Junior Cert Science Numeracy Resources

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1 Focus on Numeracy Junior Cert Science Numeracy Resources

2 Let s Talk About Measurement Measurement of Time Directions: Put a < (less than), > (greater than), or = symbol between the two amounts of time. Unit Is equal to 1 Year 365 days 1Day 24 Hours 1 Hour 60 Minutes 1 Minute 60 Seconds a) 1 minute 45 seconds b) 1 hour 60 minutes c) 1 year 15 months d) 4 days 1 week e) 20 minutes 3 hours f) 1 day 12 hours g) 453 L 453 ml h) 83 millimeters 9 meters i) 50 centimeters 5 meters j) 12 seconds 1 hour SI Unit for Time is the Second

3 Let s Talk About Measurement Measurement of Length What piece of equipment would you use to Mark out the distance for the 100M race on sports day? Find the area of a room? To find the thickness of a book? Measure the diameter of pipe? Measure the length of a table? Measure the distance between two cities on a map? Height My height is My partner s height is Unit Unit Is equal to 1 km 1000M 1M 100cm Our Average height is 1cm 10mm Wrap a piece of string around your wrist. Cut it at the point where they meet. Now measure the string next to a meter rule. Body part Wrist Length (cm) or (mm) Ankle Head SI Unit for Length is the Metre

4 Let s Talk About Measurement Measurement of Volume Volume is the amount of space that an object takes up VOLUME can be used to study amounts of LIQUIDS (water, milk, juice) GASES (air, oxygen, helium) SOLIDS (flour, sugar, blocks of wood) Unit Symbol Cubic Metre M 3 Litre L Cubic Centimetre cm 3 Millilitre ml Using this information complete the following statements: 1 teaspoon = 5mL 1 tablespoon = 15mL 1 (measuring) cup = 250mL How many teaspoons of water fit in 1 tablespoon? 15mL 5mL = 3 So, there are teaspoons in a. How many teaspoons of sugar will fit in 1 cup? 250mL 5mL = 50 So, there are teaspoons in a. How many teaspoons of milk are there in a 1L carton? 1000mL 5mL = 200 So, there are teaspoons in 1. Example Find the volume of juice in a box that is 5cm long, 3cm wide, and 10cm high. V = L x W x H = 5cm x 3cm x 10cm = 150cm³ NOTICE THE FOLLOWING ABOUT THIS ANSWER: the units are now CUBED (cm³) This exponent (3)must be used whenever we calculate the VOLUME using the L, W and H! What does this have to do with OTHER units of VOLUME (ml, L, etc.)? Well 1cm³ = 1mL so 150cm 3 = 150mL SI Unit for Volume is the Metre 3

5 Let s Talk About Measurement Question 1: Measurement of Volume Formula: Volume = L x W x H A letter 'T' shape is made by sticking together 2 cuboids as shown in the diagram. What is the total volume in cm³ of the letter 'T'? Question 2: Calculate the volume of each of the following cuboids : SI Unit for Volume is the Metre 3

6 Let s Talk About Measurement Measurement of Volume Formula: Volume = L x W x H Question 1: Calculate the volume of the cardboard box. If the box was sealed could it be used to hold 85L of sugar? Explain your answer Question 2: Find the volume of air in an room that is 15m long, 8m wide and 3m high. If you needed an air conditioning unit to cool this room should you buy this one that was on special offer? Question 3: How many 250mls can of lemonade will it take to fill a 4L jug for your party? Question 4: A rectangular hot tub measures 100cm high x 200cm long x 200 cm wide. How many litres of water will it take to fill the hot tub? Question 5: (i) The diagram shows a piece of equipment, labelled A, containing water. a) Name A. b) What is the volume in A? (ii) A stone was then added and a new volume was recorded as shown in B. a) What is the volume in B? b) What was the volume of the stone in cm 3? c) What is the curve on the top of the water called? d) Name a second item of laboratory equipment which enables more accurate measurements of volume to be made e) What other piece of laboratory equipment can be used to measure volume? SI Unit for Volume is the Metre 3

7 Let s Talk About Measurement Measurement of Density Density = Mass Volume Q1 Complete the following sentence by putting in words from the list below: The density of an object is found by dividing the of an object by its. Area Volume Length Mass Acceleration. Q2 A regular block of glass has a length of 4cm, width of 3cm and a height of 2cm. Calculate the volume of the block of glass? This block of glass was placed in a graduated cylinder which already had 50cm 3 of water in it. Underline in the following list the new level of water after the block of glass was added. 59cm 3 24cm 3 74cm 3 98cm 3 Q3 Will a ship sink further in saltwater or freshwater Q4 How could you prove that a barman was watering down the whiskey without you having to drink any of it? Q5 A block of iron or steel will sink if put into water most of the ships in the world are made of iron and steel and they float. Can you explain this? Q6 The mass of an object is measured in. Q 7 Density is measured in. Answer the following questions using the table below: Q8 Put these objects in the correct order starting with the most dense. Q9 In the diagram below which substance is the most dense. Q10 The density of some metals are as follows, using this information find out which metal would sink in mercury. Mercury Lead Gold Iron Density 13.6g/cm3 11.2g/cm3 19.3g/cm3 7.9g/cm3 SI Unit for Density is the Kg/Metre 3

8 Let s Talk About Work, Energy and Power Work, Energy and Power Energy is the ability to do Work Work done = Force distance Power is the rate at which work is done Q1: How much work is done when a force of 10N moves and object 20M? What is the formula you will use? What values will you insert Q2: A 60 watt light bulb runs for 5 seconds. How much energy does it use? What is the formula? What is the unit of energy? Q3: Stephen runs up a 3 meter high flight of stairs. His mass is 60kg. How much work did he do? How much energy did he use? What are the units for work? What are the units for energy? Q4: On a recent adventure trip, Anita went rock-climbing. Anita was able to steadily lift her 70kg body 20.0 meters in 100 seconds. Determine Anita 's power during this portion of the climb. How do you calculate the force? How do you calculate the work? What is the formula for power? Q5: A physics teacher owns a family of squirrels. The squirrels have been trained to do push-ups in a repetitive fashion. Being connected to an electrical generator, their on going exercise is used to help power the teacher s home. There are 23 squirrels in the family and their average mass is 1.0 kg. They do work on the "up" part of the push-up, raising their body an average distance of 5.0 cm. If the squirrels averages 70 push-ups per minute, then determine the total amount of work done in one minute and the power generated by their activity. Quantity Work Energy Power Unit Joule Joule Watt Power Energy Time

9 Let s Talk About Electricity Electricity Quantity Symbol Unit Symbol Measured with Symbol Current I Amps A Ammeter Potential V Volts V Voltmeter difference Resistance R Ohms Ω Ohmmeter Relationship between current, potential difference and resistance V = RI Q1: This circuit was used to take measurements of current through the resistor and voltage across the resistor. The following measurements were obtained. Plot a graph of these measurements. What mathematical relationship do you see between voltage and current in this simple circuit? Q2: Calculate the resistance of a resistor when 20 V produces a current of 4 A. Q3:. What is the current through a 40-ohm resistance that has a potential difference of 160 volts? Q 4: If the headlight on your car has a resistance of 30 ohms and the car battery put out 12 V, what is the current through the headlight circuit? Q5: The motor for your electric car is attached to a generator. The motor has a resistance of 30ohms and the current is 4 amperes (A). What is the generator s voltage? Q6: If a clock radio uses 2 x 10 4 A of current when you run it on a 9 V battery, what resistance is its circuit providing?

10 Let s Talk About Electricity Electricity Q1: Match the quantity on the left to the unit in which it is measured on the right. Q2: A resistor of 8 has a potential difference of 4 V between its ends. Calculate the current passing through the resistor? Q3: A 220 volt wall outlet supplies power to a strobe light with a resistance of 2200 ohms. How much current is flowing through the strobe light? What are you trying to find? Write the formula that you will use. Insert the values for the formula Calculate and write you answer Q4: A CD player with a resistance of 40 ohms has a current of 0.1 amps flowing through it. Calculate how many volts supply the CD player. Choose your answer below volts volts volts volts Q5: A 220-volt power source supplies a lamp with a resistance of 192 ohms. What is the current flow of the circuit? What are you trying to find? Write the formula that you will use. Insert the values for the formula Calculate and write you answer Q6: What is the resistance of the circuit conductors when the voltage is 12 volts and the current flowing through the conductors is 2 amperes?

11 Let s Talk About Electricity Cost of Electricity Q1: The kilowatt-hour is the unit of electrical energy used by electricity suppliers. The photograph shows a kwh (kilowatt-hour) meter. This meter is connected into the electricity consumer s domestic circuit and it can measure energy consumption a selected part of the circuit, the total energy used and cost it. The meter can be wall-mounted in a convenient place. in Give two advantages to the consumer of having this type of meter. Define the Watt, the unit of power. Calculate the cost of using of using the electric kettle, shown in the diagram, for ten hours if a unit of electricity costs 15 cent. Q2: A 20 W (0.02 kw) CFL bulb is equivalent to 115 W (0.115 kw) incandescent bulb. Electricity costs 15 cent per kw h. Calculate the cost of using each of these bulbs for 100 hours. Q3: Nikola Tesla ( ) showed at the Frankfurt Fair in 1891 that alternating current could be transmitted over much longer distances than direct current. This is why the electricity supply to our homes is alternating current. Distinguish between alternating and direct current. What is the average voltage of domestic alternating current in Ireland? Q4: Components, e.g. bulbs, in electrical circuits can be connected in series or in parallel. (i) It is noticed that, when one headlight fails (blows) in a car, the second remains lighting. State the way the headlights are connected and give a reason why this mode of connection is used. (ii) All of the bulbs go out in an old set of Christmas tree lights, when one of bulbs fails (blows). In what way are the bulbs connected in this set of lights? Explain why, when one bulb blows, they all go out. (iii) Calculate the resistance of the filament of a car headlamp when 12 V produces a current of 5 A in it. In what unit is resistance measured?

12 Let s Talk About Force Moment of Force = Force x Perpendicular distance Q1: Each force and distance from the fulcrum on the left causes a certain moment. Draw a straight line from each force and distance from the fulcrum on the left with its corresponding moment on the right. Q2: What is the moment of each of these force? 2 metres 1.5 metres pivot 6 Newtons pivot 3 Newtons Q3: The car tyre has a puncture. So you need to take off the tyre to put a new one on. Your friend offers you a choice of spanners. Spanner A is 10 cm long. Spanner B is 20 cm long. Spanner C is 30 cm long. Which spanner would require the least force to use? Q4: Find out, by calculating the moments of force on each side, which of the following are balanced.

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