ab x ac
ab ÷ ac
(ab)c
a0
a x ab
ab+c
ab-c
abxc
1
ab+1
a-b
xa/b
(a/b)c
a1/b
√X x √X
1/ab RECIPROCAL
(x1/b)a OR (b√X)a REMEMBER: ath power of the bth root
ac/bc
b√a
X
(a+b)2
(a+b)3
(a+b)4
a2+2ab+b2
a3+3a2b+3ab2+b3
a4+4a3b+4ab3+b4
(X+a)(X-a)
X2-a2
ax2+bx+c / [2x2+11x+12]
Times a by c / 2 X 12
Find two factors of this number (ac / 24) that add to make b / 11
Replace bx / 11x with those two numbers (+3 and +8)
ax2+nx+nx+c / 2x2+3x+8x+12
Factorise both sides / x(2x+3) +4 (2x+3)
Factorise the brackets / (2x+3) (x+4)
ax2+bx+c=0 / 2x2+11x+12=0
ac method to give factors / (2x+3) (x+4)
If pq=0 EITHER p=0 OR q=0
So EITHER 2x+3=0 OR x+4=0
Either x= -1.5 OR x= -4
When you multiply or divide an inequality by a negative number, you must…
< becomes
> becomes
≤ becomes
≥ becomes
Reverse the inequality symbol i.e. “FLIP THE SIGNS!!!!”
>
<
≥
≤
Define independent event
How do you work out the probability that A and B will both happen independently?
How do you work out the probability that either A or B will happen independently?
When the order doesn’t matter?
Define conditional probability
The outcome of one does not affect the other
P(A) x P(B)
P(A) + P(B)
P(A x B) +P(A x B)
When conditions change later events or are dependent upon earlier events
What type of data are frequency diagrams used to display?
Bar charts?
Histograms?
Grouped discrete data
Ungrouped discrete data
Grouped continuous data with unequal class widths
Volume of a prism
Volume of a pyramid
Volume of a sphere
Volume of a cone
1 litre in cm3
1 m3 in cm3 then in mm3
1 m3 in litres
Area of cross section x length
1/3 A h (1/3 x base area x height)
4/3 π r3
1/3 π r2 h
1,000cm3
1,000,000cm3 or 1,000,000,000mm3
1,000L
Surface area of a sphere
Surface area of a hemisphere
Surface area of a cone. What is L?
1 m2 in cm2 and then mm2
4πr2
3πr2 [2πr2 + πr2]
πr2 [bottom surface]+ πr L [curved area] . L is slant height [√(h2+r2)]
10,000cm2 . 1,000,000mm2
When plotting a cumulative frequency diagram from GROUPED data, which points do you plot (along the x axis)? Is it: a) the mid-point b) the upper bound c) the lower bound
b) The UPPER bound
What is the cosine rule? (cosA and a2 as subjects)
a2 = b2 + c2 - 2bc cosA
cosA = (b2 + c2 - a2) ÷ 2bc
√a x √b = ?
√a ÷ √b = ?
C√a x D√b = ?
C√a ÷ D√b = ?
Rationalising means ?
√(ab)
√(a/b)
CD√(ab)
C/D√(a/b)
Writing a fraction in the form SURD / INTEGER
What is a random sample (proper definition)?
Each member of the population has an equal chance of selection
To convert a recurring decimal into a fraction…
- Make x = the recurring decimal
- Multiply both sides by 10n, where n is the number of recurring digits
- Subtract the two equations
- Simplify the resultant equation
Vectors: what do the following mean?
—> —>
AB = 5CD
—> —>
AB = 2AX
The lines AB and CD are parallel
AB and AX are parallel; A, B and X are part of the same straight line (A is common); X is the midpoint of AB