Maths questions
Don't forget to take a ruler and calculator into the exam.
Maths questions often start with command words like Calculate, 'Determine', 'Estimate' and 'Measure'. They will then include blank space for you to show your working.
When an answer to a maths question is marked:
- full marks are given for the right answer (but it's wise to show your working so you can check your answer)
- marks are given for working, including substitution and rearrangement
- 'errors carried forward' are taken into account
If a later answer depends on an earlier answer, and you get the earlier one wrong, you could still get full marks in the later answer if your working is correct.
If your answer has many decimal places or figures, make sure you give it to an appropriate number of decimal places or significant figures. You may be asked to give units. This may earn you an additional mark, so don鈥檛 forget to check whether you need to do this.
Maths questions might ask you to plot or complete a graph or table. When you draw a graph, make sure you:
- plot each point accurately
- draw a best fit straight line or curve
You may be given a grid with axes and scales already given. Sometimes you may be given an empty grid for you to supply your own axes. When you do this:
- put the independent variable on the x-axis and the dependent variable on the y-axis
- make sensible scales so that the plotted points cover at least 50% of the area of the graph
- label the axes with their quantity and unit, eg time (s)
Learn maths skills with Dr Alex Lathbridge
Listen to the full series on 大象传媒 Sounds.
Brush up on the maths you need for your exam - percentages, averages and converting units.
Sample question 1 - Foundation
Question
Sarah does three titrations with dilute hydrochloric acid and potassium hydroxide solution.
Here is Sarah鈥檚 results table.
| Titration number | 1 | 2 | 3 |
| Final reading in cm3 | 17.8 | 37.5 | 32.1 |
| Initial reading in cm3 | 0.0 | 20.4 | 15.0 |
| Titre (volume of acid added) in cm3 | 17.1 | 17.1 |
| Titration number | Final reading in cm3 |
|---|---|
| 1 | 17.8 |
| 2 | 37.5 |
| 3 | 32.1 |
| Titration number | Initial reading in cm3 |
|---|---|
| 1 | 0.0 |
| 2 | 20.4 |
| 3 | 15.0 |
| Titration number | Titre (volume of acid added) in cm3 |
|---|---|
| 1 | |
| 2 | 17.1 |
| 3 | 17.1 |
a) Complete the table. [1 mark]
b) Sarah thinks the mean titre is 17.1 cm3. Is she correct? Explain your answer. [1 mark]
OCR Gateway Science, GCE Chemistry, J248/02 Paper 2 (Foundation Tier) Sample Question Paper Q17.
a) Titre value = 17.8 - 0.0 = 17.8 [1]
b) Yes, because titration 1 is a rough estimate/titration 1 is an outlier/titrations 2 and 3 are identical [1]
Sample question 2 - Foundation
Question
Sarah does another titration to make a fertiliser called potassium nitrate, KNO3.
Look at the equation for the reaction she uses.
KOH + HNO3 鈫 KNO3 + H2O
The relative formula masses, Mr, of each compound are shown in the table.
| Compound | Formula | Relative formula mass |
| Potassium hydroxide | KOH | 56.1 |
| Nitric acid | HNO3 | 63.0 |
| Potassium nitrate | KNO3 | 101.1 |
| Water | H2O | 18.0 |
| Compound | Potassium hydroxide |
|---|---|
| Formula | KOH |
| Relative formula mass | 56.1 |
| Compound | Nitric acid |
|---|---|
| Formula | HNO3 |
| Relative formula mass | 63.0 |
| Compound | Potassium nitrate |
|---|---|
| Formula | KNO3 |
| Relative formula mass | 101.1 |
| Compound | Water |
|---|---|
| Formula | H2O |
| Relative formula mass | 18.0 |
What is the atom economy for the reaction to make potassium nitrate? Assume that water is a waste product. [2 marks]
OCR Gateway Science, GCE Chemistry, J248/02 Paper 2, Sample Question Paper.
Atom economy = (Mr of desired products 梅 sum of Mr of all products) 脳 100
= (101 梅 119) 脳 100 [1]
= 84.9(%) [1]
Sample question 3 - Higher
Question
Sarah does three titrations with dilute hydrochloric acid and potassium hydroxide solution.
Hydrochloric acid is used to neutralise a solution of potassium hydroxide in a conical flask.
HCl (aq) + KOH(aq) 鈫 KCl (aq) + H2O(l)
Sarah uses 25.0 cm3 of potassium hydroxide solution, KOH.
She also uses hydrochloric acid with a concentration of 0.100 mol/dm3.
The mean titre of acid used is 17.1 cm3.
a) Calculate the concentration, in mol/dm3 of the KOH(aq). [2 marks]
b) Use your answer to a) to calculate the concentration of the KOH(aq) in g/d3. [2 marks]
OCR Gateway Science, GCE Chemistry, J248/04 Paper 4 (Higher Tier) Sample Question Paper Q19
a) Moles of acid = 17.1 梅 1000 脳 0.100 = 0.00171 [1]
Concentration of KOH = 0.00171 脳 1000 梅 250 = 0.0684 mol/dm3 [1]
b)Mr of KOH = 39.1 + 16 + 1 = 56.1 [1]
Concentration of KOH = 0.0684 脳 56.1 = 3.84 g/dm3 [1]
Sample question 4 - Higher
Question
The reversible reaction between carbon dioxide and hydrogen makes methane and water.
carbon dioxide + hydrogen 鈬 methane + water
Kayvan investigates this reaction.
He predicts that 11.0 g of carbon dioxide should make 4.0 g of methane.
In an experiment, he finds that 11.0 g of carbon dioxide makes 2.2 g of methane
Calculate the percentage yield of methane. [2 marks]
OCR Gateway Science, GCE Chemistry, J248/04 Paper 4, Sample Question Paper - Higher.
Percentage yield = (actual yield 梅 predicted yield) 脳 100
= (2.2 梅 4.0) 脳 100 [1]
= 55% [1]