Year 9 Other Stuff Flashcards
How to multiply fractions?
x a ax
- × - = —–
y b by
How to divide fractions?
Keep first fraction same, change ÷ to × and take reciprocal of second fraction ‘flip it’
How to add and subtract fractions
Make it so they have a common denominator, then add together
How to write a recurring decimal as a fraction?
Line up decimals, use algebra, you know how to do this omg and if you don’t look in your book
How to work out the combined multiplier?
Multiply together the multipliers
a¹
a
a‐¹
a
a‐²
a²
What does a negative power do to a fraction
It reciprocates it
(ab)³
a³ × b³
What does a power of ½ do to a number?
It square roots it
What does a power of ⅓ do to a number?
It cube roots it
When is a number in standard form?
It is in the form
a × 10^b
3 × 10³
3000
3 × 10²
300
3 × 10¹
30
3 × 10⁰
3
3 × 10^-1
0.3
3 × 10^-2
0.03
Example of multiplying standard form?
(3x10⁷) × (2×10⁴)
= (3×2) × (10⁷×10⁴)
= 6×10¹¹
Example of dividing standard form?
(3×10⁷) ÷ (2×10⁴)
= (3/2) × (10⁷×10‐⁴)
= 1.5×10³
What is the equation of a perpendicular straight line
Y = -½x +c
They have negative reciprocal gradients
General form of a quadratic equation?
y = ax² + bx + c
What is the shape of a quadratic line if a > 0?
U shape
What is the shape of a quadratic line if a < 0?
n shape
What is the shape of a quadratic line if a = 0?
Straight line
General form of a cubic equation?
y = ax³ + bx² + cx + d
What is the shape of a cubic line if a > 0?
/\/ shape
What is the shape of a cubic line if a < 0?
\/\ shape
General form of a reciprocal equation?
y = a/x
What shape are reciprocal graphs
Never quite meet intercepts
If a is positive, they occupy top right and bottom left
If a is negative, they occupy top left and bottom right
If x is squared, they occupy both top sections
Look in your yr9 book for solving simultaneous equations I beg
Equation for arc length?
x = angle
x
—– × 2πr
360
Equation for sector area?
x
—— × πr²
360
Equation for perimeter of sector?
Arc length + 2r
What is used for greater/smaller than AND equal to on a number line?
●
What is used for greater/smaller than on a number line?
○
What is the unique rule for solving inequalities?
When multiplying or dividing by a negative you MUST flip/reverse the sign
What is used for greater/smaller than AND equal to on a graph?
A solid line
What is used for greater/smaller than on a graph?
A dashed line
How to show the region you want to include in an inequality graph
Shade the region you want to EXCLUDE
denote region you want to INCLUDE with an ‘R’
How does it change from length to area to volume?
Length: k, eg. 10
Area: k², eg. 100
Volume, k³ eg. 1000
Define iff
If and only if
