the least possible number of apples Twm picked on Monday morning.

You must show all your working.

Using the axes below, find the region which satisfies the following inequalities.

You must clearly indicate the region that represents your answer.

Expand x(x² + 7).

Expand and simplify (x – 5)(3x − 4).

Sarah buys and sells antique clocks. On Monday, Sarah had n clocks. At the end of the day on Tuesday, she had 5 times as many clocks as she had on Monday. On Wednesday, she sold 27 clocks.

At the end of the day on Wednesday, Sarah had fewer clocks than she had on Monday.

Write an inequality, in terms of n, that shows this information.

Solve your inequality to find the greatest number of clocks that Sarah could have

had on the Monday.

Expand x(x² + 7).

Expand and simplify (x – 5)(3x − 4).

Sarah buys and sells antique clocks. On Monday, Sarah had n clocks. At the end of the day on Tuesday, she had 5 times as many clocks as she had on Monday. On Wednesday, she sold 27 clocks.

At the end of the day on Wednesday, Sarah had fewer clocks than she had on Monday.

Write an inequality, in terms of n, that shows this information.

Solve your inequality to find the greatest number of clocks that Sarah could have

had on the Monday.

Arthur, Sian and Kezia are all given some £1 coins.

Arthur receives £n. Sian is given five times as much money as Arthur. Kezia receives three times as much money as Arthur, plus an extra £7.

Sian was given less money than Kezia.

Write down an inequality in terms of n that illustrates the fact that Sian received less

money than Kezia.

What was the greatest amount of money that Arthur could have been given?

Arthur, Sian and Kezia are all given some £1 coins.

Arthur receives £n. Sian is given five times as much money as Arthur. Kezia receives three times as much money as Arthur, plus an extra £7.

Sian was given less money than Kezia.

Write down an inequality in terms of n that illustrates the fact that Sian received less

money than Kezia.

What was the greatest amount of money that Arthur could have been given?

Expand 3x(x² – 2).

Make g the subject of the formula f = 2 – 3g.

Solve 7x – 3 < 29.

What is the greatest integer value of x that satisfies the above inequality?

Expand 3x(x² – 2).

Make g the subject of the formula f = 2 – 3g.

Solve 7x – 3 < 29.

What is the greatest integer value of x that satisfies the above inequality?

Using the axes below, find the region which satisfies the following inequalities.

y + 2x 1

Complete the following table to give the set of inequalities that describes the shaded region

shown above.

Rashid owned n sheep.

Eifion had exactly 4 times as many sheep as Rashid.

Rashid buys 17 extra sheep. Eifion sells 8 of his sheep.

Eifion still has more sheep than Rashid.

Form an inequality, in terms of n. Solve the inequality to find the least value of n.

You must show all your working.

On the graph paper below, draw the region which satisfies all of the following inequalities.

What is the greatest possible value of x such that all three conditions are met?

What is the greatest possible value of y such that all three conditions are met?