Formulas

Exercise 1

Solve the inequalities below algebraically.

a

$10 - 2 x > 4 x + 8$

b

$60 - x^{2} \leq - 4$

c

$600 + 0.05 x > 800 + 0.025 x$

Exercise 2

Solve this inequality using your graphic calculator: $x^{2} - x > 90$ .

Exercise 3

You can drive a Smart Fortwo for no more than € 5,00 per day! Assume you bought a Smart on 1 januari 2006 and you pay this 5 euro per day. In addition you have to pay for maintenance: for 1,5 cent per driven kilometre you can have a contract that covers almost all cost of maintenance. What remains is the cost for petrol. You can drive 15 kilometres on 1 liter of petrol and 1 liter of petrol costs about € 1,50.

a

How many cents per kilometre do you have to pay for petrol and maintenance together?

b

How much does this Smart cost per year when you drive a total of $16000$ km per year?

c

Make an inequality to suit the question: What is the maximum number of kilometres per year you could drive in this Smart if you wish to spend € 4000.00 or less per year? Solve the inequality algebraically.

d

As it happens, the maintenance subscription of $1.5$ cents per driven kilometre is effective from $15000$ km/year. When you drive less, you pay a subscription as if you drive $15000$ km/year. Give the complete formula for the yearly costs $K$ , depending on the number of driven kilometres $k$ .

Exercise 4

Two cars drive on the motorway, both maintaining a constant speed. Driver A drives at a speed of $110$ km/h. Driver B drives at a speed of $120$ km/h. When driver B arrives at the IJsselbrug near Deventer he is $24$ kilometres behind driver A. This happens at time $t = 0$ . The distance (in kilometres) from Deventer is represented by $a$ .

a

For both cars write down a formula for $a$ as a function of $t$ .

b

Calculate after how many minutes car A is overtaken by car B.

c

Calculate algebraically how long the distance between the two cars is less than $4$ kilometres.

Exercises