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*If you need help on a particular question, click on the HINT button
Draw a diagram and use Pythagoras' Theorem or use a formula.
√242=15.6(to 3 s.f.)
Calculator might help.
30°
Expand the brackets
3x2 − 24x + 48
Differentiate and find the reciporacal of gradient and change sign.
4y + x − 18 = 0
What is the gradient of the line y = x?
y = x - 1
Tan = opp/adj
38.7°
if y = xn
y1 = nxn-1
12x2
Add ONE to the exponent and divide by the new exponent and then add c
2x2 + c
cos x adj/hyp
36.9°
Expand the bracket first.
24x5y7
Change 5/6 into a decimal.
x = 56.4°
Put x = 0 into the function.
i.e Find f(0)
(0,5)
Use Pythagoras' Theorem
7.1cm
P(6)xP(6)
1/36
Draw a sketch by putting x = 0 to find the y-intercept and then y = 0 to find the x-intercept.
A circle centre (1,0) radius 4 the x-intercept.
If desperate, plot a few points
It's a rectangle hyperbola
Expand the brackets first
f'(x)=12x − 18
This expression is called a trigonomical identity
1
Write 1/x as an index x-1
-1/x2
It's either the sine rule or the cosine rule!
The cosine rule is needed.
Divide both sides by 2
x = 30°
Square the brackets first
32x2 − 96x + 72
Expand the two brackets first, then multiply by the third bracket
x3 − 3x2 + 3x − 1
Differentiate term by term
f'(x) = 6x2 − 6x + 4
Cube the brackets first
32a6b3
Take all terms to one side of the equation and then factorise
x = 1 or 3
Use the equation y − y1 = m(x − x1)
3x − y − 5 = 0
Don't forget the constant!
2x2+ 3x + c
Change the angle to radians
Area = 13.1 units2
What is the probability that the first ball is blue AND the second ball is blue.
2/11
Arrange in order and then split the data into two equal parts and then split the top part of the data into havles again.
19
Use the formula
A = 0.5 r20
64cm2
Remember that exponents come before multiplying by 2
32768
Brackets first!
576
Do exponents and multiplication before adding and subtraction.
x = 20(to 2 sig. fig.)
Differentiate term by term
Remember f(x) = x
then f'(x) = 0
12x3 −2
Use the formula 1 =r θ
where θ is in radians
Lengths of arc = 12.6(to 3 sig.fig.)
Work out the total number of marks scored in both tests and divide by 30
New mean = 39.3 (to 3 s. f.)
Subtract 4 from both sides and then divide both sides by 3 and take the square root.
x = ± 2.4 (to 1 d.p.)
Write the term in index form and then multiply by the power and lower the power by 1.
-10x − −3 = -10/x3.
Change mode of calculator to RAD
x = 0.35 radians (to 2 sig. fig.)
How many numbers on a six sided die are greater than 4?
Probability = 1/3
Careful! There are two answers.
x = 5 or −1
Find the solutions between 0° and 360° and then divide by 2.
x = 30° or 150°
This is an IDENTITY!
x = 45°
Find f '(x) and then put f '(x)= 0
This value of x will then provide the minimum value of the function.
Minimum value of the function is −1.125
How often does the function repeat itself?
Period is 360° or 2Π radians
Use the grouping technique to find a common factor.
(a − 3)(b − c)
The amplitude is the height of the graph above or below the x-axis.
Amplitude is 3
Expand the brackets and then integrate term by term and don't forget the "c"!
16x3/3 − 8x2 + 4x + c
Does the -2 make the graph of y = 2sin x move up or down?
The y-intercept is -2
Think of where the graphs of y = sin x and y = cos x meet.
x = 45°
Sketch the graph and then use integration
64/3 units2
The interquartile range is the difference between the upper quartile and the lower quartile
Interquartile range = 10
This is an exponential graph.
Put x = 0 to find the y-intercept.
y-intercept is 3
The range is the set of y-values for the function.
-1 ≤ y ≤ 1
Expand brackets first , then beware of negative signs.
− x2 − 18x + 15
Use the "special " triangles
1 / √2
Use the mid-point formula!
(0, 0)
Work out a2 first
216
Use the "special" triangles.
√3/ 2
Expand the bracket and then differentiate!
y ' = 4x - 12
The period of the graph is the length of the interval over which it repeats itself.
360° / 3 = 120° or 2Π/ 3
Expand the brackets first.
x3 − 3.5x2 − 6x + c
Divide both sides by 3 first.
x = 41.8°
For x2 + y2 = 9 the centre would be (0, 0)
Minimum value of the function is −1.125
The mean is the SUM of all of the values divided by the NUMBER of values
mean = 50/5 = 10
Use Pythagoras' Theorem
The diagonal is 6.4 cm long (to 2 sig.fig.).
Find each probability, (remember WITHOUT replacement) and then MULTIPLY them together.
14 / 33
Draw a diagram and split the triangle into two equal parts.
The other side is 8.49 (to 3 s.f.) cm long.
Write 4 / x3 as 4x-3
The y-intercept is -2
Use y = mx + c
y = 2x + 3
Think of the shape of the graph.
What effect does the 2 have on the function?
Maximum value is 2
Use the general equation of a straight line: y - y1 = m(x - x1) and then re-arrange.
y = 3x − 3
Expand the brackets first
f '(x) = 2x − 4
Write g(x) in index form.
g ' (x) = 1 / (2√x)
Check it out on your calculator.
Positive
Factors of 6x2 and +10 will be needed.
(3x − 2)(2x − 5)
Whereabouts on the x-axis are the asymptotes?
x = 90° and x = 270°
Differentiate and then substitute x = 2 into the derivative.
Positive!
There are 4 solutions!
45°, 225°, 405°, 585°
Substitute 25° into the function.
y = 1.7 (to 2 s. f.)
How many ways can you fill the first digit and how many ways can you fill the second digit?
Remember both digits can be the same.
There are 9 ways from 44 through to 66
Expand the brackets first.
9x4y5
Use a diagram or a formula or Pythagoras' Theorem or all three!
13 units
You should have three solutions.
x = 0°, 180° and 360°
Make each bracket equal to zero.
x = 2, −3, 3/2
Multiply by Π / 180
7Π / 6
It is not a straight line or a circle!
An exponential function or growth curve.
Expand the brackets first then get x terms to one side and number terms to other.
x= 8 / 7
Solve the equation y + 3 = 0
or
Solve the equation x − 2 = 0
Which one?
The vertical asymptote is x = 2
The interquartile range is the difference between the lower quartile and the upper quartile.
The interquartile range is 14 − 3 = 11
Expand the brackets first.
y ' = 10x - 40
Find y ' and then put y ' = 0
(2, −4)
Divide both sides by 2 then take the cube root.
p = 4
They are held every 5 years in Australia and New Zealand.
Census
Begins with "a"!
Acceleration
Add logs - multiply
Subtract logs - divide
log 1 = 0
Don't forget the "c" when integrating.
2x4 − 2x3 − 5x + c
The period of a trigonometric function is the interval along the x-axis before the pattern of the graph is repeated.
360 / 2 = 180° or Π