The Advanced Numeracy Test Workbook - Mike Bryon [5]
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The measure of whether or not an event will happen is its probability. It is measured on a scale of 0–1, where 1 is a certain event, although the probability of an event occurring is also described as a fraction or percentage. It is calculated by dividing:
The number of positive outcomes
The number of possible outcomes
The probability of throwing a coin and it landing head first is 0.5 on the probability scale or ½, 0.5 or even.
In more complex situations tree diagrams can be used to calculate probability and to show all possible outcomes. The tree diagram below illustrates all possible outcomes if a disc is drawn from a bag containing 2 red (R), 1 green (G) and 3 white (W) discs and a second disc is drawn from another bag containing 3 green and 1 red disc. The probability of each outcome can be calculated by multiplying the fractions.
The elements of geometry
To calculate the area of a square or rectangle, multiply the length of its base by its height. The internal angles add up to 360°.
A triangle is made up of three straight lines. The internal angles add up to 180°. You calculate its area by:
½ base × height
The circumference of a circle is found by:
C = π × diameter or π × 2 radius
To approximate a circumference multiply the diameter by 3. The answer will be a greater sum.
π can be approximated as 3.14.
The area of a circle is found using:
Area = π × r2
Because it involves the operation of many of the methods just described, questions are sometimes posed requiring you to discover the surface area of a cylinder. Imagine a tin of beans! It involves calculating the area of two circles and the wall of the tin, which when opened out is a rectangle. The question may require you to calculate the length of the rectangle from the circumference of the circle. The formulae to use are:
Area of base and lid = 2πr2
Area of rectangle = circumference of lid × height = π × 2r × height
So formula for the surface area of a cylinder = 2πr2 + 2πrh
If you know the length of two sides of a right angled triangle then using Pythagoras’ theorem the length of the third side can be found. Pythagoras’ theorem states that the square of the hypotenuse (the sloping side) is equal to the sum of the squares of the two other sides. The theorem can be manipulated to find the length of any side of a right angled triangle.
C2 = A2 + B2
A2 = C2 – B2
B2 = C2 – A2
The ratios sine, cosine and tangent are used to find the angles or lengths of sides in right angled triangles. Each links two sides of a right-angled triangle with an angle. You need to relearn the ratios that relate to the particular sides of a triangle to know which ratio to use in a given situation and use the sin, cos and tan functions on a calculator. They are:
The volume of a cuboid is found by multiplying its length, width and height. The volume of a square is the cube of one side.
The volume of a sphere is found using the formula:
V = 4/3 πr3
The volume of a cylinder is found using:
V = πr2h
Test 1
Key quantitative operations
How confident are you in the key numerical skills?
Take this test, benefit from the practice, score yourself and then read the interpretation of how well you did and use it to focus your practice on the areas where you have most to gain.
Advanced numeracy tests take the basic skills for granted. So begin your practice by identifying which if any of these principles you need to relearn. If you feel confident in these operations then use this test to confirm that you already have the necessary key skills and move on to later chapters.
The test reviews the basic operations taken for granted in advanced numeracy tests. The candidates who will pass a psychometric test of their numerical skills will be confident and accurate in all parts of the test and will complete