Maths: Core Basics Flashcards
1
Q
What’s a quadrilateral. What angles add up to
A
4 sides, angles add up to 360*
2
Q
What are alternative angles
A
S or Z, equal
3
Q
What are corresponding angles
A
F shaped, equal
4
Q
What are co-interior angles
A
C, add to 180
5
Q
Equation sum of interior angles
A
Sum of interior angles = (number of sides - 2) x 180
6
Q
Interior + exterior angle
A
= 180
7
Q
All exterior angles =
A
360*
8
Q
Circle theorem for angles in same segment
A
They’re equal
9
Q
Circle theorem for angles in cyclic quadrilateral
A
Opposite angles in cyclic quadrilateral add up to 180*
10
Q
How do you work out HCF and LCM on venom diagram
A
HCF, multiply numbers in middle together
LCM, all numbers in diagram
11
Q
a^m x a^n =
A
a^m + n
12
Q
a^m / a^ n =
A
a ^ m-n
13
Q
(a^m)^n =
A
a ^ mxn
14
Q
a^ 1/m
A
m \/a
15
Q
a^n/m
A
m \/a^n
16
Q
a^-n
A
1/(a^n)
17
Q
When you’re maniluplating decimals and the denominator increases by 10 what happens
A
Overall answer decreases by 10
18
Q
When factorising expressions what do you do
A
Put highest common factor outside brackets
19
Q
a^2 - b^2 =
A
(a-b)(a+b)
20
Q
\/ab =
A
\/a \/b
21
Q
Estimating you take each number to
A
1sf
22
Q
Rationalise denominator means
A
Get rid of the surf on the denominator
23
Q
Speed =
A
Distance / time
24
Q
Density =
A
Density (g/cm^3) = mass / volume
25
Pressure =
Pressure (N/cm^2) = force / area
26
1m^2 = ?
100^2 cm^2 = 10000cm^2
27
y = mx+c meaning
M = gradient, y = y-intercept
28
What’s a parallelogram. What’s area of it
4 sided, 2 parallel sides
| Base x perpendicular height = area
29
What’s rhombus
Rhombus = parallelogram with all sides same length
30
What’s trapezium, what’s area
Trapezium is 4 sided with 1 pair parallel lines
| Area = ((parallel length + parallel length)/2) x height
31
How do work out fraction of an amount
Divide amount by denominator, times by numerator
32
What’s a sector
A slice of a circle, from the centre
33
AnB means
Both exist at same time; A and B
34
AuB means
A or B, both at once
35
A’ means
Everything not A
36
1ml = cm^3
1cm^3
37
1000ml = litres
1 litre
38
Volume of any pyramid
= 1/3 x area of base x height
39
How do you do compound interest
Original amount x percentage increase ^ years
40
What’s translation
Uses vector to describe movement
Top is move right left, bottom is move down up
41
Describe reflection
RElection in the line
42
Describe rotation
Angle of rotation, clockwise/anti clockwise, centre (x,x)
43
Describe enlargement
With scale factor x. Centre (x,x)
44
How do you write direct proportion
y fishy x
y = kx
45
How write inverse proportion.
y fishy 1/x
| Y=k/x
46
What’s graph for direct proportion look like
Four line graph. From centre, line to top right
47
What’s graph for direct proportion to square or cube look like
Four like graph. U shape, turning point in centre
48
What’s graph for inverse proportion look like
Four line graph. In top right section, a curve not touching either line. bottom left section is reflection of this
49
What’s graph for inverse proportion squared look like
Four line graph. Curve in top right section, not touching either line. This is reflected in top left
50
What does direct proportion to the root look like
y fishy \/x
| Y = k \/x
51
What does inverse proportion to root look like
y fishy 1/ \/x
| Y=k/ \/x
52
What does graph for direct proportion to the root look like
Four line graph. From centre goes up a bit to the right in top right section, then sudden line to the right
53
What does graph for inverse proportion to the root look like
A very slight curved line in top right section, doesn’t touch the lines. \ direction
54
Interquartile range
Upper quartile - lower quartile
55
How do you estimate mean from tables
Times along. Add up new total column, add up frequency. Total / frequency = mean
56
Median position =
(Total frequency + 1) / 2
57
LQ position =
(Freq + 1)/4
58
UQ position =
(Freq + 1)/2 x 3
59
In nth term rule, what does n stand for
The position in the sequence
60
Nth term rule is 4n-2 for a linear sequence
What does this mean
+4 each time, -2 is the 0th position
61
Nth term rule is 2n^2 - 2n+3 for a quadratic sequence, what does this mean
2n^2 is half the repeated difference
62
What’s a Fibonacci sequence
Add previous 2 numbers to create next one
63
What’s a arithmetic sequence
Goes up or down by constant difference
64
What’s a quadratic sequence
2 sets of differences to get a repeated doffeeemcr
65
What’s a geometric sequence
Multiply terms by ‘common ratio’ (same amount) each time
66
On number lines, what does a filled in dot mean, what does non filled in mean
Filled in = it can equal it
Not filled in = it can’t equal it
67
What happens when you multiply or divide an inequality by a negative
The inequality sign is flipped
68
When solving inequalities graphically, what is the inequalities with the line under shown as, and what is > or < shown as
> or < use a dashed line, the other ones use a solid line
69
On a graph for solving inequalities graphically, where will the section be when:
<
>
< will always be below
| > will always be above
70
Frequency density =
Frequency / class width
71
How do you find frequency on a frequency density thing
It’s the area
72
What’s stratified sampling
Sample has some proportions as the total population
73
If a quadratic graph has a positive x^2 what does it look like? Negative x^2
Positive x^2 it’s a U
| Negative x^2 it’s a n
74
Complete square x^2 + 12 x
What’s this used for
(x+6)^2 - 36
Used to find turning point
75
How do you write consecutive integers algebraically
n
n+1
n+2
76
How do you an even number algebraically
2n
77
How do you write an odd number algebraically
2n+1
78
How do you write consecutive odd numbers algebraically
2n+1
2n+3
2n+5
79
You’re writing two numbers that aren’t consecutive. How do you show this?
Change the letter
80
What’s a product
Result of numbers multiplied together
81
Give equation of a circle with curve 0,0
x^2 + y^2 = r^2
82
What are you doing when you’re solving two simultaneous equations
Working out where the two /lines/ are at the same point on the graph
83
What are congruent shapes
Identical in both shape and size, even if rotated or reflected
84
What are the conditions for congruent triangles
Three sides same length, SSS
2 sids + angle inbetween same, SAS
2 angles + 1 side same, AAS
2 sided in a right angle same (1 is hypotenuse), RHS
85
What’s bisects mean
Cuts in half
86
What’s a vector
Labelled with single bold letters or with underlined letter. Describes overall movement
87
What does it mean if it asks work out magnitude of vector a
The length of a
88
When are vectors parallel
If one is a multiple of the other
89
If y=f(x) drawn, what does f(x)+a do?
Up by a
90
If y=f(x) drawn, what does f(x)-a do?
Down by a
91
If y=f(x) drawn, what does f(x-a) do?
Right by a
92
If y=f(x) drawn, what does -f(x) do?
Reflects in x axis
93
If y=f(x) drawn, what does f(x+a) do?
Left by a
94
If y=f(x) drawn, what does f(-x)do?
Reflects in y axis
95
What are the coordinates for y= Sin x
```
0,0
90,1
180,0
270,-1
360,0
```
96
What are the coordinates for y= cos x
```
0,1
90,0
180,-1
270,0
360,1
```
97
What does the graph y=tan x have
Asymptotes
98
Sine rule
What do the letters mean
How do you change it to work out an angle
a/Sin A = b/Sin B = c/Sin C
Capital letter is the inside angle, little is side
For angle, switch upper and lowercase letters
99
Cosine rule
a^2 = b^2 + c^2 - 2bc x Cos A
100
What’s a Loci
A path moved by a point as it follows a rule
101
Give the values of Sin 0*,30*,45*,60*,90*
```
0
1/2
(Square root 2)/2
(Square root 3)/2
1
```
102
Give the values of cos 0*,30*,45*,60*,90*
```
1
(Square root 3)/2
(Square root 2)/2
1/2
0
```
103
Give the values of tan 0*,30*,45*,60*,90*
```
0
(Square root 3)/3
1
(Square root 3)
No
```
