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What is ?

What is ?

What is ?

What does mean?

What is ?
1
Remember anything raised to the power zero is worth one.

What does mean?

Rewrite in two other ways.
and

An index (plural indices) is another word for _________?
power

What is ?
32

What is ?

What is a surd?
A surd is an expression such as , which involves a mixture of rational numbers and square roots (or other roots such as cube roots).

What is a rational number?
A rational number is a number which can be written as an exact fraction. This includes whole numbers and terminating decimals.

What symbol is used for the set of rational numbers?

What symbol is used for the set of real numbers?

How would you rationalise the denominator of the expression ?
Multiply the top and the bottom of the expression by .

What is the quadratic formula?

What is a quadratic equation?
A quadratic equation is an equation of the form a + b + c = 0, where a, b and c are constants and a ≠ 0.

State three methods of solving a quadratic equation.
Factorisation, Completing the Square, Using the Quadratic Formula.

What do we mean by the completed square format?
Any quadratic expression written in the form , where A, B and C are constants.

What does the instruction "Sketch a Graph" require you to do?
Sketching a graph means drawing the right general shape of a graph, usually marking the coordinates of important points such as intersections with the coordinate axes, and turning points. A sketch should not be drawn on graph paper or be plotted.

What is the discriminant of a quadratic equation?

If the discriminant is less than zero what does this tell you about the position of a quadratic graph?
It doesn't touch or cross the xaxis, because there are no real solutions,

If the discriminant is equal to zero what does this tell you about the position of a quadratic graph?
The graph touches the xaxis and turns back. I.e. there are two identical real roots/solutions, sometimes stated as just one real solution because they are both the same.

If the discriminant is greater than zero what does this tell you about the position of a quadratic graph?
The graph crosses the xaxis twice. There are two different real solutions.

What shape is a the quadratic graph where ?
A U shape.

What shape is a the quadratic graph where ?
A n shape.

How can you find the turning point of a quadratic graph without using calculus?
Complete the Square

From the equation write down the turning point of its graph.
The turning point is

Give an example of a quadratic which is a perfect square.
Any quadratic of the form e.g. or .

When a quadratic equation is a perfect square how many real roots does it have?
Two that are identical, often stated as just one real root/solution.

What do we mean by the gradient of a graph?
The slope of a graph, i.e. how steep it is.

In the straight line graph what is the slope of the graph?

In the straight line graph what is the y intercept of the graph?

What do we mean by the term yintercept?
The point at which the graph crosses the yaxis.

What is the equation of the xaxis?

What is the equation of the yaxis?

What is the name of the point where the yaxis and xaxis intersect?
The origin (0,0).

If you are given a point (x_{1},y_{1}) and the gradient of a straight line what is the formula you should use for that line.?

Given two points and on a straight line graph how do you find its gradient ?

What is the standard format of a straight line equation, where the coefficients are integers?

Where a graph is curved what is the name of the straight line that touches it at just the one point and has the same gradient as the graph at that point?
The tangent

Where a graph is curved what is the name of a the straight line which is perpendicular to the graph at a particular point?
The Normal

If y=f(x) describe the effect of the graph transformation y=f(x+2).
This is a translation two units to the left.

If y=f(x) describe the effect of the graph transformation y=f(x3).
This is a translation three units to the right.

If y=f(x) describe the effect of the graph transformation y=f(x)+5
This is a translation of five units upwards.

If y=f(x) describe the effect of the graph transformation y=f(x)1
This is a translation of one unit downwards.

If y=f(x) describe the effect of the graph transformation y=2f(x)
This is a stretch in the ydirection scale factor 2. All the yvalues are multiplied by 2.

If y=f(x) describe the effect of the graph transformation y=f(3x)
This is a stretch in the xdirection scale factor . All the xvalues are divided by 3.

If what is the expression for ?

How many stationary points does the graph have?
One at

When given simultaneous equations, one linear and one quadratic how should you proceed to solve them?
Rearrange the linear equation so that either x or y becomes the subject and then substitute it into the quadratic equation.
Solve this quadratic to find the solutions for one of the variables.
Now use the linear equation to find the partner solutions of the other variable.

How should you solve a quadratic inequality?
Factorise it to find the critical values, then either sketch a graph or use a sign table to find the regions required.

What do you need to remember to do when dividing or multiplying an inequality by a negative number?
Reverse the inequality sign.

The number of intersections of two graphs is exactly the same as the number of ___________ of their simultaneous equations.
solutions

What is the gradient function used for?
To find the slope of a curve (which is the same as its tangent) at a given point.

What two notations are used for the gradient function?
and

If you are given the gradient function plus a point on the graph how would you find ?
Integrate and then use the point given to find the constant of integration.

If you want to find the gradient of the normal to a graph what do you need to do?
Evaluate for the point given.

If you want to find the gradient of the tangent to a graph what do you need to do?
Evaluate at the point given.

What is the rule for differentiation?
Bring the power down to the front and multiply it with any coefficient there then subtract one from the power.
Remember this means numbers become zero.

What does the word coefficient mean?
The number in front of an algebraic term. E.g. in the term the number 25 is the coefficient.

What is the name of a series where the terms increase or decrease by the same amount each time?
An Arithmetic Series

What is the difference between a series and a sequence?
A series sums the terms in a number pattern, a sequence is just the number pattern.

What is the rule for integration?
Raise the power of x by one and divide by the new power.
Remember to add C for the unknown constant of integration.

What is the formula for U_{n, }the nth term of an arithmetic series?

What are the two formulae for S_{n}, the sum of the first n terms of an arithmetic series?

 You can use which ever version is more convenient.

In the summation notation how many terms are there?
ba+1 terms

In a recurrence relationship to work out the number pattern what other information do you need apart from the recurrence relation?
The first term U_{1}

What is an integer?
A whole number

What does the term perpendicular mean?
At rightangles to one another.

When two lines are perpendicular what property do their gradients have?
The two gradients m_{1} and m_{2} mulitply together to give 1.

When two lines are parallel what property do they have?
They both have the same gradient.

How do you find out where two straight lines intersect?
Find the solution to their simultaneous equations.

What is an asymptote?
A straight line which is approached by a curve, but the curve never reaches the line. Asymptotes are marked on graphs as dotted lines.For example, the graph of has asymptotes which are the xaxis and the yaxis.

What is a Base?
In an expression involving indices, the base is the number that is being raised to a power.So, for example, in , 8 is the base and 4 is the index.

What is a common difference?
The difference between each pair of successive terms in an arithmetic sequence or arithmetic series. It is usually denoted by d.

What do we mean by a continuous graph?
A graph with no breaks or asymptotes in it.

What is the notation used for the set of integers?

What is an irrational number?
One that cannot be written as an exact fraction. e.g.

How do you find the midpoint between (x_{1,}y_{1}) and (x_{2},y_{2})

What is the formula for the distance between two points (x_{1},y_{1}) and (x_{2},y_{2})?

 Note this comes from Pythagoras Theorem.

What is the name for the shape of a quadratic graph?
A parabola

What is the notation used for the set of all real numbers?

What is a recurrence relationship?_{}
 An recurrence relationship tells you how to find a term in a sequence from the previous term. The definition must also include the value of the first term of the sequence. You can then find the second term from the first term, the third term from the second term, and so on.
 e.g.U_{k+1}=2U_{k , U1=3 gives 3,6,12,24,.. .}

What is a turning point?
A turning point on a curve is a point at which the gradient of the curve is zero. This may be a maximum point or a minimum point. A quadratic graph always has one turning point, which is often called the vertex.A cubic graph may have up to two turning points.

What is a variable?
An unknown quantity represented by a letter, such as x.

Differentiate .

 Remember constants like 7 become zero when differentiated.

Find the sum of the natural numbers from 1 to 100.
5050

What does the sign mean?
Integrate

Find
 Don't forget to add the constant of integration.

is the _________ ___ __________ of y with respect to x.
Rate of Change

Indefinite integration is the __________of differentiation.
reverse or inverse

Describe a graph with a positive gradient.
 It slopes uphill from left to right.
 A function which has a graph with a positive gradient is said to be increasing.

Describe a graph with a negative gradient.
 It slopes downhill from left to right.
 A function which has a graph with a negative gradient is said to be decreasing.

What is ?
This is the second derivative. You get it by differentiating .

What is an intersection?
 The point(s) where two lines (straight or curved) cross.

What is a translation?
A movement of the whole graph, including asymptotes, which can be in the x direction or y direction?

If what is ?

When describe the graph at that point?
 It is parallel with the xaxis.
 It is flat at this point.
 This is called a stationary point.

What is a reciprocal function?
A function of the form . The graphs of all functions of this form have asymptotes x = 0 and y = 0 (the coordinate axes).

