Final Exams Notes

Question 1

What does a sign change signify in iteration?

Answer 1

That there is a solution between the two values you have just put in, therefore you must try more values between those two.

Question 2

When you use an iteration machine, when do you know when you have found the solution?

Answer 2

When you find two values that are equal when rounded to the desired number of decimal places.

Question 3

What is the equation for a circle with centre (0,0) and radius r?

Answer 3

r^2= x^2 + y^2

Question 4

Write out the initial bracket for completing the square

Answer 4

(x + b/2)^2 - (balancing number)

Question 5

When a is positive what does the completing the square balancing number tell you?

Answer 5

the minimum y point.

The minimum y point is (-b/2, balancing number)

Question 6

If the balancing number is positive, what does this tell you?

Answer 6

There are no real roots

Question 7

What is the difference of two squares?

Answer 7

a^2-b^2 = (a + b)(a - b)

Question 8

What is a geometric sequence?

Answer 8

One where the term to term rule is to multiply or divide by the same value.

Question 9

How do you find the multiplier or divider in a geometric sequence?

Answer 9

Divide a term by the previous term

Question 10

What are the equations for exponential graphs?

Answer 10

y= k^x
y= k^-x

Question 11

Under what conditions do exponential graphs curve up?

Answer 11

If k>1 and the power is positive

Question 12

If x^2 > a^2

Answer 12

x > a or x < -a

Question 13

If x^2 < a^2

Answer 13

-a < x < a

Question 14

Explain the graph transformation: y = f (x-1)

Answer 14

Shifts to the right

Question 15

Explain the graph transformation: y = f (x) -1

Answer 15

Shifts down

Question 16

Explain the graph transformation: y = f (-x)

Answer 16

Reflects in the x axis

Question 17

Explain the graph transformation: y = f (2x)

Answer 17

Squashed by stretch factor 2

Question 18

Explain the graph transformation: y = 2f (x)

Answer 18

Height doubles

Question 19

State the alternate segment theorem

Answer 19

The angle between a tangent and a chord is always equal to the angle made at the circumference by the two lines drawn from the ends of the chord.

Question 20

What does “the angle subtended at” mean

Answer 20

The angle made at

Question 21

How do you read column vectors?

Answer 21

The numerator is the horizontal movement

The denominator is the vertical movement

Question 22

How should you write vectors?

Answer 22

Underline them

Question 23

What does
—>
AB

mean?

Answer 23

Go from point A to point B

Question 24

What is the consequence of multiplying a vector by a positive number?

Answer 24

Magnitude is changed

Question 25

What are the consequences of multiplying a vector by a negative number?

Answer 25

Direction and magnitude may change

Question 26

How do you add column vectors?

Answer 26

Add the tops then add the bottoms

Question 27

How do you find an unknown vector?

Answer 27

Find any route there made up of known vectors then simplify

Question 28

How do you show vectors to be on a straight line?

Answer 28

Show that the vectors are all in the same direction by showing that they are multiples of each other.

Question 29

How do you prove congruency?

Answer 29

SSS, AAS, SAS, RHS

Question 30

How do you prove similarity?

Answer 30

All the sides are proportional, All the angles are the same, Any two sides are proportional and the angle between them the same.

Question 31

How are scale factors calculated?

Answer 31

new length ----------------- old length

Question 32

Explain scale factors for sides, areas and volumes

Answer 32

The sides are n times bigger The areas are n^2 times bigger The volumes are n^3 times bigger

Question 33

How do you calculate scale factor n^2

Answer 33

New area ----------------- Old area

Question 34

How do you calculate scale factor n^3

Answer 34

New volume ------------------- Old volume

Question 35

What is the lower quartile?

Answer 35

The value 25% of the way through a data set

Question 36

What is the median?

Answer 36

The value 50% of the way through the data set

Question 37

What is the upper quartile?

Answer 37

The value 75% of the way through the data set

Question 38

In probability, how is "and" written?

Answer 38

n

Question 39

In probability, how is "or" written?

Answer 39

u

Question 40

How is relative frequency calculated?

Answer 40

How many times an event occurs ------------------------------------------------ Total no. outcomes

Question 41

How many probabilities when rolling 4 dice?

Answer 41

6 x 6 x 6 x6

Question 42

How do you add and subtract in standard form?

Answer 42

Make sure the powers are all the same

Question 43

Define equation

Answer 43

A statement that the values of two expressions are equal

Question 44

Define formula

Answer 44

A rule written with mathematical symbols

Question 45

Define identity

Answer 45

An equation that is true regardless of the values chosen

Question 46

Define term

Answer 46

A single number or variable

Question 47

Define expression

Answer 47

Numbers, symbols and operators grouped together to show the value of something.

Question 48

Define inequality

Answer 48

An equation that uses < and > rather than =

Question 49

Define factor

Answer 49

A number that multiplies with another number to produce a multiple

Question 50

What do functions mean?

Answer 50

The function f takes a value for x, multiplies it by 5 then adds 2

Question 51

Equation for a line (not y = mx +c)

Answer 51

y - y1 = m (x - x1)

Question 52

For inequalities on number lines, when do you use dotted and filled lines?

Answer 52

Solid lines means including points on the line | Dotted lines means not including points on the line

Question 53

For inequalities on graphs, when do you use open and closed dots

Answer 53

Open dots, not including the values | Closed dots, including the values

Question 54

How do you calculate the sum of the internal angles of any polygon with n sides

Answer 54

180(n-2)

Question 55

What is the sine rule?

Answer 55

a/sinA = b/sinB = c/sinC

Question 56

What is the normal cosine rule?

Answer 56

a^2 = b^2 + c^2 - 2bc cos A

Question 57

What is the cosine rule for finding angles?

Answer 57

Cos A = b^2 + c^2 - a^2 ----------------------------- 2bc

Question 58

How do you calculate the area of a triangle?

Answer 58

0.5 ab sin c