The question bank, in the open

Work out 2/3 + 3/4 − 1/6, giving your answer as a fraction in its lowest terms.

Write 0.00042 in standard form.

Simplify (2x³y)² × 3x⁻²y⁴ ÷ 6xy², leaving your answer in terms of x and y.

Work out 8^(2/3).

A bakery spends P4,800 a year on fuel. The cost rises by 6% in the first year, and the new amount rises by a further 4% in the second year. Work out the fuel cost after two years.

A jacket is marked at P1,250. In a sale the price falls by 20%. The sale price is later increased by 20% to become the new normal price. Show that the new normal price is P1,200.

Expand and simplify (2x − 3)(x + 5).

Solve the simultaneous equations: 3x + 2y = 16 and x − y = 2, showing your method.

Solve 3(2x − 1) = 2(x + 4) + 5.

Find the nth term of the sequence 5, 8, 11, 14, …

The nth term of a sequence is 4n − 3. (a) Find the 20th term. (b) Is 100 a term of this sequence? Show how you decide.

Each exterior angle of a regular polygon is 24°. How many sides does the polygon have?

In triangle ABC, angle A = 2x, angle B = 3x and angle C = 4x. Find the value of x and the size of the largest angle.

A, B, C and D lie on a circle in that order. Angle ABC = 74°. Find angle ADC, giving a reason for your answer.

In a right-angled triangle the hypotenuse is 9.6 m. One of the sides next to an angle is 7.2 m. Work out that angle, giving your answer to one decimal place.

A rectangle measures 9 cm by 12 cm. Work out the length of a diagonal.

A tuck shop records bags of crisps sold each day: 0–4 bags on 6 days, 5–9 on 12 days, 10–14 on 8 days and 15–19 on 4 days. Estimate the mean number of bags sold per day.

Find the median of 4, 7, 2, 9, 5, 7, 3.

A bag contains 5 red counters and 3 blue counters. Two counters are taken at random without replacement. Find the probability that both counters are red, giving your answer as a fraction in its lowest terms.

A fair six-sided dice is rolled twice. What is the probability of rolling a six both times?

A straight line passes through the points (2, 5) and (6, 13). Find the equation of the line in the form y = mx + c.

Which instrument is most suitable for measuring 25.0 cm³ of dilute acid to the nearest 0.1 cm³?

A uniform metre rule is pivoted at its 50 cm mark. A 2.0 N weight hangs at the 20 cm mark. A 3.0 N weight is hung on the other side to balance the rule. Calculate the position of the 3.0 N weight.

A car travels 150 m in 12 s. What is its average speed?

A 2.0 kW kettle is used for 6 minutes each day for 30 days. Electricity costs P1.85 per kWh. Calculate the total cost of running the kettle for the 30 days.

A learner of mass 45 kg climbs a 4.0 m staircase in 6.0 s. Take g = 10 N/kg. Calculate the power she develops.

0.50 kg of water is heated from 20 °C to 60 °C. The specific heat capacity of water is 4200 J/kg°C. Calculate the energy supplied.

A radio station broadcasts at a frequency of 9.0 × 10⁷ Hz. The speed of light is 3.0 × 10⁸ m/s. Calculate the wavelength of the waves.

A 12 V battery is connected across a 6.0 Ω resistor. Calculate the current in the circuit and the power dissipated by the resistor.

Two 6.0 Ω resistors are connected in parallel. What is their combined resistance?

A bottle of ammonia is opened at one end of a classroom. Explain, in terms of particles, why the smell is noticed at the other end of the room several seconds later.

Which method is used to obtain solid copper(II) sulfate from copper(II) sulfate solution?

A neutral atom is written as ³⁵₁₇Cl. How many protons, neutrons and electrons does it contain?

Zinc reacts with hydrochloric acid: Zn + 2HCl → ZnCl₂ + H₂. 6.5 g of zinc reacts completely. The relative atomic mass of zinc is 65 and the molar volume of a gas at room temperature is 24 dm³. Calculate the volume of hydrogen produced.

Balance the equation __Fe + __O₂ → __Fe₂O₃ and state whether the reaction is oxidation or reduction.

25.0 cm³ of 0.100 mol/dm³ sodium hydroxide solution is exactly neutralised by 20.0 cm³ of hydrochloric acid. Calculate the concentration of the hydrochloric acid in mol/dm³.

The same mass of marble reacts with the same volume and concentration of hydrochloric acid twice: once as large chips and once as a fine powder. Explain why the powder reacts faster.

Which is the general formula of the alkanes?

A cell is 0.05 mm long. In a photograph it appears as 25 mm long. Calculate the magnification of the photograph.

Which structure is present in a plant cell but not in an animal cell?

Explain how water reaches the leaves at the top of a 20 m tall tree.

A digestive enzyme works fastest at 37 °C. Explain why its activity falls sharply at 60 °C.

In an experiment, amylase digests 0.80 g of starch in 2.0 minutes. Calculate the rate of reaction in g per minute.

Write the word equation for anaerobic respiration in human muscle.

A plant in a sealed greenhouse is given extra carbon dioxide and its rate of photosynthesis increases. Providing more carbon dioxide then makes no difference, but increasing the light intensity does. Explain these observations.

Two parents are both carriers of a recessive condition (genotype Bb). State the expected ratio of unaffected to affected children, and explain your reasoning.

Explain why a food chain rarely contains more than five trophic levels.

State two practical measures a settlement can take to reduce the spread of a water-borne disease such as cholera, and explain how each measure works.

Read the passage The garden that learned to wait, then summarise the practical steps the gardeners took in response to the drought, and the results that followed. Write in your own words as far as possible.

Read the passage about the community garden. The writer says the gardeners did not claim credit for the rise in school attendance, and then reports what they did claim. Explain, in your own words, what the writer is suggesting about how the gardeners see their own success.

How does the writer make the arrival of the first storm feel like a turning point? Quote three or four words and explain the effect of each choice.

Read the passage about the night market. How does the writer make the market feel busy and improvised? Quote three or four words and explain the effect of each choice.

You are a resident of a ward in Gaborone where a street light has been broken for three months. Write a letter to the editor of a local newspaper describing the problem and what you want done about it.

Which sentence is correctly punctuated?

Write a composition of about 400 to 600 words on one of these titles: (a) The morning the taps ran dry. (b) A journey that did not go as planned. (c) Write a description suggested by the photograph of a busy bus rank: the noise, the heat, the waiting. This app has no photograph of people, so for (c) work from what you know of a bus rank you have stood in.

A composition title asks you to write about a time you were lost in a familiar place. Explain how you would plan the piece before writing: what you would decide, and why each decision helps the reader.

Define the term isotope, and explain why two isotopes of the same element have identical chemical properties but different relative atomic masses.

A student has two lamps and one battery. Describe what happens when the lamps are connected in series, then compare that with connecting them in parallel, referring to current, p.d. and brightness in each case.

A bakery in Serowe wants to open a second branch in a town where it already sells through two supermarkets. Suggest and justify two factors the owner should consider when choosing where to open, and recommend one location.

Figure 1 describes a cross-section of a leaf: an upper layer of tightly packed cells containing many chloroplasts; a lower layer of loosely packed cells with air gaps; a waxy layer across the top surface; and small openings on the lower surface, each bordered by two curved cells. Describe the structure of the leaf shown in Figure 1, and state one function of each of the four parts listed.

A farmer ploughs a field and leaves the bare soil exposed for three weeks before planting. Compare the soil conditions on the ploughed field with those under the undisturbed grassland beside it, and explain why the ploughed field loses more topsoil.

Figure 2 describes four features of a root hair cell: a long, thin extension of the cell surface; a large permanent vacuole filling much of the cell; no chloroplasts; and many mitochondria. Name each feature and state what it is for, in the form you would write on the lines beside a diagram.

A bakery in Molepolole is set up and owned by one person, who is personally responsible for its debts. Which type of business organisation is this?

A juice producer has fixed costs of P18,000 a month. Each bottle sells for P25 and has variable costs of P10. Calculate the break-even output and the margin of safety if the business sells 1,500 bottles.

A hardware store in Gaborone shows a profit in its accounts but cannot pay its suppliers on time. Explain two reasons why a profitable business can still run short of cash.

Define "contribution per unit" and calculate the total contribution for a business that sells 1,000 units with a selling price of P40 and variable costs of P25 per unit.

A new fitness studio in Gaborone has P8,000 to spend on market research before opening. Recommend how the money should be spent and justify your recommendation.

A fruit juice producer is deciding whether to build its factory next to a farm in the Tuli Block or on the edge of Gaborone. Explain one advantage of each location.

Which of the following is a non-financial method of motivating employees?

A guesthouse in Maun is considering a large expansion, adding twelve rooms, to be built during the low season. Evaluate whether the owner should go ahead.

Which of the following would NOT appear as a cash inflow in a cash-flow forecast?