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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.
Remember BEDMAS
3 x 16 x 5 = 240
6 x −3 = ? A positive or negative number?
−22
The EXTERIOR angles of ANY polygon always adds up to the same number.
360°
A parallelogram has two pairs of parallel sides.
A parallelogram has 4 sides.
Remember BEDMAS (Do exponents before multiplication)
32
Square numbers are whole numbers multiplied by themselves e.g. 9 is a square number because 3 x 3 = 9
16, 25, 36, 49, 64, 81
There are 10 millimetres in a centimetre.
70 mm
Sum means "add"
15
To get started, add 3 to both sides of the equation.
3x − 3 = 21 3x = 24 x = 8
The 6 is in the "tenths" column.
6/10 = 3/5
Think carefully - are the diagonals axes of symmetry?
A parallelogram has NO axis of symmetry
There are 24 hours in a day.
15 x 24 = 360 seconds
= 6 minutes
How many eggs would ONE person need?
5 eggs are needed
How many sides does a regular hexagon have?
Six sides and six axes of symmetry
Draw a set of x-axis and y-axis and mark the point (1,1) then carry out each of the change.
(−1, 1)
Find the area of one face of the cube. Now work out how many faces a cube has.
6 faces each of area 4 square centimetres Total surface area = 24 square centimetres
When multiplying by 1000, move the decimal point 3 places to the RIGHT.
9500
Remember that NORTH is 0° and direction is measured CLOCKWISE.
180°
The HUNDREDTHS column is the second one to the right of the decimal point.
0.46
Multiply 3 by x then 3 by −6
6x −18
Simplify the x terms first and then the numbers
6x + 9
To find the x% of an amount you multiply it by x/100
450 x 0.30 = 135
First find the area of the wall Remember that 1 m = 100 cm
Eight cans of paint would be needed
Multipy numbers first and then the variables. Be careful with b x b!
12b2
Subtract 5 from both sides then divide both sides by 4.
x = 5
AB is NOT an arc, radius, diameter or sector.
AB is a chord
There are 10 mm in 1 cm
4.5 cm
Multiply and divide first before adding subtracting.
11
Do NOT multiply 3 by 3 !!!!
27
Do the exponent first!!
16
Write 50 out of 400 as a fraction i.e. 50/400
and now change to a percentage by multiplying by...
12.5%
Remember that squaring comes before multiplying by 2
8
Multiply 2 by 3 by 5 Easy!
30
Work out each bracket before adding.
970
Add together the lengths of the bits that are being cut off.
121 cm = 1.21 metres
4 is a square number
2 is the first prime number.
3ab means 3 x a x b
18
Subtract 3 from both sides then divide both sides by 2.
x = 19
The area of a triangle is half of the base multiplied by the height.
300 cm2
"To square a number you multiply it by itself."
121
How many numbers on a six-sided die are less than 3?
Probability = 1/3
Careful! There are two answers
x = 4 or −4
Do the EXPONENT first then the MULTIPLYING!!
19
"To calculate something by the power of 2, you multiply it by itself."
1.5 x 1.5 = 2.25
The perimeter of a shape is the distance around the outside of the shape.
Perimeter of square = 4 x 3 cm = 12 cm
0.45 means 45/100
0.45 = 45%
To find one quarter of anything divide it by 4
$150
Calculate 100 รท 400 and then multiply by 100
25%
Think of the area of a triangle as being half of that of a rectangle with a similar base and height.
Area of Triangle A = 0.5 x b x h
You could write 400 as 4 x 100
20
Work out each exponent first then multiply them together.
9 x 8 = 72
If the perimeter of a rectangle is 48 cm and its width is 6cm, how long is its other side?
180 cm2
The exterior angles of ANY polygon add up to 360°
360 / 60 = 6 The polygon would have SIX sides. i.e. It is a regular hexagon.
A rhombus is a quadrilateral with two pairs of opposite parallel sides and all sides equal in length.
4 sides
Work from left to right.
24
Find 5% of $350,000 and add it on OR Multiply $350,000 by 1.05
$367,500
Multiply the amount by 0.9 (100 - 10)/100 OR Work out 10% of $50,000 and subtract it.
$45,000
Use the rule that begins "The exterior angle of a triangle equals the sum of..."
25°
2ab means 2 x a x a
12
To change a decimal to a percentage multiply by 100
54%
A square has four sides equal length.
64 square metres
Find the width by halving the length. Then add the four lengths together.
150 metres
There are 1000 metres in 1 kilometre.
2000 metres
"Remember BEDMAS!" Do the multiplying first
23
The inside angles of a triangle add up to 180°
39°
The median is the MIDDLE number when all the numbers are arranged in order.
median = 13
Read the question carefully. How many people are there altogether?
$125
Remember: am means morning pm means afternoon
20 hours
How many "parts" are there altogether?
$27
"There are 1000 metres in a kilometre."
2 kilometres
The answer is NOT a rectangle
A square
Either use the fact that 30% is the same as three tenths OR Multiply 30 by 0.3
30 x 0.3 = 9
Choose from: acute, reflex and obtuse
REFLEX angles are greater than 180°
Speed = Distance/Time
80 kilometres/hour
Time = Distance / Speed
5 hours
"What? x What? = 81!"
The square root of 81 is 9 (because 9 x 9 = 81)
Is there a COMMON factor?
2(x + 4)
Prime numbers have only themselves and 1 as factors.
Yes, the only factors of 29 are 1 and 29.
There are 100 cm in 1 m
200 cm
To "square" a number multiply if by itself.
441
10% is one tenth of $240 or multiply $240 by 0.10
$24
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
Calculate 2 x 2 x 2
8
You've been given a clue already!
Obtuse angle
What FRACTION is 50% OR Multiply 200 by 0.5
100
There are 10 parts altogether so divide 300 by 10. The biggest share will be 7 of those parts.
$210
Start from the inside bracket and work out.
50
No clues, too easy!
47°
Divide both sides by 3.
x = 5
The vertices are the corners of the shape.
A triangle has 3 vertices.
The mean of a set of numbers is calculated by adding all of the numbers together and then dividing by however many numbers there are.
The mean is 6
There are 1000g in 1kg
3000 grams
When working out the surface area of the cube remember there are 6 faces to consider.
Surface area = 6 x 16
Combine the x terms and then the constant terms.
5x − 10
To find 20% of a quantity multiply it by 0.2. Remember there are 1000 g in 1 kg
400 grams of sugar
There are 1000 metres in one kilometre.
10 000 metres
There are 1000 mL in a litre
5L is the bigger of the two!
There are 100 cm in 1 m
Each piece of wood is 20 cm thick.
(0.2)3 = 0.2 x 0.2 x 0.2
The statement is true
Work from left to right.
4p
Is 4.4 closer to 4 or 5 on the number line?
4
Axes of symmetry are like mirror lines. They divide a shape into two equal parts.
2
Multiply the numbers first and then the variables (letters).
6p2
Substitute y = 2 and z = 4 in to get 22 x 4 and work it out.
16
What is a negative number multiplied by a negative number? Positive or Negative?
9
Double the length of each side and then multiply them together to find the area.
48 square centimetres
Add the numbers and then add and subtract the pees!!
12 + 2p
Subtract 10 from both sides first.
n = 7
How many of the numbers on the die are greater than 4?
The numbers could be 5 or 6, giving a probability of 2/6 = 1/3
Write the answer as a fraction with a denominator of 7
Two days begin with T (Tuesday and Thursday) This gives a probability of 2/7
Area of triangle = 0.5 x base x height
Area = 15 m2
The volume of a cuboid is the length x the width x the height.
Volume = 144 cm3
The angles of a triangle are SUPPLEMENTARY (they add up to 180°).
58°
Choose from scalene, isosceles or equilateral triangle.
Equilateral triangle
Move the decimal point three places to the right.
8370
Work out the two brackets first.
300 + 300 = 600
An equilateral triangle has 3 equal sides, an isosceles triangle has 2 equal sides and a scalene triangle has...
Isoceles triangles have two equal sides.
1 m = 100 cm
300 centimetres
Axes of symmetry are mirror lines drawn through the shape that divide the shape into two equal parts.
An equilateral triangle has three axes of symmetry.
There are 24 hours in a day and 7 days in a week.
1680 seconds = 28 minutes. Not a very good clock!
Either: Divide 2 by 25 or Change the bottom line into hundredths
0.08
Draw a diagram. The perimeter is 2 x length + 2 x width
The width is 8 metres.
An isosceles triangle is a triangle with two sides of equal length and two angles of equal size.
One axis of symmetry
Prime numbers have only two factors: Themselves and 1.
13 is the next prime number after 11.
Subtract 9 from both sides and then divide by 2.
x = 8
Distance = Speed x Time
The car travels 250 kilometres.
Add the two numbers and then divide by 60 to change to hours.
4 hours
Multiply the price by (100 − 10)/100 = 0.9 OR Multiply by 0.1 and substract from $400.
$360
1 m = 100 cm
320 cm
Add 5 to both sides of the equation and then divide by 2.
x = 13
Work from left to right.
10p
3.92 means 3.9 x 3.9
15.21
North is a bearing of 000° Sounth is a bearing of 180°
270°
Remember BEDMAS. Squaring comes first!
64
The mean is the result of adding all of the numbers together and dividing by 6.
Mean = 6
Start from the innermost brackets.
6
Axes of symmetry are mirror lines which divide the shape into two equal parts.
A square has 4 axes of symmetry. Note that the diagonals are axes of symmetry.
How many surfaces (square faces) does a cube have?
6 faces at 36 cm2 each = 216 cm2
Which number multiplied by itself gives 36. (There are two answers!)
x = 6 or −6
Area of square = length x length
New area = 16 cm2
Divide by 5
17 km/L
Change each fraction to twentieths
Three tenths is the smallest.
Remember BEDMAS. Multiply before Adding or Subtracting
15
Add the two measurements and then decide which whole number the answer is closest to.
6 cm
How many minutes in an hour? How many hours in a day?
5760 minutes
Add 4 to both sides and then divide by 5
5x − 4 = 16 5x = 20 x = 20/5 x = 4
Remember there are 60 minutes in an hour.
47 minutes
Faces are the surfaces.
A cube has 6 faces.
Prime numbers have only themselves and 1 as factors.
17
Area of triangle = 0.5 x base x height
Area = 20 cm2
Multiples of 4 are numbers such as 4, 8 ,12 etc.
There are 4 multiples of four between 20 and 40: 24, 28 , 32 and 36.
Find the cost of ONE book first by dividing by 50, and then multiplying this amount by 30.
30 books would cost $480
A hexagon has 6 sides and a decagon has 10 sides.
An octagon has 8 sides.
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.)
Highest common factor is 4.
The median is the middle score when they are arranged in order.
The median is 6
The prefix "kilo" means a thousand.
6 000
The interior angles of ANY triangle always add up to ...
180°
Volume of a rectangular prism = length x width x height
180 m3
Subtract 3 from both sides of the equation then divide both sides by 2.
x = 4
Area of a rectangle = length x width
1650 m2
Work out the volume of the pool in cubic metres (length x width x depth) Then use 1 m3 = 1000 litres
500 000 litres of water would be needed to fill the pool.
Write out the multiples of 3 and 4 and find the lowest common one. 3, 6, ... 4, 8, ...
12 is the lowest common multiple of 3 and 4
An edge is where two faces meet.
There are 12 edges in a cuboid.
Are there any common factors?
4(a + 2b + 3)
One of the angles in the triangle is 90° So what do the other two equal angles add up to? Now divide this by 2
45°
There are 1000 milligrams in 1 gram and 1000 grams in 1 kilogram.
There are 2 000 000 mg in 2 kg.
Expand 2(p + 3)
5p + 2(p + 3) = 5p + 2p + 6 = 7p + 6
Remember BEDMAS! Do that exponent first!
68
Divide 64 by 4 and then work out what x2 has to be.
x2 = 16 so x = +4 or −4
Multiply each of the terms inside the bracket by 3.
6x + 9
You'd better expand the brackets first.
2(x + 3) = 10 2x + 6 = 10 2x = 10 − 6 2x = 4 x = 2
The interior angles of a triangle add up to 180°
66°
The perimeter of a square is made up of the lengths of 4 equal sides.
The length of each side is 8 cm so the area of the square is 64 cm2
Draw a diagram of a rhombus (a squashed square) and mark on the diagonals.
True
1. Add all of the numbers together. 2. Count how many numbers there are. 3. Divide the answer to part 1 by the answer to part 2. This is the mean.
The mean is 60/15 = 4
Draw a rectangle.
90°
Collect the p terms together and then the numbers.
10p − 9
Use BEDMAS (work out the exponent first)
7 + 3 − 9 = 1
Not as difficult as it sounds! The sum of the exterior angles of ANY polygon is 360°. In a pentagon there are 5 of them and they are all equal.
72°
Multiply before adding!
FALSE! The left hand side comes out to be 7 not 10.
The exterior angles of ALL polygons always add up to 360°
The polygon has 360/36 = 10 sides
Multiply each of the terms in the bracket by 3.
3x − 12
The 500 gram can is 4 times as heavy as the 125 gram can.
The 500 gram can is better value.
The possibilities are:
(H, H), (H, T), (T, H) and (T, T)
P(head,head) = 0.5 x 0.5 = 0.25
When she spends three quarters, what fraction is left?
1 − 3/4 = 1/4 So one quarter remains Half of a quarter = 1/2 x 1/4 = 1/8
Find the missing inside angle of the triangle and then take it away from 180°
OR
The exterior angle of a triangle equals the sum of the two interior opposite angles.
x = 97°
There are two answers because:
"A negative number times a negative number = a positive number"
x = −6 or +6
There are 100 x 100 x 100 cubic cemtimetres in a cubic metre.
0.5 m3
What total is needed on 3 rounds to average 70?
She would need a round of 66 strokes!
List the factors of 42 and list the multiples of 7. Then find the biggest!
42
How many x are there? The sum of the angles in a quadrilateral is 360 degrees.
9x = 360
x = 40
The smallest angle is 40°
Simplify the left hand side of the equation first to give
4x + 8 = 12
Now solve this equation.
x = 1
If the perimeter of the square is 44 cm, how long is each side?
The area would be:
112 = 121 cm2
Expected value = Number of people x Probability of not passing
600 would be expected NOT to pass.
When multiplying by 1000 move the decimal point 3 places to the...
3650
The angles in a triangle add up to 180°
50°
Multiply everything in the brackets by 8.
16x − 40
There are 1000 metres in 1 kilometre.
1 500 m = 1.5 km
To get the mean of six amounts of money, add the six amounts together and then divide by 6.
Mean = $40