AQA GCSE Science 9-1 Equations Practice Pack

AQA GCSE (9-1) Science Equations Practice Pack

AQA GCSE

Science (9-1) Equations Practice Pack

This Required Practicals Lab Book is designed to support you when undertaking the practical work requirement of your AQA GCSE (9-1) Biology course. It covers all ten practicals and will:

••help you complete all the required practicals with detailed instructions, apparatus lists and safety tips

••provide one place to record the outcomes of your practical work, with write-in spaces for your results

••help you revise for your exams, with a selection of brand-new exam-style questions

••anticipate problems that might arise during your practical work by highlighting common mistakes

••test your knowledge and understanding of the practical work you have completed with challenging questions

••allow you to check your answers in the back of the book.

ISBN 978-0-00-845851-5

Title 978-0-00-XXXXXX-X

9 780008 458515

AQA GCSE

Science (9-1)

Equations Practice Pack Peter Edmunds

Elastic potential energy Any object that has been stretched or compressed stores elastic potential energy.

2 1 The equation for elastic potential energy is: Ee = 2 k e

This equation gets given to you.

Basic questions: No rearranging or unit conversion needed.

Model example: A spring has a spring constant of 50 N/m. Calculate the elastic potential energy stored by the spring if it is extended by a distance of 0.2 m.

[3 marks] 1

Write down the equation:

Ee = 2 k e

Substitute the variables into the equation:

Ee = 2

Calculate the answer:

Ee = 2

Write down the units:

joules / J

Q1.

2

1

× 50 × 0.22

[1 mark]

1

× 50 × 0.22 = 1

[1 mark] [1 mark]

A spring has a spring constant of 40 N/m. Calculate the elastic potential energy stored by the spring for each extension: a) 2 m

b) 1.5 m

c) 0.3 m

d) 0.1 m

[3 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q2.

An elastic band has a spring constant of 18 N/m. Calculate the elastic potential energy stored for each extension: a) 0.2 m

b) 0.05 m

c) 1.1 m

d) 3 m

[3 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Medium questions: Rearranging needed. Some unit conversion (but with hints in boxes).

Q3.

A spring has a spring constant of 400 N/m. Calculate the extension for each of the stored potential energies: a) 200 J

b) 0.8 kJ

c) 50 J

kJ → J

d) 1.8 kJ

× 1000

[3–4 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................

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Elastic potential energy

c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q4.

A spring stores 40 J of elastic potential energy. Calculate the spring constant of the spring for each of the following extensions: a) 50 cm

b) 80 mm

c) 160 mm

d) 4 cm

cm → m ÷ 100 mm → m ÷ 1000 [4 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Hard questions: Word-based questions that involve rearranging and use of standard form.

Q5.

Each arm of a car’s suspension has coil springs of spring constant 4 × 10 N/m.

When the car goes over a speed bump, each coil spring stores 2 J in elastic potential energy.

Calculate how much the coil spring is compressed by.

[3 marks] 4

..................................................................................................................................................................... .....................................................................................................................................................................

Q6.

At maximum extension, a bungee cord stores 1.5 × 10 J of elastic potential energy.

If a bungee jumper extends the cord by a maximum of 50 m, calculate the spring constant.

5

[3 marks]

..................................................................................................................................................................... .....................................................................................................................................................................

Mixed practice: Requires more than one equation.

Q7.

An arrow of mass 250 g is fired by a bow. The string on the bow has a spring constant of 1500 N/m, and it is extended by 10 cm. a) Calculate the maximum elastic potential energy stored by the bow.

[4 marks]

................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ b) Assuming that all the elastic potential energy store is converted into kinetic energy store, calculate the initial velocity of the arrow.

[4 marks]

................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

[Total marks

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Answers Elastic potential energy Mark scheme for Q1–2 (example for Q1.a)

Correct substitution into equation:

Correct substitution into equation:

800 = 0.5 × 400 × e

Ee = 0.5 × 40 × 2

2

[1]

Correct calculation of answer: 2

Ee = 0.5 × 40 × 2 = 80

[1]

Write units: joules / J

[1]

e=

!""

[1]

".$ × '""

Correct calculation of answer: e=

!"" ".$ × '""

=2

[1]

Write units: metres / m

Q1. a) 80 J b) 45 J

Q3. a) 1 m

c) 1.8 J

b) 2 m

d) 0.2 J

c) 0.5 m d) 3 m

Q2. a) 0.36 J

Q4. a) 320 N/m

b) 0.023 J c) 11 J

b) 13 000 N/m

d) 81 J

c) 3100 N/m d) 50 000 N/m

Mark scheme for Q3–7 (example for Q3.b): 3 marks if unit conversion not required, 4 marks if there is a unit conversion

Q5. 0.01 m Q6. 120 N/m

Correct unit conversion: Ee = 0.8 kJ = 800 J

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Q7. a) 7.5 J [1]

64

b) 7.7 m/s

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[1]

Moles 23

If you have one mole of a substance, it means that you have 6.02 × 10 particles of that substance. That number is known as the Avogadro constant. The mass (in grams) of one mole of a substance is equal to its relative formula mass, Mr. To calculate the number of moles of a substance, !"## %& #'(#)"*+, (.) you can use the equation number of moles =

You need to remember this equation!

0,1")23, &%0!'1" !"## (./567)

For these questions, give your answers to three significant figures.

Basic questions: Calculations involving elements.

Model example: Calculate the number of moles in 96 g of titanium.

Write down the equation:

number of moles = 89

Substitute the variables into the equation: Q1.

:;

[1 mark] !"## %& #'(#)"*+, (.)

0,1")23, &%0!'1" !"## (./567)

= 2 mol

[1 mark]

Calculate the number of moles in: a) 20 g of calcium

b) 460 g of sodium

c) 96 g of sulfur

d) 0.35 g of lithium

[1 mark each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q2.

Calculate the mass of the following elements: a) 3 moles of iron

b) 2 moles of carbon c) 0.2 moles of tin

d) 0.05 moles of zinc [1 mark each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q3.

Calculate the relative formula mass of the following elements. Use this to identify the element: a) 2 moles of this element have a mass of 150 g b) 10 moles of this element have a mass of 635 g c) 5 moles of this element have a mass of 480 g d) 0.5 moles of this element have a mass of 19.5 g

[2 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

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Moles

Medium questions: Calculations involving compounds.

Model example: Calculate the number of moles in 0.32 g of Fe2O3.

Write down the equation:

number of moles =

Calculate the relative formula mass:

!"## %& #'(#)"*+, (.)

0,1")23, &%0!'1" !"## (./567)

(2 × 56) + (3 × 16) = 160 <.>?

Substitute the variables into the equation: Q4.

[2 marks]

@9<

[1 mark]

= 0.002 mol

[1 mark]

Calculate the number of moles in: a) 80 g of O2

b) 4 g of NaOH

c) 204 g of Al2O3

d) 74 g of Mg(NO3)2 [2 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q5.

Calculate the mass of: a) 0.6 moles of H2O

c) 4 moles of NH4Cl

b) 2 moles of Mg(OH)2

d) 0.03 moles of CaCO3

[2 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Hard questions: Calculations involving compounds. Requires unit conversions.

Q6.

Calculate the number of moles in 4.59 kg of Al2O3.

kg → g × 1000

[3 marks]

..................................................................................................................................................................... .....................................................................................................................................................................

Q7.

Calculate the number of moles in 2.12 mg of Na2CO3.

mg → g ÷ 1000

[3 marks]

..................................................................................................................................................................... .....................................................................................................................................................................

Q8.

Calculate the number of moles in 1.89 kg of HNO3.

[3 marks]

..................................................................................................................................................................... .....................................................................................................................................................................

[Total marks

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Answers Moles

Q4. a) 2.5 mol

Q1. a) 0.5 mol

b) 0.1 mol

b) 20 mol

c) 2 mol

c) 3 mol

d) 0.5 mol

d) 0.05 mol

Q5. a) 10.8 g

Q2. a) 168 g

b) 116 g

b) 24 g

c) 214 g

c) 23.8 g

d) 3 g

d) 3.25 g

Mark scheme for Q6–8 (example for Q6)

Mark scheme for Q3 (example for Q3.a)

Correct unit conversion:

Correct relative formula mass calculation:

4.59 kg = 4590 g

relative formula mass = @A< ?

!"##

Correct relative formula mass calculation:

*'!(,0 %& !%1,#

= 75 g/mol

[1]

Correct identification of the element: arsenic (as it has a relative atomic mass of 75)

[1]

(2 × 27) + (3 × 16) = 102 g/mol Correct substitution and calculation:

[1]

relative formula mass = :A8<

Q3. a) Mr = 75; arsenic

@<?

!"## *'!(,0 %& !%1,#

= 45 mol

b) Mr = 63.5; copper

Q6. 45 mol

c) Mr = 96; molybdenum

Q7. 2 × 10

d) Mr = 39; potassium

Q8. 30 mol

−5

[1]

mol

Mark scheme for Q4–5 (example for Q4.a) Correct relative formula mass calculation: (2 × 16) = 32 g/mol

[1]

Correct substitution and calculation: relative formula mass = ;< >?

!"## *'!(,0 %& !%1,#

= 2.5 mol

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Surface area to volume ratio Some organisms and single cells have a high surface area to volume ratio and are able to exchange substances directly with the environment through diffusion. Most multicellular organisms have a much lower ratio and therefore must have a dedicated exchange system. These exchange systems are adapted to increase the rate of diffusion by having a large surface area.

For example, the small intestine is long and folded, with villi and microvilli 2 that give it a total surface area of approximately 30 m .

The equation for surface area to volume ratio is:

You need to remember this equation!

surface area volume

Basic questions: No rearranging or unit conversion required.

2

3

Model example: A cell has a surface area of 20 μm and a volume of 5 μm . Calculate the surface area to volume ratio for the cell.

[1 mark] Write down the equation:

surface area

Substitute the variables into the equation:

surface area

volume

Write as ratio: Q1.

volume

=

20 5

=4

surface area : volume ratio = 4 : 1

[1 mark]

2

A cell has a surface area of 16 μm . Calculate the surface area to volume ratio for each volume: a) 5 μm

3

b) 3.2 μm

3

c) 4 μm

3

d) 2.5 μm

3

[1 mark each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Medium questions: Requires calculating surface area and volume individually.

Model example: Calculate the surface area to volume ratio for a cube of side length 0.5 cm.

Calculate the surface area of the cube:

Each side = 0.5 × 0.5 = 0.25 cm

2

Six sides overall, so total surface area 2 = 6 × 0.25 = 1.5 cm Calculate the volume of the cube: Calculate the surface area to volume ratio:

volume = 0.5 × 0.5 × 0.5 = 0.125 cm surface area volume

=

1.5 0.125

[1 mark] 3

[1 mark]

= 12

surface area : volume ratio = 12 : 1 Q2.

[3 marks]

[1 mark]

Calculate the surface area to volume ratio of a cube of side length: a) 1 cm

b) 2 cm

c) 3 cm

d) 4 cm

[3 marks each]

a) ................................................................................................................................................................ ................................................................................................................................................................

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Surface area to volume ratio

b) ................................................................................................................................................................ ................................................................................................................................................................ c) ................................................................................................................................................................ ................................................................................................................................................................ d) ................................................................................................................................................................ ................................................................................................................................................................

Q3.

What happens to the surface area to volume ratio as the size of a cube increases?

[1 mark]

.....................................................................................................................................................................

Hard questions: Requires rearranging.

Q4.

2

A red blood cell has a surface area of 136 μm and a surface area to volume ratio of 1.5 : 1.

Calculate the volume of the red blood cell.

[2 marks]

..................................................................................................................................................................... .....................................................................................................................................................................

Q5.

3

A cell has a volume of 50 μm and a surface area to volume ratio of 3 : 1. Calculate the surface area of the cell.

[2 marks] ..................................................................................................................................................................... .....................................................................................................................................................................

Mixed practice: Requires unit conversions and more than one equation.

Q6.

The image of an amoeba is 10.5 mm long under a microscope of ×15 magnification. a) Calculate the size of the amoeba in μm.

[3 marks]

................................................................................................................................................................ ................................................................................................................................................................ b) The microscope is now changed to a magnification of ×25. Calculate how long (in mm) the image of the amoeba would appear under this magnification.

[2 marks] ................................................................................................................................................................ ................................................................................................................................................................ c) Assume that the amoeba is a cube of side length equal to what you calculated in Q6.a.

Calculate the surface area to volume ratio of the amoeba.

[3 marks]

................................................................................................................................................................ ................................................................................................................................................................

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Answers 2

Surface area to volume ratio

Q5. 150 μm

Q1. a) 3.2 : 1

Mark scheme for Q6

b) 5 : 1

Q6. a) Correct substitution into equation: 10.5

c) 4 : 1

Size of real object =

d) 6.4 : 1

Correct size calculation:

Mark scheme for Q2 (example for Q2.a)

0.7 mm

Correct surface area calculation:

Correct unit conversion

Each side = 1 × 1 = 1 cm

2

volume

6 1

Size of image = 25 × 0.7

[1]

Correct image size calculation:

3

[1]

Correct surface area to volume calculation: =

[1]

b) Correct substitution into equation: [1]

Correct volume calculation:

surface area

[1]

0.7 mm = 700 μm

Six sides overall, so total surface area 2 = 6 × 1 = 6 cm volume = 1 × 1 × 1 = 1 cm

[1]

15

18 mm

[1]

c) Correct surface area calculation:

=6

Each side = 0.7 × 0.7 = 0.49 mm

surface area : volume ratio = 6 : 1

[1]

Q2. a) 6 : 1

2

Six sides overall, so total surface area = 6 × 0.49 = 2.94 mm

2

[1]

b) 3 : 1

Correct volume calculation:

c) 2 : 1

Volume = 0.7 × 0.7 × 0.7 = 0.343 mm

d) 1.5 : 1

Correct surface area to volume calculation:

Q3. As the size of the cube increases, the surface area to volume ratio decreases.

Mark scheme for Q4 and Q5: 1 mark for correct substitution and 1 mark for the correct answer.

Q4. 91 μm

surface area volume

=

2.94 0.343

3

= 8.6

surface area : volume ratio = 8.6 : 1

3

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Rearranging equations On the previous pages, you learned the general strategy for answering basic equation-based questions.

However, the equation that you need to use will not always be in the correct format. Sometimes, you need to rearrange an equation so that it can be used correctly. These pages will go over how to do this.

Basic questions: Basic rearranging of equations like P = V I Take the equation P =V I. Here, P is the symbol for the power of an electronic device (with units of watts / W).

I is the symbol for current through the device (with units of amps / A), and V is the potential difference across the device (with units of volts / V).

Model example: A lamp is connected to a 6 V battery and has a power of 24 W. Calculate the current through the lamp.

[3 marks] Write down the equation:

P=VI

Substitute the variables into the equation:

24 = 6 × I

Rearrange the equation to make I the subject. Note how the right-hand side of the equation is “6 × I”. To get I by itself, you can divide both sides by 6:

!" #

Calculate the answer:

Q1.

=𝐼

I=4

Remember to add the units:

[1 mark]

amps / A

[1 mark] [1 mark]

An LED is connected to a 12 V power supply. Calculate the current for each power: a) 6 W

b) 24 W

c) 18 W

d) 90 W

[3 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

Q2.

A motor has a power of 60 W, and a current of 1.2 A flowing through it. Calculate the potential difference across the motor.

[3 marks] ..................................................................................................................................................................... '

Medium questions: Rearranging of equations like P = ( Take the equation 𝑃 =

' (

. The power is again denoted by P, and W is the work done (with units of joules / J)

and t is the time (with units of seconds / s).

Model example: An electric motor has a power of 2000 W and does 40 000 J of work. Calculate the time for which the motor is on.

[3 marks]

𝑃=

Write down the equation:

(

40 000 2000 = 𝑡

Substitute the variables into the equation:

AQA GCSE (9–1) Equation Practice Maths

'

8

[1 mark]

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Rearranging equations Rearrange the equation to make t the subject.

Firstly, multiply both sides by t, then divide both sides by 2000:

2000 × t = 40 000 𝑡=

Calculate the answer:

!...

t = 20

Remember to add the units: Q3.

". ...

[1 mark]

seconds / s

[1 mark]

A kettle has a power of 2500 W. Calculate the time taken to do the following amounts of work: a) 50 000 J

b) 1 000 000 J

c) 75 000 J

d) 600 000 J

[3 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

1

Hard questions: More complex rearranging of equations like Ek = ! mv2 1

The equation 𝐸0 = 𝑚𝑣 ! gives the amount of kinetic energy a moving object has (with units of joules / J). !

The symbol m gives the mass (with units of kg) and v is the velocity (with units of m/s).

Model example: A van has a kinetic energy of 150 000 J and a mass of 3000 kg. Calculate the velocity of the van.

[3 marks] 1

𝐸0 = 𝑚𝑣 !

Write down the equation: Substitute the variables into the equation, then simplify the right-hand side of the equation: 2

Rearrange the equation to make v the subject; divide both sides by 1500. Then simplify the left-hand side: To calculate the answer, take the square root of both sides of the equation: Remember to add the units: Q4.

150 000 =

!

1 !

× 3000 × v

150 000 = 1500 × v 14. ...

14..

2

2

[1 mark]

= 𝑣!

100 = v

2

10 = v

[1 mark]

meters per second / m/s

[1 mark]

A car has a kinetic energy of 120 000 J. Calculate the velocity of the car for the following masses: a) 800 kg

b) 1200 kg

c) 900 kg

d) 1600 kg

[3 marks each]

a) ................................................................................................................................................................ b) ................................................................................................................................................................ c) ................................................................................................................................................................ d) ................................................................................................................................................................

[Total marks

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Answers Rearranging equations

Q2. 50 V

Mark scheme for Q1–4 (example for Q1.a)

Q3. a) 20 s

Correct substitution into equation: 6 = 12 × I

b) 400 s [1]

Correct calculation of answer: I = 0.5

d) 240 s [1]

Write units: amps / A

c) 30 s Q4. a) 17 m/s b) 14 m/s

[1]

Q1. a) 0.5 A

c) 16 m/s d) 12 m/s

b) 2 A c) 1.5 A d) 7.5 A

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