general rules

On a histogram, what does the width of the bar represent?

The width of each class interval [the difference]

On a histogram, what does the height of each base represent?

The frequency density

On a histogram, what does the area of each bar represent?

Frequency

Give the equation for frequency [histograms]

Freq = FD x CW

How do we find classwidth on a histogram?

Freq / freq density

What is the quadratic formula?

What is the sine rule?

How do we calculate the angle of a sector?

What is $8^{\frac13}$ ?

2

How to work out $8^{\frac43}$ ?

$\left(3\sqrt8\right)^4$ (The cube root of 8 to the power of four)

What does a negative index do?

Give you the the same answer but as a fraction

What is $3^{-2}$ ?

$$\frac19$$

How to find the area of a sector?

How do you find the nth term of a quadratic sequence?

1. Find the difference between each pair of terms.

2. Work out the second difference

3. Divide this value by two (this is the coefficient of the nth term.

4. Subtract the n**2 term from each term in the sequence. This will give you a linear sequence.

5. Find the rule for the nth term of the linear sequence and add this to the nth term.

1. Find the __1__ between each pair of terms.

2. Work out the second difference

3. Divide this value by two (this is the __2__ of the n**2 term.

4. Subtract the n**2 term from each term in the sequence. This will give you a __3__ sequence.

5. Find the rule for the nth term of the linear sequence and add this to the nth term.

1= difference

2= coefficient

3= linear

What would the ratio 4:8 be as a fraction?$\frac{4}{12}$

$$\frac{4}{12}$$

When faced with a hard ratio question what should you do?

Make the given information into algebraic fractions and solve simultaneously

How would you work out$\left(3\cdot10^3\right)\cdot\left(2\cdot10^4\right)$

Do 2×3 = 6

And 10³ x 10^4 =10^7

Answer = 6 × 10^7

when adding or subtracting in standard form, what first step should you take?

Changing all the powers of ten to be the same value

How do we find the coefficient of n² in a quadratic sequence?

Second difference

---

2

How do we find the coefficient of the n in a quadratic sequence (if there is one)

Subtract the xn² terms from the origional sequence to make a linear sequence, the first term difference is the coefficient

Reflecting a line in the x-axis is equivalent to a…

Vertical flip [y = -f(x)]

Reflecting a line in the y-axis is equivalent to a…

Horizontal flip [y = f(-x)]

The line y = x² - 2x - 24 is reflected in the x axis, what is the new equation of the curve?

Y= -f(x) —→ y= -1(x² - 2x - 24)

y = -x² + 2x + 24

The line y = x² - 2x - 24 is reflected in the y-axis, what is the new equation of the curve?

Y = f(-x) —→ (-x)² - 2(-x) - 24

y = x² + 2x - 24

How would you find the acceleration between two points on a speed-time graph?

1. Draw a tangent joining the two points

2. Write coordinates of points

3. Change in y/change in x

How would you find the acceleration of one point on a speed time graph?

1. Mark given point

2. Draw tangent

3. Pick a second point and put coords

4. Change in y/change in x

What’s a rule/fact that will help you answer this questions?

Side AN= OB-OA

The Gradient on a speed-time graph represents the…

Acceleration

When plotting a cumulative frequency graph, plot the _____ boundaries of your xaxis data

Upper

What is the graph for y= 1/x

What is the graph for y= $4^{x}$

If two shapes are mathematically similar, one will be the ________ of the other

Enlargement

How do we calculate interquartile range?

UQ-LQ

Describe this transformation:

Y= f(x)-3

F(x) is translated 3 units down

Describe this transformation:

Y= f(x+6)

F(x) is translated 6 units to the left

Describe this transformation:

Y= -f(x)

F(x) is reflected in the x axis

Describe this transformation:

Y= f(-x)

F(x) is reflected in the y axis

What does M/N = R/T mean

Total marked / total pop = number recaptured / 2nd total

What do you do first whencompleting the square?

Factor out the first 2 terms - eg

6x²+24x-5 → 6[x²+4x]-5

6[(x+2)²-4] -5

6(x+2)²-24-5

==6(x+2)²-29

When finding the equation of a tangent to a circle, what do we do first?

Find the gradient of the radius

$\left(9a^4\right)^{\frac12}\cdot\frac{2ab^2}{6a^3b}$ ?

= b

Simplify the fraction first and then multiply the numerator by the 3a²

$$A\cap B$$

$$A\cup B$$

$$A\cap B^{\prime}$$

What does P(A I B) mean?

Give the probability of A, Given B (has already occured)

𝑃(𝐴I𝐵)- give a formula to work this out

𝑃(𝐴∩𝐵)/𝑃(𝐵)