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*If you need help on a particular question, click on the HINT button

An octagon has 8 sides and a pentagon has fewer!

A pentagon has 5 sides.

Work out each of the two terms separately then add them. If you use your calculator the EXP button may be useful.

30000 + 4000
= 34000

= 3.4 x 10^{4}

Remember that the square of a negative number gives a positive number.

25

Any quadrilateral can be split into 2 triangles. How many degrees in a triangle?

360°

The exterior angles of any octagon add up to 360°?

135°

Remember BEDMAS

32

Prime numbers have only two factors.Themselves and 1. i.e. 37

23 and 29

There are 1000 millilitres in a litre.

1300 ml

Product means "multiply". Sum means "add". Difference means "subtract"

12 or −12

Add 2.1 to both sides of the equation then divide both sides by 4.

4.0475

How many hundredths are there in 0.42?

Now simplify.

21/50

Total order of symmetry = NUMBER of AXES of SYMMETRY plus the ORDER of ROTATIONAL SYMMETRY.

Total order of symmetry = 1 + 1 = 2

How many minutes in a day?

Percentage Loss = [15/(24 x 60)] x 100

= 1% (to 2 s.f.)

How many eggs would ONE person need?

Three eggs

Draw a 5 sided regular polygon and see how many times you can rotate it onto itself!

5

Draw a set of x-axis and y-axis and mark the point (3,2) then carry out each of the changes.

(−2, −3)

Find the area of one face of the cube. Now work out how many faces a cube has.

24 cm^{2}

For a NEGATIVE index move the decimal point to the LEFT.

0.94

Remember that NORTH is 0° and direction is measured CLOCKWISE.

135°

The THOUSANDTHS column is the third one to the right of the decimal point.

0.077

Multiply 4*x* by 3*x* then

4*x* by −1

12*x*^{2} −10*x* +2

Expand (4*x* − 1)(4*x* − 1)

16*x*^{2} −8*x* +1

Multiply 20 by 0.06

(This is the DECIMAL form of 6%)

20 x 0.06 = 1.2

Find the area of each of the six faces of the cuboid.

Three cans of paint would be needed.

Multipy numbers first and then the variables.

24*abc*

Divide both sides of the inequation by 3 first.

*x* < 3.666666666666

i.e. 3

This term is also used in music.

Chord

There are 10 mm in 1 cm

76 cm

Brackets. Exponents. Multiplication and division. Addition and subtraction

2

Do NOT multiply 0.2 by 3 !!!!

0.008

You could use your calculator...or...you could use the laws of indices.

0.25

Write 6 out of 30 as a fraction i.e. 6/30

and now change to a percentage by multiplying by...

20%

Remember that when you square a negative number you get a positive number.

27

Substitute 3 into *a*
and 2 into *b* and then work it out!

8

Leave the answer in standard form to 3 decimal places.

On the calculator use the EXP button after typing 5.2 to enter numbers in standard form.

3.380 x 10^{−2}

How many millilitres in a litre?

4

Yes or no?

A rational number is one which can be written as a fraction.

Yes!

Substitute the numbers and then multiply the three things together.

−24

Turn both sides of the equation upside down.

*x* = 9

The minimum value for a measurement of 15 m is 14.5 m

50.025m^{2}

There is a reciprocal button on your calculator (1/x or x−1 OR If you are finding the reciprocal of a fraction −turn it upside down.

0.29 (to 2 decimal places)

What is the probability that a head and a tail come up ?

There are 4 possibilities when two coins are tossed. HH,TT,HT,TH

0.5

Add three to both sides and then divide both sides by 2.

*x* = 5

Do EXPONENTS first !!!!

−23

What is the value of anything to the power of 0? (And the answer is not 0)

3

The volume of a sphere (assume the Earth is spherical) is V = 4/3 ^{1}r^{3}

1080 000 000 000 km3

167% means 167/100

1.67

To find one third of anything divide it by 3

$64

Calculate 75 ÷ 300 and then multiply by 100

25%

How many faces does a cube have? The area of each face will be the same.

6*L*^{2}

(try to work it out without your calculator)

The positioning of the decimal point is crucial. Check your answer by multiplying it by itself.

0.4

Work out the exponents first then multiply your two answers.

8 x 9 = 72

If the perimeter of a square is 64, how long is each of its equal sides?

256 cm^{2}

The interior angle and the exterior angle are the only two angles on the same straight line, so what do they add up to?

360°

A rhombus is a quadrilateral with all sides equal in length and opposite sides are parallel.

4

7 ⁺ − 8 ⁺ 5

Watch the negative!

4

Multiply by 100 and divide by 112.5 i.e. Multiply by 8/9

$222,222.22

Multiply the amount by 0.8 (100 - 20)/100

$120,000

Use the rule that begins "The exterior angle of a triangle equals the sum of..."

25°

Work out *a*^{2} first

216

Which is the thousandths column?

0.012

Draw a diagram!

15 metres

BEDMAS! Multiply before adding and subtracting.

23

There are 1000 grams in 1 kilogram and 1000 milligrams in a gram.

3 500 000 g

Remember BEDMAS

17

An angle and its complement add up to 90°

44°

The mean of 6, 5, 6, 3

OR

The median of 6, 5, 6, 3

Mean is average.

Median is middle mark.

The median is the bigger.

Read the question carefully. How many people are there altogether?

$3360

Remember these are TIMES and not DECIMAL numbers. (There are 60 minutes in an hour!)

764 minutes

How many "parts" are there altogether?

$18

There are 1000 grams in a kilogram.

1.36 kg

The EXTERIOR angles of ANY polygon add up to 360°

360/36 = 10

Therefore there are 10 sides.

To find 2.8% of a quantity multiply it by 0.028

30 x 0.028 = 0.84

The equation for a triangle containing parallel lines gives

6 . *x* = 9 . 4 for this triangle. The dot means "multiply")

*x = 6*

To change km/hr to metres/min multiply by 1000 and then divide by 60.

1500 metres/minute

To change km/hr to metres/min multiply by 1000 and then divide by 60.

1500 metres/minute

Speed equals distance divided by time.

46 km/hr

Is there a COMMON factor?

10(*x*^{2} − 8*x* + 7)

= 10(*x* − 7)(*x* − 1)

Prime numbers have only themselves and 1 as factors.

43

A hectare (ha) is a square with sides of 100m.

25000 m^{2}

A calculator with an exponent button such as x^{y} will obviously be of great value here!

794.28

%increase = amount of increase × 100 / original amount × 100

22 x 100 /220 = 10%

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 11 through to 33

ANYTHING to the power of zero is 1 but be careful with the negative sign.

−1

Use corresponding angles but be careful!

B = 118°

Multiply by 0.55 to find 55%

115.5

How many parts are there altogether?

$150

Start from the inside brackets first.

10 000

What do you know about the base angles of an isosceles triangle?

110°

Subtract 4 from both sides and then divide both sides by 2

*x = 1*

The vertices are the corners of the cube.

A cube has 8 vertices.

The mode of a set of numbers is the most common number.

The mode is 5

There are 1000g in 1kg

2137 grams

When working out the surface area of the cuboid remember there are 6 faces to consider.

107 : 105

If the equation is written in the form *y = mx + c*

the c stands for the y = intercept.

*y-intercept = −1*

To find 12% of a quantity multiply it by 0.12. Remember there are 1000 g in 1 kg

720 grams of sugar

There are 100 centimetres in a metre and 1000 metres in a kilometre. So there's not going to be much of a kilometre in the answer!

0.008 km

There are 1000 kg in a tonne

300 tonnes is much heavier!

There are 10 mm in 1 cm

Each piece of paper is 0.18 mm thick.

(0.2)

You don't even need to get your calculator out for this one.

False

(0.2)^{4}= 0.0016

Remember BEDMAS

5*x*

Start counting the decimal places from the decimal point

8.4

Rotational symmetry is the number of times a shape maps onto itself when rotated about its middle.

2

Multiply the numbers first and then the variables (leave variables in alphabetical order).

30*cpw*/p>

4

Rearrange the equation into the form *y* = *mx* + *c*

The gradient is the value of *m*.

Gradient = −4

Replace each *x* with 0 and work out the value of the expression.

−3

Draw a diagram!

(3, −2)

Add the twos and then add the pees!!

4 + 3*p*

Add 13 to both sides and then divide both sides by 2.

*n* = 12

Remember a 5 followed by a 3 is different from a 3 followed by a 5.

5 ways

(5, 3), (3, 5), (2. 6), (6, 2), (4, 4)

Write the answer as a fraction with a denominator of 7

4/7

Area of triangle = 0.5 x base x height

Area = 15 m^{2}

Remember a cuboid has 6 faces

One can

The angle at the centre of a circle equals twice the angle at the circumference.

110°

Choose from rhombus, square, parallelogram, kite or rectangle

Square

Move the decimal point two places to the ...

0.0837

Use the EXP button on your calculator to enter the two standard form numbers.

1.47 x 10^{−2}

An equilateral triangle has 3 equal sides, an isosceles triangle has 2 equal sides and a scalene triangle has...

...no equal sides.

Cover a range of half of the smallest unit on either side of the measurement.

i.e 0.05 m

*0.45 ≤ x < 0.55*

Axes of symmetry are mirror lines drawn through the shape.

Only 2 (the diagonals are not axes of symmetry)

% gain = amount of gain/original amount x 100

0.15

Use calculator to divide 5 by 6 then round off.

0.833

Draw a diagram. Let the width be *x*. Form an equation.

27 cm^{2}

An isosceles trapezium is a trapezium (one pair of parallel sides) and the two other sides are of equal length.

One axis of symmetry

Does it have any factors apart from 43 and 1?

Yes, it is a prime number as are 41 and 47.

This is a quadratic equation.Expand the bracket and then subtract 45 from both sides of the equation. THEN you can solve the quadratic equation by factorising.

*a* = 5

Multiply by 1000 to change it to metres .. .then divide by 60 x 60 to change the hours to seconds.

17 m/s

Add the two numbers and then divide by 60 to change to minutes.

9 minutes

Multiply by 8 and divide by 9 (i.e. 100/112.5)

$355.56

1 Ha = 10 000 m^{2}

32 500 m^{2}

Expand the brackets first and then find *x* on its own

*x* = −2.5

Remember that BEDMAS applies to algebra too.

*a* + 5*a*^{2}

Use the x^{y} or similar button on your calculator.

378.23

North is a bearing of 000°

270°

REMEMBER a (negative number)^{2} is equal to a positive number.

16

The MEAN is the AVERAGE. Add all of the numbers together and then divide by how many numbers there are.

Mean = 6

Start from the innermost brackets.

15

Axes of symmetry are mirror lines.

A rhombus has NO axes of symmetry

Work out the surface area and volume of each and then simplify the ratio

6:5

Combine the *x* terms and then add 13 to both sides of the equation

*x* = 4

Invariant means that they do not move.

The *x-axis* itself is invariant. *(The line y = 0)*

Divide by 20 to find out how far it would travel on ONE litre. Then multiply by ...

113.75 km on 13 litres of petrol.

Change them all to hundredths

Thirteen twenty - fifths

Remember BEDMAS. Multiply before Adding or Subtracting

5

Decimal places start at the decimal point.

0.09

How many hours in a day? How many days in a week?

168 hours

Expand the brackets and then take x terms to one side and numbers to other.

*x* = 10

Remember there are 60 minutes in an hour.

98 minutes

Edges are where two faces meet.

8 edges

Prime numbers have only themselves and 1 as factors.

19

Does the left hand vertex of the smaller triangle BISECT the base of the larger triangle?

Shaded area = 0.75 x 15.6 cm^{2} =11.7 cm^{2}

Multiples of 3 are numbers such as 24, 27, 30 etc.

There are 3 multiples of three 33, 36 and 39

Find the cost of ONE book first by dividing, and then...

Six books would cost $48.36

An edge is where two faces meet.

A cube has 12 edges.

List all of the factors of each number and then find the largest. (A FACTOR is a number that divides into another without a remainder.)

H.C.F is 4

The median is the middle score when they are arranged in order.

The median is 16

The prefix m means one thousandth

16 000

The EXTERIOR angles of any polygon always add up to ...

...360°

Change the km into m

8000 m^{3}

Add 4*x* to both sides of the equation.

*x* = 1

1 Ha = 10000 m^{2}

52 000

Don't forget to change the 5 km into metres first!

50 000 m^{3}

Write out the multiples of 10 and 12 and find the lowest common one

60

There are two horizontal planes. How many vertical ones?

There are 4 vertical planes.

One of the factors is (*x* + 3)

(*x* + 3)(*x* − 1)

One of the angles in the triangle is 90°

90°

There are: 100 centimetres in 1 metre and 1000 metres in 1 kilometre

There are 800 000 cm in 8 kilometres.

What effect does the negative sign OUTSIDE the bracket have on the negative sign INSIDE the bracket?

5*p* − (3 − *p*) = 5*p* − 3 + *p* = __6 p − 3__

Remember BEDMAS! Exponents before addition.

22

Use a combination of corresponding angles and angles on a straight line.

x = 48°

There should be three terms in the final answer.

2*x*^{2} − 11*x* − 21

You'd better expand the brackets first and then take all of the *x* terms to one side and all of the numbers to the other.

*x* = -3

The interior opposite angles of a cyclic quadrilateral add up to 180°

77° and 159°

Think of where the dotted lines are on the tangent graph ( the asymptotes)

90° and 270°

It will be flatter (a smaller number) and it will be a negative gradient.

- 0.5

Arrange them in order then split the numbers into 4 equal sets.

Upper quartile is 6

Each outside angle is 360/(number of sides)

45°

Expand the brackets first.

*p* = −1.5

Remember that when you minus a negative it is equivalent to adding a positive. Strange but true!

−7

The sum of the exterior angles of any polygon is 360° and in a hexagon there are 6 of them. The interior angle plus the exterior angle add to 180°.

120°

−42 + −4 x −5 = −26 −4

Apply the BEDMAS rule.

FALSE! The left hand side comes out to be −22 and the right hand side is −30

The exterior angles of ALL polygons always add up to 360°

The polygon has 360/24 = 15 sides

Look for the common factor

3*x*(*x* + 2)

By division, work out the cost of 1 g of pears for each can.

The 0.405 kg can is better value.

If neither of the coins is a head, what must they both be!

P(Tail,Tail) = 0.5 x 0.5 = 0.25

When he spends two thirds, what fraction is left?

1/6

The exterior angle of a triangle equals the sum of the two interior opposite angles.

*x = 97°*

Factorise it first!

*x* = -5 or +1

There are 100 x 100 x 100 cubic cemtimetres in a cubic metre.

0.245 m^{3}

What total is needed on 6 rounds to average 72?

She would need a round of 67 strokes!

List the factors of 18 and list the multiples of 3. Then find the biggest!

18

How many *x* are there? What is the total number of degrees in a quadriltateral?

9*x* = 360, *x* = 40

The biggest angle is 3*x* = 120°

There are two ways. EITHER...take the square root of both sides first. (Remember plus AND minus 3!) OR...expand the brackets, re-arrange and then re-factorise.

*x* = -5 or 1

Limits of accuracy lie within half a unit either side of the measurement.

The perimeter would lie between 49.8 cm and 50.2 cm

Expected value = Number of people x Probability of passing

270 would be expected to pass.

34.45 x 10

Give the answer in standard form.

To enter a number in standard form into your calculator use the EXP button.

1.0295 x 10^{8}

Which is the biggest angle?

90°

This looks like the "difference of two squares" i.e. Two brackets

(2*x* + 7)(2*x* − 7)

There are 1000 grams in 1 kilogram.

3.502 kg = 3502 g

To get the mean of four amounts of money, add the four amounts together and then divide by 4.

Mean = $4.23