When you subtract a negative number it's the same as adding. Minus a minus number and effectively you add.
The question told you that the average temperature in India is +13 degrees and the average temperature in Siberia is -16.
To find the difference in these temperatures you have to count down 13 degrees to zero and then another 16 degrees down below zero until you get to -16 degrees.
+13 - -16 = 13 + 16 = 29
squares cubes and roots
f you multiply a number by itself, you have "squared" the number. Therefore the square of 9 is 9 x 9, which equals 81.
We can go the opposite way for any number and find that the square root of 81 is 9.
We can also "cube" numbers. To cube a number you multiply it by itself three times.
It is easy to muddle up square and square root, or cube and cube root. One common mistake is to think you square a number by multiplying it by 2 and you cube a number by multiplying it by 3. Make sure you're clear about the difference between these calculations.
volumes of prisms
Remember, to find the volume of any prism you always first find the area of the cross section and then multiply this by the depth or length of the prism.
One common mistake is to add the dimensions, or measurements. Another is to get the formula for the area of the cross section wrong. Don't forget, to work out the area of a triangle, use the formula:
1/2 x base x height
So in this question, the area of the cross section is:
1/2 x 10 x 5 = 25
The volume of the prism = cross section x length:
25 x 20 = 500 cubic cm
A ratio is a way of comparing two or more quantities or amounts. They don't have units and, like fractions, they can be simplified.
The question told you that the farmer has 15 cows and 85 sheep. The ratio 15:85 can be simplified by dividing 15 and 85 by 5.
15 divided by 5 = 3
85 divided by 5 = 17
So 15:85 in its simplest form is 3:17
substituting into formulae
A formula is a general rule, written using letters to represent numbers. The formula given to you in the question was v = u + at.
This is a general rule which tells you the speed (v) of something such as a car or rocket if you know the starting speed (u), the acceleration (a) and for how long (t) the car was accelerating.
We were told that u = 3, a = 4 and t = 6. So, to find v in our formula, we replace the letters with numbers:
v = u + at
=> 3 + (4 x 6)
=> 3 + 24 = 27.
circumfrence of a circle
The circumference of a circle is the distance around its outside, or its perimeter. The diameter is the distance across the circle, from one side to the other, going through the centre. The value of Pi to two decimal places is 3.14.
Remember, to calculate the circumference of a circle the formula is:
circumference = Pi x diameter
Using this formula to calculate the circumference of a circle of with a diameter of 3cm:
Circumference = 3 x 3.14
Circumference = 9.42 cm
If you draw a right-angled triangle, you can find the angles of the triangle by measuring the lengths of the triangle sides. There are three formulae that help you do this. They're called the trigonometric ratios, and they are as follows:
sin theta = length of opposite divided by length of hypotenuse
cos theta = length of adjacent divided by length of hypotenuse
tan theta = length of opposite divided by length of adjacent
To solve a problem involving trigonometry you need to choose the correct trigonometric ratio. In the question, you know the following:
length of hypotenuse = 12
angle between hypotenuse and adjacent = 36°
You want to know the length of the opposite. You need to use the ratio which involves the opposite and hypotenuse, or the sine ratio:
sin 36° = opposite divided by 12
opposite = 12sin 36°
There are two rules for bearings:
1) Bearings are always measured clockwise from north.
2) The bearing must have three digits. For bearings less than 100°, the first digit will be 0.
So, to calculate the bearing of the crossroads from the cottage in this question, imagine that you are standing at the cottage on the diagram and facing north. Turn clockwise until you are facing the crossroads.
Turning in a complete circle would mean turning 360°. The crossroads is 26° anticlockwise from the cottage.
Therefore, because the bearing is measured clockwise, it must be:
360° - 26° = 334°
mean median and mode
Make sure you know the difference between mean, median and mode. The question asked you to find the median of the following set of data:
9 10 10 10 10 11 11 12 12 12 19
The median is the middle number, which in this case is 11.
To find the mean, you would add the numbers together and divide by the total amount of numbers. So:
9 + 10 + 10 + 10 + 10 + 11 + 11 + 12 + 12 + 12 + 19 = 126
There are eleven numbers, so the mean is 126 divided by 11 = 11.46
The mode is the number which occurs most often, which is 10.