Formulae and Equations Flashcards
Substitution
Substitution involves replacing pronumerals in an algebraic expression with numbers. The resulting
numerical expression is evaluated and expressed to the specified level of accuracy.
Substitution of values
- Write the algebraic expression.
- Replace the variables in the expression with the numbers given in the question.
- Evaluate using the calculator.
- Write the answer to the specified level of accuracy and correct units if necessary.
Distance, Speed and Time
Speed is a rate that compares the distance travelled to the time taken. The speed of a car is measured in kilometres per hour (km/h). The speedometer
in a car measures the instantaneous speed of the car. A speedometer is not totally accurate but has
a tolerance of 5%. GPS devices are also capable of showing speed readings. Most cars also have an odometer to indicate the distance travelled by the vehicle.
Distance, Speed and Time - formula
Speed = Distance over Time
Time = Distance over Speed
Distance = Speed x Time
Stopping distance
The stopping distance is the distance a vehicle travels from the time a driver sees an event occurring to the time the vehicle is brought to a stop. It is calculated by adding the reaction distance and the braking distance. Reaction distance (or thinking distance) is the distance travelled by the vehicle from the time that a hazard, such as a pedestrian stepping into the road, first occurs, to when the driver first commences braking. The reaction time averages 0.75 seconds for a fit and alert driver. The braking distance is affected by the road surface (wet, slippery, uneven or unsealed), the slope of the road (uphill or downhill), the weight of the vehicle and the condition of the brakes and tyres.
Stopping distance - formula
Stopping distance =. Reaction distance + Braking distance
Stopping distance = 5 x velocity x reaction time over 18 + velocity squared over 170
Stopping distance - example
Trevor was driving at a speed of 45 km/h and he had a reaction time of 0.75 seconds when a hazard occurred. Calculate the stopping distance using the formula
d = 5Vt + V2 .
18 170
1. Write the stopping distance formula.
d = 5Vt + V2 .
18 170
2. Substitute V = 45 and t = 0.75 into the formula.
= 5×45×0.75 + 45 (squared)
18 170
3. Evaluate.
= 21.28676471
4. Express the answer as required.
= 21 m
Linear Equations
In linear equations all the variables are raised to the power of 1. The process of finding the unknown value for the variable is called solving the equation. When solving an equation, look to perform the opposite operation:
* + is opposite to −
* × is opposite to ÷
When solving an equation, the equation must be kept
balanced on either side of the equals sign. The same
operation needs to be done on both sides of the equals sign to keep the balance. The goal when solving an equation is to get the pronumeral by itself on one side of the equation.
Linear equations - steps to perform
- Look to perform the opposite operation (+ is opposite to −, × is opposite to ÷).
- Add or subtract the same number to both sides of the equation.
- Multiply or divide both sides of the equation by the same number.
- To solve two-step or three-step equations, repeat the steps 1 to 3 as required. It is often easier
to first add or subtract the same number to both sides of the equation
Solving formulas after substitution - formula
Solving equations after substitution Formula
A formula is a mathematical relationship between two or more variables. For example:
- a2 = b2 + c2 is Pythagoras’ formula for relating the sides of a right-angled triangle; a, b and c are
the variables - A = πr2 is a formula for relating the area and radius of a circle. A and r are the variables.
By substituting all the known variables into a formula, we are able to find the value of an unknown variable. If the unknown is not the subject of the equation, solve the equation.
Using a formula
- Write the formula.
- Replace the variables in the formula with the numbers given in the question.
- If the unknown is not the subject of the equation, solve the equation.
- Evaluate using the calculator.
- Write the answer to the specified level of accuracy and correct units if necessary.
Changing the subject of a formula
Move the pronumerals and numbers, other than the pronumeral you want as the subject, to the right-hand side of the equation.
To move any term or number:
1 Look to perform the opposite operation (+ is opposite to −, × is opposite to ÷).
2 Add or subtract the same term or number to both sides of the equation.
3 Multiply or divide both sides of the equation by the same number.
Changing the subject of the formula - example
The total cost of a child’s birthday party is given
by the formula:
C = 40n + 75
where C ($) is the total cost and n is the number of children attending.
Make n the subject of the equation.
Solution:
1 Write the formula.
2 The opposite operation to adding 75 is
subtracting 75. Subtract 75 from both sides
of the equation.
3 Rearrange the equation with the subject on
the left-hand side.
4 The opposite operation to multiplying by
40 is dividing by 40. Divide both sides of the equation by 40.
Blood Alcohol Content
blood alcohol content
Blood alcohol content (BAC) is a measure of the amount of alcohol in your blood. The measurement is the number of grams of alcohol in 100 millilitres of blood. For example, a BAC 0.05 means 0.05 g or 50 mg of alcohol in every 100 mL of blood. BAC is influenced by the number of standard drinks consumed in a given amount of time and a person’s mass. Other factors that affect BAC include gender, fitness, health and liver function.
BAC - formula
Male - ( 10 x number of standard drinks - 7.5 x hours of drinking ) over 6.8 time mass in kg
Female - ( 10 x number of standard drinks - 7.5 x hours of drinking ) over 5.5 x mass in kg
