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Grade A facts to memorise

Grade A Flashcards

Grade A Facts to memorise

What does 'standard form' mean?

Number x 10power

Where Number is less than 10 but greater than or equal to 1.

How do you multiply numbers that expressed in 'standard form'?

Multiply the numbers.

Multiply the 10's (add powers)

Convert to Standard Form (if necessary)

What is the 'upper bound' of a number?

Upper Bound < number + 0.5

eg, for 17, the UB < 17.5

 

NB in calculations, use 17.5

What is the 'Lower Bound' of a number?

Lower Bound ≤ number - 0.5

 

eg. for 17, LB ≤ 16.5

How do you add two rounded numbers so as to get the MAXIMUM result?

Upper Bound + Upper Bound

How do you add two rounded numbers to get the MINIMUM result?

Lower Bound + Lower Bound

How do you subtract two rounded numbers to get the MAXIMUM result?

Upper Bound - Lower Bound

How do you subtract two rounded numbers to get the MINIMUM result?

Lower Bound - Upper Bound

How do you mulitply two rounded numbers to get the MAXIMUM result?

Upper Bound x Upper Bound

How do you multiply two rounded numbers to get the MINIMUM result?

Lower Bound x Lower Bound

How do you divide two rounded numbers to get the MAXIMUM result?

Upper Bound ÷ Lower Bound

How do you divide two rounded numbers to get the MINIMUM result?

Lower Bound ÷ Upper Bound

How do you calulate the limits of accuracy of your answer to a question?

Use Upper and Lower bounds to calculate the lowest possible answer and the highest possible answer.

What is a rational number?

Any number which can be written as a fraction.

What is an irrational number?

Any number which cannot be written as a fraction?

 

eg √2

How do you convert a recurring decimal to a fraction

(eg 0.121212...)

let r = 0.121212...

100r = 12.121212...

subtract, 99r = 12

divide, r = 12/99

 

OR

 

(Number of recurring digits)/(same number of 9s)

eg 0.1212... is 12/99)

 

What is an x am?

an+m

What is an ÷ am ?

an-m

What is (an)m ?

anm

What is a0 ?

1

What is a1 ?

a

What is a-1 ?

1/a

What is (a/b)-1 ?

b/a

What is a-n ?

1/(an)

What is (a/b)-n ?

(b/a)n

what is a½ ?

√a

What is (a)1/n ?

nth root of a

What is (a)n/m ?

(mth root of a)n

What is (a)-n/m ?

1/(mth root of a)n.

What is (a/b)-n/m ?

(mth root of b/a)n

If A is proportional to B, how is this written as an equation?

A = kB

If A is inversely proportional to B, how is this written as an equation?

A = k/B

If A is proportional to the square of B, how is this written as an equation?

A = kB2

If A is proportional to the square root of B, how is this written as an equation?

A = k√B

If A is inversely proportional to the square of B, how is this written as an equation?

A = k/(B2)

If A is inversely proportional to the square root of B, how is this written as an equation?

A = k/(√B)

What is the formula for solving a quadratic equation?

if ax2 + bx + c = 0

then,

 

x = [-b ± √(b2 - 4ac)]/2a

What is the sine rule?

a/sinA = b/sinB = c /sinC

What is the 'ambiguous case' in the sine rule?

  • When finding an angle using 'sine rule', there may be 2 possible angle solutions (a and 180-a).
  • Always find both angles and then check to see if the larger one is possible:
  • check that (180-a) plus the other 2 angles does not exceed 180. If it does exceed 180, then the only possible solution is 'a'. If it does not exceed 180, then 'a' and '180-a' are both possible solutions.

What is the 'cosine rule'?

a2 = b2 + c2 - 2bc.cosA

How do you solve an equation in the form f(x) = n, where n is a number, by a graphical method?

Draw the graphs of y = f(x) and y = n.

The solution(s) are the 'x' value where the two graphs cross.

what does f(x) mean?

It means 'the function of x'.

It means 'f' is an expression using 'x'

 

eg if f(x) = 2x + 3

then the expression '2x + 3', is called 'f'.

if f(x) = 2x + 3, what does f(n) mean, where 'n' is a number?

Substitute x with the number.

 

eg if f(x) = 2x + 3

then, f(5) = 2x5 + 3

What are congruent shapes?

Shapes that are identical in every respect.

What is the formula for the volum of a cone?

∏r2h/3

What is the formula for the volume of a sphere?

4∏r3/3

What is the formula for the curved surface area of a cone?

∏rL

What is the formula for the total surface are of a cone?

∏r(L + r2)

What is the formula for the surface area of a sphere?

4∏r2

What are the 2 formalae for area of a triangle?

A = bh/2

 

or

 

A = absinθ/2