Substitution
Substitution means putting numbers in place of letters to calculate the value of an expression.
For example, in the expressionNumbers, symbols and operators grouped together - one half of an equation, eg 2bf + 2f + 3k. \(2b^2c\), where \(b = 4\) and \(c = 3\), use the values of \(b\) and \(c\) to calculate the numerical value of the expression:
\(2b^2c = 2 \times b^2 \times c\)
Remember that the rules of BIDMAS/BODMAS show that the order of operations (the order sums should always be completed in) is: Brackets, Indices or Powers, Divide/Multiply and Add/Subtract. This means that the value of \(b^2\) should be calculated before multiplying by 2 or \(c\), as indices come before multiplication.
This gives: \(2b^2c = 2 \times b^2 \times c = 2 \times 4^2 \times 3\) (substituting \(b = 4\) and \(c = 3\)) = \(2 \times 16 \times 3 = 96\)
Question
Work out the value of \(d + (3e + f)^2\) when \(d = 2\), \(e = -3\) and \(f = 1\).
This expression contains brackets and index/indicesShows how many times a number has been multiplied by itself. The plural of index is indices.. The brackets should be worked out first, and then the indices should be calculated before the multiplication. The addition should be worked out last.
\(d + (3e + f)^2 = 2 + (3 \times - 3 + 1)^2\)
The letters \(d\), \(e\) and \(f\) have been substituted for their numerical values.
\(2 + (3 \times - 3 + 1)^2 = 2 + (-9 + 1)^2 = 2 + (-8)^2\)
The bracket has been worked out first.
\(2 + (-8)^2 = 2 + 64\). \(-8^2\) means \(-8 \times -8\), which is +64 using sign rules (two signs that are the same make a positive).
\(2 + 64 = 66\). (The addition part of the expression has to be worked out last following BIDMAS.)
Substitution into formulae
Substitution into formulae works the same way as substitution into expressions, and it is important to follow the rules of BIDMAS.
A common formula is used to convert Celsius (C): to Fahrenheit (F) \(F = \frac{9C}{5} + 32\)
Example
What is the temperature in Fahrenheit if it is 20掳C?
Substitute the value of \(C\) into the equation \(F = \frac{9C}{5} + 32\) to work out the temperature in Fahrenheit.
\(F = \frac{9C}{5} + 32 = \frac{9 \times 20}{5} + 32 = \frac{180}{5} + 32 = 36 + 32 = 68^\circ \text{F}\)
The temperature of 20掳C is the same as 68掳F using the formula.
Question
The formula to work out the force in Newtons of an object is \(F = ma\), where \(m\) is mass in kilograms and \(a\) is the acceleration in m/s2. What is the force of an object that has a mass of 16 kg and an acceleration of 7 m/s2?
Remember that \(ma\) means \(m \times a\).
\(F = ma = 16 \times 7\) (the values for \(m\) and \(a\) have been substituted)
\(16 \times 7 = 112\) (the units for force are Newtons, which was given in the question)
The final answer is 112 Newtons or 112 N.
More guides on this topic
- Algebraic expressions - AQA
- Solving linear equations - AQA
- Solving simultaneous equations - AQA
- Solving quadratic equations - AQA
- Inequalities - AQA
- Sequences - AQA
- Straight line graphs - AQA
- Other graphs - AQA
- Transformation of curves - Higher- AQA
- Algebraic fractions - AQA
- Using and interpreting graphs - AQA