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30 cardsIndependent School Entrance (ISEB Pre-Test and 11+ CEM style)

Independent School Entrance: Reasoning and Maths Methods

30 flashcards on quick number methods, percentage and ratio steps, sequence rules and verbal reasoning strategies for selective independent-school entrance practice. Study material written for practice.

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Divisible by 9
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1
Divisible by 9
Add the digits. If the digit sum is a multiple of 9, the number is divisible by 9. 5,238: 5 + 2 + 3 + 8 = 18.
2
Divisible by 4
Check the last two digits. If they make a multiple of 4, the whole number is. 3,712: 12 is a multiple of 4.
3
Lowest common multiple (LCM)
The smallest number that is a multiple of two or more numbers. Use it for timetable problems. LCM of 18 and 24 is 72.
4
Highest common factor (HCF)
The largest number that divides exactly into two or more numbers. HCF of 18 and 24 is 6.
5
Order of operations
Brackets, then powers, then multiplication and division from the left, then addition and subtraction from the left.
6
Percentage increase
New price = old price multiplied by (1 + rate). A 25% increase multiplies by 1.25.
7
Percentage decrease
New price = old price multiplied by (1 - rate). A 20% decrease multiplies by 0.8.
8
Reverse percentage
To find the original, divide the new value by the multiplier. After a 15% discount, original = sale price ÷ 0.85.
9
Percentage change
Change ÷ original value × 100. Always divide by the starting value.
10
Sharing in a ratio
Add the parts, divide the total by that number to find one part, then multiply. £240 in the ratio 2 : 3 : 7: one part is £240 ÷ 12 = £20.
11
Mean
Total of the values divided by how many values there are. To find a missing value, use total = mean × number of values.
12
Median
The middle value when the numbers are in order. If there are two middle values, find their mean.
13
Mode and range
The mode is the most common value. The range is the largest value minus the smallest.
14
Speed, distance, time
Speed = distance ÷ time. Distance = speed × time. Time = distance ÷ speed. Average speed = total distance ÷ total time.
15
Converting km/h to m/s
Divide by 3.6. 72 km/h ÷ 3.6 = 20 m/s.
16
Simple interest
Interest per year = principal × rate. Total after n years = principal + n × yearly interest.
17
Angles in a polygon
The interior angles of a polygon with n sides add up to (n - 2) × 180 degrees. Each exterior angle of a regular polygon is 360 ÷ n.
18
Area of a trapezium
Half × (sum of the parallel sides) × perpendicular height.
19
Volume to litres
1,000 cm³ = 1 litre. 1 m³ = 1,000 litres.
20
Scale factor and area
If lengths are enlarged by a scale factor k, areas are multiplied by k², and volumes by k³.
21
Probability without replacement
After one item is removed, the total changes. Two reds from 4 red in 12: 4/12 × 3/11.
22
Triangle inequality
In any triangle, the two shorter sides together must be longer than the longest side.
23
Number sequences: first checks
Find the differences. If the differences are the same, it is linear. If the differences change by a fixed amount, it is quadratic. If terms are multiplied, look for a ratio.
24
Nth term of a linear sequence
The common difference gives the number before n. Then adjust. 7, 11, 15, 19: 4n + 3.
25
Fibonacci-style sequence
Each term is the sum of the two terms before it, so check whether the third term equals the first plus the second.
26
Caesar-style letter code
Find how far each letter moves in the alphabet and check that the shift is the same for every letter.
27
Reverse-alphabet code
A pairs with Z, B with Y, C with X. The positions of each pair add up to 27.
28
Hidden words
Ignore the spaces and read the letters in a line. The word is spread over the end of one word and the start of the next.
29
Ordering puzzles
Turn each clue into a short chain (A > B > C), then merge the chains. Use fixed clues such as 'first' or 'immediately after' first.
30
Logic: if-then rules
'If A then B' does not mean 'if B then A'. If B is false, then A must be false.

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