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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 104
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 cm2
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 4x by 3x then
4x by −1
12x2 −10x +2
Expand (4x − 1)(4x − 1)
16x2 −8x +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.
24abc
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
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
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
50.025m2
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)
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 1r3
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.
6L2
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 cm2
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
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 a2 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°
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(x2 − 8x + 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 m2
A calculator with an exponent button such as xy 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.
You don't even need to get your calculator out for this one.
False
(0.2)4= 0.0016
Remember BEDMAS
5x
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).
30cpw/p>
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 + 3p
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 m2
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 cm2
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 m2
32 500 m2
Expand the brackets first and then find x on its own
x = −2.5
Remember that BEDMAS applies to algebra too.
a + 5a2
Use the xy 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 cm2 =11.7 cm2
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 m3
Add 4x to both sides of the equation.
x = 1
1 Ha = 10000 m2
52 000
Don't forget to change the 5 km into metres first!
50 000 m3
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?
5p − (3 − p) = 5p − 3 + p = 6p − 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.
2x2 − 11x − 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°
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
3x(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 m3
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?
9x = 360, x = 40
The biggest angle is 3x = 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.
To enter a number in standard form into your calculator use the EXP button.
1.0295 x 108
Which is the biggest angle?
90°
This looks like the "difference of two squares" i.e. Two brackets
(2x + 7)(2x − 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