Botswana PSLE Mathematics cheat sheet

Place value: each position is 10 times the one on its right; in 47 302 the 4 is worth 40 000 and the 7 is worth 7 000.

Rounding rule: look at the digit to the right of the target place; 5 or more rounds up, 4 or less stays the same.

Order of operations: work in brackets first, then powers, then multiplication and division left to right, then addition and subtraction left to right.

Multiplying by powers of 10 shifts digits left; dividing shifts them right, so 3.6 x 100 = 360 and 3.6 / 100 = 0.036.

A fraction is a division: 3/4 means 3 divided by 4; to compare fractions, rewrite with a common denominator.

To find a percentage of an amount, divide by 100 then multiply: 15% of 80 = 80 / 100 x 15 = 12.

Divisibility: by 2 if the last digit is even; by 3 if the digit sum is a multiple of 3; by 5 if the last digit is 0 or 5; by 10 if it ends in 0.

Factors come in pairs, so 24 = 1x24 = 2x12 = 3x8 = 4x6; the highest common factor is the largest shared one.

Estimate before computing: round to convenient numbers, then compare the exact answer with the estimate to catch place-value slips.

Metric conversions: 1 km = 1 000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1 000 g, 1 litre = 1 000 ml.

Perimeter of a rectangle = 2 x (length + width); perimeter of any polygon is the sum of all side lengths.

Area of a rectangle = length x width; area of a triangle = 1/2 x base x height, where height is perpendicular to the base.

Volume of a cuboid = length x width x height; capacity in litres equals volume in cubic units converted by 1 litre = 1 000 cm3.

Time: 1 hour = 60 minutes, 1 minute = 60 seconds; elapsed time is found by subtracting start time from end time, borrowing 60 minutes.

Speed = distance / time, distance = speed x time, time = distance / speed; keep units consistent.

Money: write amounts to two decimal places; total cost = unit price x quantity, and change = amount paid minus total cost.

To convert between units, multiply when going to a smaller unit and divide when going to a larger unit.

Angles on a straight line add to 180 degrees; angles around a point add to 360 degrees; vertically opposite angles are equal.

The angles inside any triangle add to 180 degrees; in a quadrilateral they add to 360 degrees.

An equilateral triangle has three equal sides and three 60-degree angles; isosceles has two equal sides and two equal base angles.

A square has four equal sides and four right angles; a rectangle has opposite sides equal and four right angles.

Parallel lines cut by a transversal give equal corresponding angles and equal alternate angles.

Area of a parallelogram = base x perpendicular height; area of a trapezium = 1/2 x (sum of parallel sides) x height.

Symmetry: a line of symmetry folds the shape onto itself; an equilateral triangle has 3, a square has 4, a circle has infinitely many.

A right angle is 90 degrees, an acute angle is less than 90, an obtuse angle is between 90 and 180, a reflex angle is over 180.

The circumference of a circle is about 3.14 x diameter, and the area is about 3.14 x radius x radius.

Mean = sum of all values / number of values; it uses every data point and is affected by very large or small values.

Median is the middle value when data are arranged in order; with an even count, average the two middle values.

Mode is the value that occurs most often; a data set can have no mode or more than one mode.

Range = largest value minus smallest value; it measures spread, not centre.

In a bar graph, the height of each bar shows frequency; in a pictograph, each symbol stands for a stated number of items.

To read a pie chart, each sector is a fraction of 360 degrees or of 100%; a sector of 90 degrees represents one quarter.

When drawing a frequency table, tally marks are grouped in fives and the total frequency must equal the number of data items.

Always label axes with units and give a graph a title before interpreting or comparing values.

In an arithmetic sequence, the difference between consecutive terms is constant; the nth term = first term + (n - 1) x common difference.

To find a missing term, identify the rule between terms (add, subtract, multiply, divide) and apply it consistently.

Square numbers are 1, 4, 9, 16, 25; triangular numbers are 1, 3, 6, 10, 15, formed by adding consecutive counting numbers.

A variable such as x stands for an unknown number; an equation states that two expressions are equal.

Solve an equation by doing the same operation to both sides, undoing addition and subtraction before multiplication and division.

Substitution: replace each letter with its given value and follow order of operations, so 3a + 2 when a = 4 gives 14.

Like terms have the same letter part and can be combined: 5x + 3x = 8x, but 5x + 3 cannot be simplified further.

A formula links quantities, for example cost = price x number of items; use it by substituting known values and solving for the unknown.

Check a solution by substituting it back into the original equation; both sides must give the same value.

For word problems, state what is given, what is asked, and the operation or formula that connects them before calculating.

Unitary method: find the value of one item by dividing, then multiply by the required number of items.

For two-step problems, work backwards from the answer using inverse operations to check the result.

Draw a simple diagram or table for comparison and sharing problems; it makes the relationship between quantities visible.

Give the final answer with its unit (m, kg, litres, Pula) and check that the size of the answer is reasonable.