Maths Flashcards
Section A: Algebra
This section requires you to know the following principles of algebra to answer the questions.
Term
A term is anything that is joined together by multiplication and/or division. Example. 5b (5 * b)
Pronumeral
A pronumeral is a letter that is used to represent a number we don’t know. It can be any letter of the alphabet.
Coefficient
A coefficient is the number that goes before the pronumeral. For example, 8h. 8 is the coefficient. This means that 8 is multiplied with h.
Constant Term
A constant term is a term that doesn’t have a pronumeral. This is basically any number.
Invisible multiplication and division signs
If using multiplication or division, we would make it invisible to save space. So 9 * x = 9x. With division, you would turn it into a fraction. So 10 ÷ y = 10/y.
Substitution
Substitution is the process of substituting a pronumeral with a number. So if we say n = 4, we can solve 5n, which is 5*4, equals 20.
Equivalent Expression
If expressions are equivalent, their values are the same. So, 3x + 5x is equivalent to 8x.
Like terms
To find which terms are like, we must look at the pronumeral. So, 5a and 6a are like, but 7b and 9c aren’t. This is because they have different pronumerals.
Combining like terms
When you combine like terms, you simplify them. Fo example, 5x + 6x can be simplified to 11x. However, 9x + 4y + 2x cannot be simplified into 15xy. It can only be simplified into 11x + 4y.
Multiplying expressions
If you were asked to multiply different expressions, all you need to do is mash them up. So, 5a * 7b is 35ab.
Dividing expressions
When dividing fractions, all you need to do is put them on top of each other on a fraction. So, 4m ÷ 9s = 4m/9s. If the expression became 3ab/6b, you can simplify it into a/2. (As 3 and 6 can both be divided by 3, and b and b can be divided by b, so both cancel each other out.).
The distributive law
The distributive law requires you to expand brackets. If you get the expression y(3+x), you can expand it by multiplying y with both numbers in the brackets SEPARATELY. This gives 3y + xy.
Section B: Linear Equations
This section requires you to know the following principles to answer these questions.
What is the aim of an equation, anyway?
The aim of an equation is to find whatever the pronumeral is. If you give the equation x + 7 = 12, the goal is to find what x is. Here, it is obvious that x = 5, but in more complicated equations, you must know what the steps are to solving the equation.
How do you solve equations?
You must first see what “journey” the pronumeral took to get to the final result. If you look at the equation 3x + 4 = 22, you will find out that x first multiplied by 3, then added 4. Its final number is 22. So, to find out x, you reverse the steps. You first subtract 4, then divide by 3. Doing this leaves you with 6. To, make sure your answer is correct, do the equation with the number you think x is to see if it is correct.
How do you make an equation for real life situations?
You need to think about what the problem is talking about. If it says, “A pen costs $x while and the cost for 4 pens is $6,” You know that x multiplied by 4 to get 6. The equation is 4x = 6.
Section C: Measurement
This section requires you to know the following things to answer these questions.
Formulas
For the next few cards, we will talk about formulas for different shapes.
Square
Perimeter = 4h
Area = h^2
Rectangle
Perimeter = 2(h+w), [or if you remember the distributive law, you can expand this into 2h + 2w]
Area = hw
Triangle
Perimeter = a + b + c
Area = (1/2bh)
Trapezoid
Perimeter = a + b + c + d
Area = 1/2(a + b) * h
Parallelogram
Perimeter = 2(h + w) [or 2h + 2w]
Area = bh
Converting
For the next few cards we will be talking about different measuring systems and how to convert to one unit or the other. Other than the metric system and capacity, these cards aren’t really worth learning.
Metric
1km = 1000m 1m = 100cm 1cm = 10mm
Imperial
1 mile = 8 furlongs 1 furlong = 40 rods 1 chain = 22 yards 1 rod = 22.5 feet 1 yard = 3 feet 1 foot = 12 inches
Roman
1 mile = 1000 paces
1 pace = 5 feet
1 cubit = 6 palms
1 foot = 4 palms
Capacity
1cm3 = 1mL 1000cm3 = 1L 1m3 = 1kL
Composite shapes
There are two ways of finding the area of composite shape. One is to divide the shape into simpler shapes, then add their area all together. Another is to add bits on to make it a simpler shape, and then subtract the extra bits after working it out. The way to find the perimeter is by adding all the sides together. If not all the measurements are given, use reasoning to fill in the gaps.
Volume
To find the volume of an object, find the area of the cross section of the prism and multiply by the depth. If the cross section is a composte shape, you can divide it into simpler prisms, or find the area of the composite cross section and multiply by the height.
Section D: Statistics
This section requires you to know the following to answer these questions.
Range
The range is the biggest number in the data set, minus the smallest number in the data set.
Mean
The mean is the average of all numbers. To find the mean, simply add all the numbers and divide by how many numbers there are.
Median
The median is the number in the middle of the data set, when put in ascending order. For example, the median of the data set [4, 6, 8, 10, 12] is 8, because it is the middle number. If there are two middle numbers, find the average of both.
Mode
The mode is the number that occurs most frequently. If there is more than one mode, you can state them all or find the average of all of them.
The different categories of data.
Categorical: Where the answers a words. For example, dog, red, excellent.
Numerical: Where the answers are numbers. For example, 1, 7, 20.
Subcategories under Categorical
Categorical Nominal: Where there is no specific order in the results. For example, pets: dog, cat, fish.
Categorical Ordinal: Where the results can be put in a certain order. For example, exam scores: poor, average, excellent.
Subcategories under Numerical
Discrete Numerical: Where there is a set range of results. This is usually written as a column or pie graph. For example, number of siblings: 1, 1, 1, 2, 3, 5.
Continuous Numerical: Where there is no set range of results. This is usually written as a line graph. For example, the temperature during a day (°C) 10, 12, 15, 20, 24, 23, 16.
How do you find the proportion and sector size of a pie graph?
A circle has 360°. Take the total of all results and divide them into the nearest common factor. Take the full 360° and divide by the denominator, them multiply by th numerator. For example. If the total of the results was 10 and the results for one answer was 4, the proportion would be 4/10. The sector size would be 144°, as 1/10 = 36°, so 4/10 should be 36 * 4 = 144.
How do you make a divided bar graph?
You find the proportion of the results and you divide the bar into however many parts needed. Then divide the bar according to your results. If you have 2/10 as one of the answer’s proportions, divide the bar into 10 and spare 2 segments for this answer.
The formula for converting Farenheit to Celsius and vice versa is…
F = [9c/5] + 32 C = [5( F - 32 )]/9
Best of luck for your Maths Exam.
(This is the end of the deck)
