Interpreting and drawing more real-life graphs | Maths

Starter quiz

Interest which is calculated on the original amount and the interest accumulated over the previous period is called __________.

compound interest ✓

simple interest
£200 is invested into an account with 3% simple interest each year. How much will be in the account after 5 years?

'£230' ✓
£200 is invested into an account with 3% compound interest each year. Which of these calculations will give the amount in the account after 5 years?

$200 \times 1.03^5$ ✓

$200 \times 1.15$

$200 \times 1.3^5$
£1000 is invested into an account with 2% compound interest paid monthly. How much would be in the account after 1 year? Round to the nearest pence.

'£1268.24' ✓
Select the coordinates that lie on the curve $y=3^x$

$\left({1\over 3}, 1\right)$

(1,3) ✓

(2,6)

(3, 27) ✓

(4,64)
The general form for an exponential equation is:

$x = a$

$y=mx+c$

$y=ab^x$ ✓

$y=ax^2+bx + c$

Exit quiz

Which would be the equation of the line if graphing £300 invested at a simple interest rate of 2% per month?

$y=2x+300$

$y=6x+300$ ✓

$y=300x + 2$

$y= 2 \times 300^x$

$y = 300 \times 1.20^x$
Which would be the equation of the exponential curve if graphing £500 invested at a simple interest rate of 3% per month?

$y = 500 \times 0.03^x$

$y = 500 \times x^3$

$y = 500 \times 3^x$

$y = 500 \times 1.03^x$ ✓

$y = 500 \times 1.3^x$
Which of these equations could model the value of a car depreciating over time?

$y = 20 000 \times -1.15^x$

$y = 20 000 \times -0.85^x$

$y = 20 000 \times 0.85^x$ ✓

$y = 20 000 \times 1.00015^x$

$y = 20 000 \times 1.15^x$
Which of these journey segments show deceleration on a displacement-time graph?
Match the sections of the graph labelled a)-f) with the correct part of the journey.

a)

⇔

Increasing in speed moving away from the fixed start point. ✓

b)

⇔

Decelerating moving away from the fixed start point. ✓

c)

⇔

Object is stationary. ✓

d)

⇔

Increasing in speed moving towards the fixed start point. ✓

e)

⇔

Travelling at a constant speed. ✓

f)

⇔

Decelerating moving back towards the fixed start point. ✓
Here is a displacement-time graph for a journey. Which of these could be a speed-time graph of the same journey?

Worksheet

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Lesson Details

Key learning points

Not all real-life graphs can be drawn using sections of different linear graphs.
The graphs are models, which means that we want them to be useful.

Common misconception

Pupils may think the gradient of the line to model simple interest is always the interest rate.

This works when investing £100 but not with other start values. The gradient is the amount of interest added each time which depends on the amount invested and the interest rate. There are examples to show this in the lesson.

Keywords

Simple interest - Interest is money added to savings or loans. Simple interest is always calculated on the original amount.
Compound interest - Compound interest is calculated on the original amount and the interest accumulated over the previous period.
Exponential - The general form for an exponential equation is $y = ab^x$ where $a$ is the coefficient, $b$ is the base and $x$ is the exponent.
Speed - Speed is the rate at which something is moving. It is measured as the distance travelled per unit of time.
Acceleration - Acceleration is the rate of change of speed with respect to time.