All gust lines in the V-n graph originate from a point where the
- Fractions
Add/subtract: make the bottom number the same first
Multiply: top × top, bottom × bottom
Divide: keep, change, flip
Example:
1/2 + 1/4 = 2/4 + 1/4 = 3/4
2/3 × 4/5 = 8/15
2/3 ÷ 4/5 = 2/3 × 5/4 = 5/6
- Sig fig and decimal places
Decimal places: count digits after the decimal point
Significant figures: start at first non-zero digit
If next digit is 5 or more, round up
Example:
3.456 to 2 decimal places = 3.46
0.00456 to 2 sig fig = 0.0046
- Factorization
Common factor: take out the biggest factor
Quadratic: find two numbers that multiply to last term and add to middle term
Example:
6x + 9 = 3(2x + 3)
x² + 5x + 6 = (x + 2)(x + 3)
- Transposition
Move terms across and do the opposite operation
Example:
y = 2x + 4
y – 4 = 2x
x = (y – 4)/2
- Inequalities
Solve like normal
If you multiply or divide by a negative, flip the sign
Example:
-2x > 8
x < -4
- Triangle construction
Draw the side given
Measure the angle
Draw the next side
Join the last point - Functions
Substitute the number for x
Inverse: swap x and y, then make y the subject
Composite: put one function inside the other
Example:
f(x) = 2x + 1
f(3) = 7
- Transformations
Translation = slide
Reflection = flip
Rotation = turn
Rules:
(x, y) → (x + a, y + b)
(x, y) → (x, -y)
(x, y) → (-x, y)
(x, y) → (-y, x)
(x, y) → (y, -x)
(x, y) → (-x, -y)
- Gradient and line
Gradient:
m = (y2 – y1)/(x2 – x1)
Equation of line:
y = mx + c
- Statistics
Mean = Σfx / Σf
Median: find total frequency, divide by 2, locate that value
Histogram: bars touch
Frequency polygon: join points with straight lines
Cumulative frequency curve: keep adding frequencies - Trigonometry
SOH CAH TOA
sin = opp/hyp
cos = adj/hyp
tan = opp/adj - Pythagoras
a² + b² = c²
c is the longest side - Sine rule and cosine rule
Sine rule:
a/sinA = b/sinB = c/sinC
Cosine rule:
a² = b² + c² – 2bc cosA
- Circle theorem
Angle in semicircle = 90°
Angle at centre = 2 × angle at circumference
Angles in same segment are equal
Opposite angles in cyclic quadrilateral add to 180° - Matrices
Add/subtract: match positions
Multiply: row by column
Inverse of 2×2:
[a b]
[c d]
Inverse =
1/(ad – bc)
[d -b]
[-c a]
- Simultaneous equations
Use substitution or elimination
Example:
x + y = 7
x – y = 1
Add:
2x = 8
x = 4
- Distance-time graph
Gradient = speed
Flat line = stopped
Steeper line = faster - Vectors
Add matching parts
Example:
[2]
[3]
+
[1]
[4]
[3]
[7]
Magnitude:
√(a² + b²)
THINGS TO MEMORIZE
SOH CAH TOA
a² + b² = c²
a/sinA = b/sinB
a² = b² + c² – 2bc cosA
m = (y2 – y1)/(x2 – x1)
y = mx + c
mean = Σfx / Σf
SUPER SHORT REMINDERS
Fractions: same bottom first
Sig fig: start at first non-zero digit
Transposition: do opposite
Inequalities: flip sign for negative
Functions: substitute
Trig: use SOH CAH TOA
Pythagoras: longest side is c
Line: y = mx + c
Distance-time graph:
gradient is speed
Example:
-2x > 8
x < -4
- Triangle construction
Draw the side given
Measure the angle
Draw the next side
Join the last point - Functions
Substitute the number for x
Inverse: swap x and y, then make y the subject
Composite: put one function inside the other
Example:
f(x) = 2x + 1
f(3) = 7
- Transformations
Translation = slide
Reflection = flip
Rotation = turn
Rules:
(x, y) → (x + a, y + b)
(x, y) → (x, -y)
(x, y) → (-x, y)
(x, y) → (-y, x)
(x, y) → (y, -x)
(x, y) → (-x, -y)
- Gradient and line
Gradient:
m = (y2 – y1)/(x2 – x1)
Equation of line:
y = mx + c
- Statistics
Mean = Σfx / Σf
Median: find total frequency, divide by 2, locate that value
Histogram: bars touch
Frequency polygon: join points with straight lines
Cumulative frequency curve: keep adding frequencies - Trigonometry
SOH CAH TOA
sin = opp/hyp
cos = adj/hyp
tan = opp/adj - Pythagoras
a² + b² = c²
c is the longest side - Sine rule and cosine rule
Sine rule:
a/sinA = b/sinB = c/sinC
Cosine rule:
a² = b² + c² – 2bc cosA
- Circle theorem
Angle in semicircle = 90°
Angle at centre = 2 × angle at circumference
Angles in same segment are equal
Opposite angles in cyclic quadrilateral add to 180° - Matrices
Add/subtract: match positions
Multiply: row by column
Inverse of 2×2:
[a b]
[c d]
Inverse =
1/(ad – bc)
[d -b]
[-c a]
- Simultaneous equations
Use substitution or elimination
Example:
x + y = 7
x – y = 1
Add:
2x = 8
x = 4
- Distance-time graph
Gradient = speed
Flat line = stopped
Steeper line = faster - Vectors
Add matching parts
Example:
[2]
[3]
+
[1]
[4]
[3]
[7]
Magnitude:
√(a² + b²)
THINGS TO MEMORIZE
SOH CAH TOA
a² + b² = c²
a/sinA = b/sinB
a² = b² + c² – 2bc cosA
m = (y2 – y1)/(x2 – x1)
y = mx + c
mean = Σfx / Σf
SUPER SHORT REMINDERS
Fractions: same bottom first
Sig fig: start at first non-zero digit
Transposition: do opposite
Inequalities: flip sign for negative
Functions: substitute
Trig: use SOH CAH TOA
Pythagoras: longest side is c
Line: y = mx + c
Distance-time graph: gradient is speed
- Statistics
Mean = Σfx / Σf
Median: find total frequency, divide by 2, locate that value
Histogram: bars touch
Frequency polygon: join points with straight lines
Cumulative frequency curve: keep adding frequencies - Trigonometry
SOH CAH TOA
sin = opp/hyp
cos = adj/hyp
tan = opp/adj - Pythagoras
a² + b² = c²
c is the longest side - Sine rule and cosine rule
Sine rule:
a/sinA = b/sinB = c/sinC
Cosine rule:
a² = b² + c² – 2bc cosA
- Circle theorem
Angle in semicircle = 90°
Angle at centre = 2 × angle at circumference
Angles in same segment are equal
Opposite angles in cyclic quadrilateral add to 180° - Matrices
Add/subtract: match positions
Multiply: row by column
Inverse of 2×2:
[a b]
[c d]
Inverse =
1/(ad – bc)
[d -b]
[-c a]
- Simultaneous equations
Use substitution or elimination
Example:
x + y = 7
x – y = 1
Add:
2x = 8
x = 4
- Distance-time graph
Gradient = speed
Flat line = stopped
Steeper line = faster - Vectors
Add matching parts
Example:
[2]
[3]
+
[1]
[4]
[3]
[7]
Magnitude:
√(a² + b²)
THINGS TO MEMORIZE
SOH CAH TOA
a² + b² = c²
a/sinA = b/sinB
a² = b² + c² – 2bc cosA
m = (y2 – y1)/(x2 – x1)
y = mx + c
mean = Σfx / Σf
SUPER SHORT REMINDERS
Fractions: same bottom first
Sig fig: start at first non-zero digit
Transposition: do opposite
Inequalities: flip sign for negative
Functions: substitute
Trig: use SOH CAH TOA
Pythagoras: longest side is c
Line: y = mx + c
Distance-time graph: gradient is speed
- Simultaneous equations
Use substitution or elimination
Example:
x + y = 7
x – y = 1
Add:
2x = 8
x = 4
- Distance-time graph
Gradient = speed
Flat line = stopped
Steeper line = faster - Vectors
Add matching parts
Example:
[2]
[3]
+
[1]
[4]
[3]
[7]
Magnitude:
√(a² + b²)
THINGS TO MEMORIZE
SOH CAH TOA
a² + b² = c²
a/sinA = b/sinB
a² = b² + c² – 2bc cosA
m = (y2 – y1)/(x2 – x1)
y = mx + c
mean = Σfx / Σf
SUPER SHORT REMINDERS
Fractions: same bottom first
Sig fig: start at first non-zero digit
Transposition: do opposite
Inequalities: flip sign for negative
Functions: substitute
Trig: use SOH CAH TOA
Pythagoras: longest side is c
Line: y = mx + c
Distance-time graph: gradient is speed
1(a)
1 – (1/30 + 4/15)
First make the fractions have the same denominator:
4/15 = 8/30
So:
1/30 + 8/30 = 9/30 = 3/10
Now:
1 – 3/10 = 7/10
Answer: 7/10
1(b)
At 06:30, 1/30 of 1020 spaces were filled:
1/30 × 1020 = 34
During the next hour, another 4/15 of 1020 spaces were filled:
4/15 × 1020 = 272
Total filled at 07:30:
34 + 272 = 306
Not filled:
1020 – 306 = 714
Answer: 714 parking spaces
1(c)
20% of 1020:
20/100 × 1020 = 204
Answer: 204 parking spaces