Algebra

Question 1

(a+b)²

Answer 1

a²+2ab+b²

Question 2

(a-b)²

Answer 2

a²-2ab+b²

Question 3

a²-b²

Answer 3

(a+b)(a-b)

Question 4

Quadratic formula

Answer 4

Question 5

Find the sum of roots of quadratic equation?

Answer 5

-b/a

Question 6

Find the product of roots of quadratic equation?

Answer 6

c/a

Question 7

distance between 2 points equations?

Answer 7

OR Find triangle: a²+b²=c²

Question 8

Slope of a line equation

Answer 8

Slope of y=mx + c, slope =m

Question 9

Equation to graph a circle

Answer 9

a,b is the centre of the circle
R = radius

Question 10

Area of circle?
Circumferance?

Answer 10

Area = πr²
Circumferance = πd or 2πr

Question 11

How to remember the slope of a line?

Answer 11

Rise over run ie if it’s y=3/4x then whenever you move up 3, move right 4

Question 12

What is an even function?
Where is there symmetry?

Answer 12

• A function is an even function if f of x is equal to f of −x for all the values of x. This means that the function is the same for the positive x-axis and the negative x-axis, or graphically, symmetric about the y-axis.
• Where all the x exponents are even i.e. X²+6 (i.e. 6 is seen is x⁰)

Question 13

What is an odd function?

Answer 13

Where all the x exponents are odd i.e. X³+6x

Symmetry with the origin

Question 14

Where is there symmetry for functions with both even and odd exponents?

Answer 14

None

Question 15

Other ways to show reflection along x-axis?
y-axis?

Answer 15

Reflection along x-axis: y=-f(x)

Reflection along y-axis=f(-x)

Question 16

What are the rules to remember when looking for remainders when dividing by 2,5,10, other numbers?

Answer 16

5 - For UD numbers 1-4, UD =R. For UD numbers 6-9 UD = R-1
10 - UD = R
2 - Even UD, R=0. Odd UD, R =1
Other number - Find the pattern by finding 1st 4 and finding the remainder pattern

Question 17

Difference between supplementary angle and complementary?

Answer 17

Supplementary angles - add up to 180
Complementary angles - add up to 90

Question 18

Number of degrees in any polygon?

Answer 18

(n-2)*180

N = Number of sides in polygon

Question 19

2 non congruent triangles?

Answer 19

AAA - 3 angles the same, doesnt guarantee sides the same
ASS - i.e. where angle NOT between 2 sides, doesnt guarantee congruence

Question 20

What are the pythagorean triplets?

Answer 20

Question 21

30-60-90 triangles

Answer 21

Question 22

What’s special about a 45,45,90 triangle?

Answer 22

Question 23

Area of an equilateral triangle?

Area of a regular hexagon?

Answer 23

1.half half √3

= √3a²/4

2. 6 x half x half x √3

Question 24

Area of other regular polygons?

Answer 24

The number you multiply = number of sides

Question 25

How do you maximise a polygon's area?

Answer 25

As long as perimeter is the same, make it regular --> max area

Question 26

Area of a similar triangle whose base:height is p:q

Answer 26

area = p²:q² basically once know ratio of a side of triangle a:triangle b, the area is the square of that ratio

Question 27

Area of a trapezium?

Answer 27

Question 28

Area of a larger square that has a smaller square inscribed at the midpoint?

Answer 28

Larger square area is double the smaller square area

Question 29

What is the longest diagonal of a cube?

Answer 29

Side x √3

Question 30

Longest diagonal of a rectangular solid?

Answer 30

D = √(l² + w² + h²) units

Question 31

rule for the 3rd side of a triangle?

Answer 31

1. 3rd side > the difference of 2 sides 2. 3rd side < the sum of 2 sides

Question 32

How to find the median of a symmetrical set?

Answer 32

(first number + last number) / 2

Question 33

Population Standard deviation

Answer 33

x= numbers u = average N = number of numbers

Question 34

Sample standard deviation

Answer 34

Question 35

Difference between sets and lists?

Answer 35

Sets = NRIC - no repeats = SD > 0 - can be finite/ infinite - number of elements in set = |S| i.e. |4| means 4 elements in set - Curly brackets List = FOR - Finite - order matters - repeats = SD could be 0 or more

Question 36

What's the formula for inclusion-exclusion principle?

Answer 36

Question 37

Formula to find out probability of A or B not both

Answer 37

Question 38

Formula to find out how many people have neither in inclusion-exclusion principle

Question 39

Formula to find out how many people have neither in inclusion-exclusion principle

Answer 39

Question 40

Formula to find out 3 overlapping sets

Answer 40

Question 41

Difference between permutations and combinations?

Answer 41

Permutations - order = important Combinations - order NOT important

Question 42

Formula to calculate permuations? Alternative?

Answer 42

Alternative = choice method i.e. if asked how many ways 4 leters from the word KEYBOARD can be arranged. Initially 8 choices, then 7, then 6, then 5 therefore answer = 8x7x6x5 = 1680

Question 43

Permutations with repeats

Answer 43

Question 44

Permutations in a circle

Answer 44

(N-1)!

Question 45

Formula for choosing combinations

Answer 45

Question 46

Combination pattern when n = even

Answer 46

Question 47

Combination pattern when n = odd

Answer 47

Question 48

How is an empty set represented?

Answer 48

Question 49

What does skewness tell us about mean and median relationship?

Answer 49

Average follows the tail - postive skew: mean > median - negative skew: mean < median

Question 50

What is the normal distribution

Answer 50

Question 51

Sum of intergers in interval (even)

Answer 51

| No. of pairs = N/2

Question 52

Sum of intergers in interval (even)

Answer 52

Question 53

Sum of intergers in interval (odd)

Answer 53

No. of pairs P= (n-1)/2 Middle number M = (n+1)/2 Sum = (P x (n+1) ) + M

Question 54

How do know if any number is prime?

Answer 54

If n is the number we’re checking eg 107: - square root n - check all the prime numbers less than that value ie check 2,3,5,7 NOT 11