maths non calc

Question 1

theorem 1

Answer 1

The angle at the top of a semicircle is 90 degrees

Question 2

theorem 2

Answer 2

The angle at the centre is twice the angle at the circumference

Question 3

theorem 3

Answer 3

Angles in the same segment are equal

Question 4

theorem 4

Answer 4

Opposite angles in a cyclic quadrilateral sum to 180 degrees

Question 5

theorem 5

Answer 5

A tangent is perpendicular to a radius

Question 6

theorem 6

Answer 6

Tangents from a point are equal

Question 7

theorem 7

Answer 7

Angles in alternate segments are equal

Question 7

congruency

Answer 7

SSS, SAS, ASA, RHS

Question 8

inequalities

Answer 8

When multiplying or dividing by a negative number SWAP the SIGN

Question 9

box plot info (describing the distribution)

Answer 9

workout median and IQR

higher median - higher something on average

higher IQR - something less consistent

the bigger the range, the more varied the data

Question 10

geometric

Answer 10

First term x ratio to the power of the position -1

Question 11

sum of arithimetic

Answer 11

Total number of terms/2 x (2 x the first term + (n-1) x by the difference between two consecutive terms)

Question 12

sum of geometric

Answer 12

First term x (1 - ratio to the power of n) / 1 - ratio

Question 13

quadratic

Answer 13

2a 3a+b a+b+c

Question 14

sphere surface area

Answer 14

4 pi r squared

Question 15

sphere volume

Answer 15

4/3 pi r cubed

Question 16

pyramid volume

Answer 16

1/3 x area of base x perpendicular height

Question 17

cone surface area

Answer 17

Pi r squared + pi r l (slant height)

Question 18

cone volume

Answer 18

1/3 x pi r squared x perpendicular height

Question 19

exact trig table

Answer 19

Right the root of 0 to 4
Divide EVERYTHIBG by 2
Write in reverse for cos
Divide sin by cos for tan

Question 20

venn diagram notations

Answer 20

A n B = and
A u B = or

Question 21

circle equation

Answer 21

(x - a) squared + (y - b) squared = r squared

(a, b) centres
r = radius

Question 22

graphs of sin, cos and tan

Answer 22

Sin starts at 0
Cos starts at 1
Tan starts at 0 asymptotes at 90

Sin repeats every 360
Cos repeats every 360
Tan repeats every 180

Sin x = sin 180 - x
Cos x = cos 360 - x
Tan x = tan x + 180

Question 23

capture recapture

Answer 23

Marked birds / total birds = birds with marks / total birds caught on second day

They’re like ratios are proportional

Use numbers to figure out if the person who is wrong should be higher or lower

Question 24

Iqr

Answer 24

Only add one to n if you’re getting values from a table

Question 25

Histogram finding where a person lies

Answer 25

From the smaller cumulative frequency before your number Subtract position needed from that smaller cumulative frequency Divide the answer by the frequency of the class width you’re looking for the person in Turn it into a percentage Multiply by the class width Add the answer to the smaller value of the class width And hey presto flipping long day man

Question 26

Finding a mean from a histogram

Answer 26

Find the total frequency Then like you would in a normal frequency table Multiply frequency by midpoint of class width Add them all together Divide them by the sum of the normal frequency

Question 27

Finding the mean from a frequency table

Answer 27

Find the frequency x the first column, if they’re inequalities use the midpoint Find their sum Divide it by the cumulative frequency of the normal frequency column

Question 28

To prove something is a straight line with vectors

Answer 28

So the vector of the total line needs to be a multiple of the vector of one of the small segments

Question 29

Finding magnitude of a vector

Answer 29

If a is (x y) magnitude is square root of x squared + y squared