Algebra
Factorise -8x2 + 100x - 48
-4(2x - 1)(x - 12)
State the general equation of a straight line graph.
y = mx + c
What is the Pythagoras' Theorem?
a2 + b2 = c2
There are an unknown number of different coloured buttons in a bag.
Johan selects a button at random, notes its colour and replaces the button in the bag.
Repeating this 30 times, Johan notes that on 18 occasions he selected a red button.
Use Johan’s results to estimate the probability that a button drawn at random from the bag is red.
P(red) = 3/5
What is a prime number?
a number with exactly 2 factors, 1 and itself
Rearrange the formula p = (2 - ax)/(x - b)
to make x the subject.
x = (2 + pb) / (p + a)
Find the equation of the line that passes through the point (2, 1) and is parallel to the straight line y = 3x + 7
y = 3x - 5
Without using a calculator, find the exact value of
cos 45 tan 60 - sin 30
(sqrt(6) - 1)/2
A box contains 3 blue counters and 8 red counters.
A counter is taken at random and its colour is noted.
A second counter is then taken at random, and its colour is noted.
Find the probability that both counters are the same colour.
P(same colour) = 31/55
State the formula for compound interest.
A = P (1+r)t
The function f(x) = 5 - 3x.
Find f-1 (x).
f-1 (x) = (5 - x)/3
Sketch the graph of y = x2 - 5x + 6,
showing the x and y-intercepts clearly.
x - intercepts = 2, 3
y - intercept = 6
State the Sine rule
sin A/a = sin B/b = sin C/c
or
a/sin A = b/sin B = c/sin C
The mass, correct to the nearest kilogram, of 11 parcels is recorded below.
24, 23, 23, 26, 25, 27, 18, 96, 16, 17, 32.
Find the mean, median and mode.
mean = 29 8/11 kg
median = 24 kg
mode = 23 kg
Find the HCF of 36 and 120
12
9, 5, 1, -3, -7...
Find an expression for the nth term of the sequence.
Tn = 13 - 4n
The exterior angle of a regular n - sided polygon is 45°.
Find the value of n.
n = 8
State the Cosine rule
a2 = b2 + c2 - 2bc cos A
The mass, correct to the nearest kilogram, of 11 parcels is recorded below.
24, 23, 23, 26, 25, 27, 18, 96, 16, 17, 32.
Find the range.
range = 80 kg
Find the value of n when 610 X 6n = 62
n = -8
The time, t hours, it takes to complete a project is inversely proportional to the cube root of the number, n, of people working on it.
If 27 people work on the project, it takes 50 hours to complete.
Find an equation connecting t and n.
t = 150 / cuberoot(n)
A curve has the equation y = x3 - 3x2 - 4x + 1
Find the coordinates of the point(s) when the gradient of the curve is 5.
(3, -11) and (-1, 1)
The points P and Q have coordinates (3, 2) and
(6, -10) respectively.
Find the column vector PQ.
PQ = (3 -12)
The mass, correct to the nearest kilogram, of 11 parcels is recorded below.
24, 23, 23, 26, 25, 27, 18, 96, 16, 17, 32.
Find the interquartile range.
Interquartile range = 9 kg
Without using a calculator, find the value of
(2.8 X 10-6) + (9.7 X 10-8)
expressing your answer in standard form.
2.897 X 10-6