maths Year 10(part 1)

what is a set?

A set is a collection of objects

how is a set defined?

{ } with , in between

what does ∈ mean?

is an element of

what does ∉ mean?

is not an element of

what is ξ?

The universal set is a set of all objects you are interested in

what does n mean?

number of elements of

what does A’ mean?

the complement(all the things not in A)

what does A∩B mean?

intersection(Both in A and B)

what does A∪B mean?

union(things in A or B)

what does ∅ mean?

The empty set(the set which contains no element)

empty set vs 0?

) is considering somethign so a value whereas the empty set is not considered anything.

eg:ξ=all positive numbers

E=all even numbers

O=all odd numbers

P=all prime numbers

then:EnP={2}

En0=∅

represent A∩B on venn diagram?

represent A∪B on a venn diagram

reprent A’ on a venn diagram

P(A)

probability of A

what does ⊂ mean?

(It is a propersubset of)not the same elements in both circles

what does ⊆ mean?

(is a subset of)The line underneath means it may include all the same elements in both circles.

what does the top and bottom number mean in a vector in relations to x and y?

top=x

bottom=y

what does vector top -1 bottom 3 mean

so mean 1 to the left on the x axis

3 up on the y axis

when describing a reflection what x2 pieces of info do you need?

→reflection

→line of reflection

when desdcrbing a rotation what x4 pieces of info do you need?

→rotation

→rotation angle

→direction

→centre of roatation

Ina non-square rectangle are the diagonals lines of symetry?

No

Does an enlargement change the angle size?

No it does not change the angle size

name method for enlargement:

1)make dotted lines going through each vertex of shaoe from COFE

2)count how many up and down for corresponding vertices

3)Now enlarge by scale factor

4)do the same for a couple of points

5)join up points

what does a fractional enlargement do?

→shape gets smaller

→towards centre of enlargement but not on opposite side

→shape does not become flipped

negative enlargement

→shape gets bigger

→on other side of line

→go opposite way

→shape flipped

negative fractional

→smaller if under 1 SF ,larger if over 1 SF

→shape flipped

→on other side

what is different about any negtaive enlargement vs normal enlargement?

→shape flipped(upside down)

→opposite way from centre of enlargeemnt

what equation do you use to calcul;ate the gradient?

change in y/change in x

x2 charachteristics ofparallel lines

→gradient is the same

→y intercept is different

x1 charachteristics of perpendicular lines

→gradient is opposite of the other gradient(negative reciprocal)

what is the rule for perpendicular lines

M1 x m2=-1

in other words the gradients will multiply to give -1

what is the rule when solving inequalities if you / or x by a negative number?

you have to fip the sign the other way

is 0 a positive or negative integer?

0 is a negative integer

when solvign an equation with 3 parts what is best to do?

seperate into chunks

on a number line which way is less than and whioch way is more than?

less than=to the left

more than=to the right

when statisfying grpahical inequalities what does the dashed line vs solid line mean?

dashed line=<>

solid line=<>(with a line underneath)

name steps to solve graphical inequality:

1)draw lines

2)cross out what is not needed(lightlty)

3)pick a co oridnate so as to chek where to shade

what is the rule for mutiply terms with the same base for indices?

what is the rule whenm dividing indices with the same base

what is the rule when doing an indicie which is a power of a power

what is 7 to the power of 0

1

what is 43 to the power of 1

43

what is the rule for negative indices?

for negative or fractional indices

you flip the opther number

for fractional indices….

you root denominator

to the power for numerator

(must do this for both)

what are the steps for simplifying a surd

1)look for a factor that is a square number

2)use the rule to split your square root

3)simplify

when dividing/multiplying a surd

times everything together

when adding/subtracting surds you can add the roots together….

if they are the same

how do you rationalise a surd with only one term that is a surd

times top and bottom by the surd