IGCSEMathsCambridge (CIE)CoreFlashcardsAlgebra & SequencesInequalities

Inequalities (Cambridge (CIE) IGCSE Maths: Core): Flashcards

Exam code: 0580 & 0980

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FrontInterpreting Inequalities
What is a strict inequality?

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What is a strict inequality?
A strict inequality is one that does not allow the two sides to be equal, so the symbols are $<$ and $>$ .
For example $x > 5$ does not include $5$ itself, whereas $x \geq 5$ does.
Complete the list of integers that satisfy $3 < x \leq 6$ :
$x =______, 5,______$
The completed list is:
$x = 4, 5, 6$
$3$ is left out because the inequality is strict at that end, while $6$ is included because it is not.
True or False?
$x > 3$ means that the smallest possible value of $x$ is $4$ .
False.
Unless the question says that $x$ is an integer, $x$ can take any value greater than $3$ , such as $3.1$ or $π$ .
There is no smallest such value at all.
What is the smallest integer that satisfies $x > 6.5$ ?
The smallest integer is $7$ .
$6.5$ is not itself an integer, and the next whole number above it is $7$ .
List all the integers that satisfy $- 4 \leq x < 2$ .
$x = - 4, - 3, - 2, - 1, 0, 1$ .
Remember that zero and negative whole numbers are integers too, so the list does not begin at $1$ .
True or False?
There are infinitely many integers that satisfy $x > 2$ .
True.
Only one end is fixed, so the integers $3, 4, 5, 6, \dots$ carry on without limit.
An inequality needs two end points before the list of integers is finite.
How do you find the integers that satisfy both $0 < x < 5$ and $x \geq 3$ ?
List the integers for each inequality separately, then pick out the values that appear in both lists.
Here that gives $1, 2, 3, 4$ and $3, 4, 5, 6, \dots$ , so the answer is $x = 3$ and $x = 4$ .
Complete the rule for drawing an inequality on a number line:
For $<$ or $>$ , use an $______$ circle.
For $\leq$ or $\geq$ , use a $______$ circle.
The completed rule is:
For $<$ or $>$ , use an open circle.
For $\leq$ or $\geq$ , use a closed circle.
An open circle shows that the end point is left out, and a closed circle shows that it is included.
How do you show $- 2 \leq x < 1$ on a number line?
Draw a closed circle at $- 2$ and an open circle at $1$ , then join them with a horizontal line.
The line between the circles shows that every value in between satisfies the inequality.
How do you show $x > 5$ on a number line?
Draw an open circle at $5$ and a horizontal arrow pointing to the right.
There is no second circle, because the inequality has only one end point and the values carry on without limit.
For $t < 3$ , which way does the arrow on the number line point, and why?
The arrow points to the left.
Every value less than $3$ satisfies the inequality, and those values lie to the left of $3$ on the line.
True or False?
On a number line, the left-hand end point of an inequality always has a closed circle.
False.
Each end point is decided only by the symbol at that end, not by which side it is on.
So $- 3 < x \leq 4$ is open on the left and closed on the right, while $- 2 \leq x < 1$ is the other way round.

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