GCSE Maths

Numbers
32 Topics | 2 Quizzes
Rounding to the Nearest 10, 100, 1000, and Beyond
Significant Figures
Significant Figures
Percentages
Simple Interest
Rounding and Estimation
Standard Form
Four Operational Rules
Conversion of Units to other Units
Compound Interest
Surds
Rational and Irrational Numbers
Greatest and Least Possible Values
2 of 2
Algebra
29 Topics | 1 Quiz
Algebraic Notation
Algebraic Vocabulary
Collecting Like Terms
Substituting Values into Formulae
Rearranging Equations
Algebraic Fractions
Expanding Brackets and Simplifying
Expanding Double Brackets
Factorisation
Factorising Quadratic Expressions
Factorising Quadratics with a Coefficient of x Squared Greater than 1
The Quadratic Formula
The Difference of Two Squares
Subject of Formula
Solving Linear Equations
Quadratic Equations
Completing the Square
Sequences and Nth Term
Arithmetic and Geometric Sequences
Quadratic Sequences
1 of 2
Ratio, Proportion and Rates of Change
7 Topics
Ratios
Scaling Ratios
Direct Proportion
Inverse Proportion
Reverse Percentages
Units and Conversions
Scale Factors
Geometry and Measures
16 Topics | 3 Quizzes
2D Shapes
2D Shapes Quiz
3D Shapes
3D Shapes Quiz
Types of angles
Angle Properties
Angle in Parallel Lines
Triangles
Triangles Quiz
Angles in Triangles
Polygons
Lines of Symmetry
Bearings
Loci and constructions
Constructing Triangles
Transformations
Enlargement
Plans and elevations
Areas and Volumes in Map Scale Problems
Probability
10 Topics
Introduction to Probability
Relative Frequency
Sample Space
Probability of Single Events
Probability of Combined Events
Probability Trees
Conditional probability
Set Notation
Venn diagrams
The Complement of a Set
Statistics
2 Topics
Population and samples
Representing data
Vectors
Mensuration and Calculation
7 Topics
Area
Volume
Congruence and similarity
Pythagoras’ theorem
Sine and cosine rule
Area of a triangle
Standard units of measure
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Conversion of Units to other Units

GCSE Maths Numbers Conversion of Units to other Units

Converting Speed Units

To convert between different units of speed, we can use conversion factors. Let’s look at the following examples:

1. Converting from kilometres per hour (km/h) to metres per second (m/s)

2. Converting from metres per second (m/s) to kilometres per hour (km/h)

3. Converting from kilometres per hour (km/h) to centimetres per minute (cm/min)

Example 1: Converting km/h to m/s

Convert 12 km/h to m/s.

First, note the following conversion factors: 1 km = 1000 m and 1 hour = 3600 seconds.

Now, use these conversion factors to cancel out the undesired units and obtain the desired units:

12\text{ km/h} = \frac{12\text{ km}}{1\text{ hr}} \times \frac{1\text{ hr}}{3600\text{ s}} \times \frac{1000\text{ m}}{1\text{ km}}

= \frac{12,000}{3,600}\text{ m/s}

= 3\frac{1}{3}\text{ m/s}.

Example 2: Converting m/s to km/h

Convert 15 m/s to km/h.

Use the conversion factors to change the units:

15\text{ m/s} = \frac{15\text{ m}}{1\text{ s}} \times \frac{3600\text{ s}}{1\text{ hr}} \times \frac{1\text{ km}}{1000\text{ m}}

= \frac{15 \times 3600}{1000}\text{ km/h}

= 54\text{ km/h}

Example 3: Converting km/h to cm/min

Convert 200 km/h to cm/min.

First, note the following conversion factors: 1 km = 100,000 cm and 1 hour = 60 minutes.

Now, use these conversion factors to change the units:

200\text{ km/h} = \frac{200\text{ km}}{1\text{ hr}} \times \frac{1\text{ hr}}{60\text{ min}} \times \frac{100,000\text{ cm}}{1\text{ km}}

= \frac{20,000,000}{60}\text{ cm/min}

= 333,333\frac{1}{3}\text{ cm/min}.

Typist Problems

Example 1:

A typist can type 15 words per minute. How long will it take the typist to type 3000 words, assuming the same rate of typing per minute?

To find the time required, divide the total number of words by the words per minute:

\text{Time} = \frac{\text{Total words}}{\text{Words per minute}} = \frac{3000}{15} = 200\text{ minutes}

Convert the minutes to hours and minutes: 200\text{ minutes} = 3\text{ hours}\ 20\text{ minutes}.

Example 2:

A typist types 20 words per minute. How many words can she type in 5 hours and 40 minutes, assuming the same rate of typing?

First, convert the given time to minutes: 5\text{ hours}\ 40\text{ minutes} = 5 \times 60 + 40 = 340\text{ minutes}.

Now, multiply the time in minutes by the typing speed:

\text{Total words} = \text{Typing speed} \times \text{Time} = 20 \times 340 = 6,800\text{ words}.

Converting Price Units

Convert £20/kg into pence/gram.

We know £1 = 100 pence and 1 kg = 1000 grams.

Now we can calculate the conversion:

£20/kg = £20/1 kg × 1 × 1 (Nothing changes)

= \frac{\text{£}20}{1\,\text{kg}} \times \frac{1\,\text{kg}}{1000\,\text{g}} \times \frac{100\,p}{\text{£}1})

= \frac{(20 \times 100)}{1000} p/g = 2 pence/gram

So, £20 per kg is equivalent to 2 pence per gram.

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