Mathematics practice questions.

Two masses, 12.51 g and 3.4 g, are added. Which value shows the sum with the correct precision?

• 15.9 g
• 15.91 g
• 15.910 g
• 16 g

Answer: 15.9 g

For addition and subtraction the result keeps the fewest decimal places of any value used; 3.4 g has only one decimal place, so 12.51 + 3.4 = 15.9 g. Note this rule uses decimal places, unlike multiplication and division which use significant figures.

Experimental results are plotted as a straight line of the form y = mx + c. What does the intercept c represent?

• The value of y when x is zero
• The gradient of the line at the origin
• The value of x when y is zero
• The largest value that y reaches

Answer: The value of y when x is zero

In y = mx + c the intercept c is the value of y where the line crosses the axis at x = 0. The gradient m, a separate quantity, gives how steeply y changes with x.

Identify the correct pair of rules for the precision of a calculated result.

• Multiplying uses the fewest significant figures; adding uses the fewest decimal places
• Multiplying uses the fewest decimal places; adding uses the fewest significant figures
• Both multiplying and adding use the fewest significant figures of the input values
• Both multiplying and adding use the fewest decimal places of the input values

Answer: Multiplying uses the fewest significant figures; adding uses the fewest decimal places

Multiplication and division carry relative uncertainty, which significant figures track; addition and subtraction carry absolute uncertainty, which decimal places track. Applying the significant-figure rule to 34.62 − 34.51 would give a four-figure result, 0.1100, when the correct answer is 0.11, which has only two.

The volume of gas collected, in cm³, is plotted against time, in s. State the unit of the gradient of the graph.

• s cm⁻³
• cm³ s⁻¹
• cm³ s
• mol dm⁻³ s⁻¹

Answer: cm³ s⁻¹

A gradient is the unit of the y-axis divided by the unit of the x-axis, so here it is cm³ per second. This is worth doing routinely, because the unit of a gradient is often the fastest check that the right two quantities have been plotted on the right two axes.

The hydrogen ion concentration of a solution is increased by a factor of ten. Determine the change in its pH.

• It falls by a factor of ten
• It rises by exactly one unit
• It falls by exactly one unit
• It rises by a factor of ten

Answer: It falls by exactly one unit

pH = −log[H⁺], so multiplying [H⁺] by ten adds one to log[H⁺], and the minus sign turns that into a fall of one unit. Forgetting the minus sign gives a rise of one unit, and forgetting the logarithm gives a change by a factor of ten.

A concentration is calculated as 0.0123456 mol dm⁻³ from measurements that were all quoted to 3 significant figures. Identify the correctly quoted result.

• 0.0123456 mol dm⁻³
• 0.012 mol dm⁻³
• 0.01235 mol dm⁻³
• 0.0123 mol dm⁻³

Answer: 0.0123 mol dm⁻³

The result cannot be more precise than the least precise measurement it came from, so it is quoted to three significant figures: 1, 2 and 3. Copying the full calculator display claims a precision the apparatus never had, and rounding to two figures throws away a figure that was genuinely measured.