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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

3*x*^{2} − 24*x* + 48

Differentiate and find the reciporacal of gradient and change sign.

4*y* + *x* − 18 = 0

What is the gradient of the line *y* = *x*?

*y* = *x* - 1

Tan = opp/adj

38.7°

if *y* = *x ^{n}*

12*x*^{2}

Add ONE to the exponent and divide by the new exponent and then add c

2*x*^{2} + c

cos *x* adj/hyp

36.9°

Expand the bracket first.

24*x*^{5}*y*^{7}

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*)=12*x* − 18

This expression is called a trigonomical identity

1

Write 1/*x* as an index *x*^{-1}

-1/*x*^{2}

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

32*x*^{2} − 96*x* + 72

Expand the two brackets first, then multiply by the third bracket

*x*^{3} − 3*x*^{2} + 3*x* − 1

Differentiate term by term

f'(*x*) = 6*x*^{2} − 6*x* + 4

Cube the brackets first

32*a*^{6}*b*^{3}

Take all terms to one side of the equation and then factorise

*x* = 1 or 3

Find its equation in the form a

Use the equation *y* − *y*_{1} = m(*x* − *x*_{1})

3*x* − *y* − 5 = 0

Don't forget the constant!

2*x*^{2}+ 3*x* + c

Change the angle to radians

Area = 13.1 units^{2}

(The marbles are drawn together.)

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 r^{2}0

64cm^{2}

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

12*x*^{3} −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.)

3

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.

-10*x* − ^{−3} = -10/*x*^{3}.

Change mode of calculator to RAD

*x* = 0.35 radians (to 2 sig. fig.)

What is the probability that a number greater than a 4 comes up?

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°

(where 0° <

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"!

16x^{3}/3 − 8*x*^{2} + 4*x* + c

Does the -2 make the graph of *y* = 2sin *x* move up or down?

The y-intercept is -2

for 0° <

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 units^{2}

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.

− *x*^{2} − 18*x* + 15

Use the "special " triangles

1 / √2

the point A = (2, 5) to the point B = (−2, −5)?

Use the mid-point formula!

(0, 0)

Work out *a*^{2} first

216

Use the "special" triangles.

√3/ 2

Expand the bracket and then differentiate!

*y* ' = 4*x* - 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.

*x*^{3} − 3.5*x*^{2} − 6*x* + c

Divide both sides by 3 first.

*x* = 41.8°

For *x*^{2} + *y*^{2} = 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 / *x*^{3} as 4*x*^{-3}

The y-intercept is -2

Use *y* = m*x* + c

*y* = 2*x* + 3

Think of the shape of the graph.

What effect does the 2 have on the function?

Maximum value is 2

Give your answer in the form

Use the general equation of a straight line:
*y* - *y*_{1} = m(*x* - *x*^{1})
and then re-arrange.

*y* = 3*x* − 3

Expand the brackets first

f '(*x*) = 2*x* − 4

Write g(*x*) in index form.

g ' (*x*) = 1 / (2√*x*)

Check it out on your calculator.

Positive

Factors of 6*x*^{2} and +10 will be needed.

(3*x* − 2)(2*x* − 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.

9*x*^{4}*y*^{5}

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* ' = 10*x* - 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.

2*x*^{4} − 2*x*^{3} − 5*x* + 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