Maths · OCR Paper 1
Number Without a Calculator
The number skills tested on OCR Paper 1: place value and the four operations, factors and primes, fractions, percentages, and powers and roots, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Place Value, Negatives and the Four Operations
How to read, order and calculate with whole numbers, decimals and negative numbers by hand, and how BIDMAS decides what to do first.
10 terms -
2
Factors, Multiples and Primes
Prime factors, HCF and LCM: how to find them without a calculator and how to use them to solve problems.
10 terms -
3
Fractions
Simplifying, adding, subtracting, multiplying and dividing fractions and mixed numbers, exactly and without a calculator.
10 terms -
4
Fractions, Decimals and Percentages
Converting between the three forms, finding percentages by hand, and solving percentage change and reverse percentage problems.
10 terms -
5
Powers, Roots and Indices
Squares, cubes and roots to recall, the laws of indices, and zero, negative and fractional powers.
10 terms
Key terms in this chapter
All 50, gathered from every lesson.
- Estimate
- An approximate answer found by rounding the numbers in a calculation first.
- Place value
- The value a digit has because of the column it is in.
- Integer
- A whole number, which may be positive, negative or zero.
- Decimal place
- The position of a digit after the decimal point.
- Sum
- The result of adding numbers together.
- Difference
- The result of subtracting one number from another.
- Product
- The result of multiplying numbers together.
- Quotient
- The result of dividing one number by another.
- Negative number
- A number less than zero.
- BIDMAS
- The order in which to do operations: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
- Common factor
- A number that is a factor of two or more different numbers.
- Factor
- A whole number that divides exactly into another number.
- Multiple
- A number in the times table of a given number.
- Prime number
- A number greater than 1 with exactly two factors, 1 and itself.
- Prime factor
- A factor that is also a prime number.
- Product of prime factors
- A number written as prime numbers multiplied together, such as \(12 = 2^2 \times 3\).
- Highest common factor (HCF)
- The largest number that divides exactly into two or more numbers.
- Lowest common multiple (LCM)
- The smallest number that is a multiple of two or more numbers.
- Square number
- The result of multiplying a whole number by itself.
- Cube number
- The result of multiplying a whole number by itself and then by itself again.
- Proportion
- A part compared with the whole, written as a fraction.
- Numerator
- The top number of a fraction, which counts the parts taken.
- Denominator
- The bottom number of a fraction, which shows how many equal parts make the whole.
- Equivalent fraction
- A fraction with a different numerator and denominator but the same value.
- Simplest form
- A fraction whose numerator and denominator have no common factor except 1.
- Improper fraction
- A fraction whose numerator is bigger than or equal to its denominator.
- Mixed number
- A number made of a whole number and a proper fraction, such as \(2\frac{3}{4}\).
- Common denominator
- A denominator shared by two or more fractions, found using a common multiple.
- Reciprocal
- The fraction turned upside down; a number multiplied by its reciprocal gives 1.
- Unit fraction
- A fraction with a numerator of 1.
- Recurring decimal
- A decimal with one or more digits that repeat for ever, shown with a dot above them.
- Percentage
- A number written as a fraction of 100, using the symbol %.
- Per cent
- Out of every hundred.
- Equivalent
- Having the same value but written in a different form.
- Multiplier
- The number you multiply by to apply a percentage change, such as 1.2 for a 20% increase.
- Percentage increase
- A rise in a quantity written as a percentage of its original value.
- Percentage decrease
- A fall in a quantity written as a percentage of its original value.
- Percentage change
- The change divided by the original amount, multiplied by 100.
- Reverse percentage
- A problem where you are given the value after a change and must find the original.
- Original value
- The amount before a percentage increase or decrease is applied.
- Power of 10
- A number such as \(10^2\), \(10^3\) or \(10^{-2}\), where 10 is raised to a whole-number index.
- Index (power)
- The small raised number that shows how many times the base is multiplied by itself.
- Indices
- The plural of index.
- Base
- The number that is being multiplied by itself in a power, such as 2 in \(2^5\).
- Square number
- The result of multiplying a whole number by itself.
- Cube number
- The result of multiplying a whole number by itself twice.
- Square root
- A number that, when multiplied by itself, gives the original number.
- Cube root
- A number that, when multiplied by itself twice, gives the original number.
- Reciprocal
- One divided by the number; the reciprocal of \(a\) is \(\dfrac{1}{a}\).
- Laws of indices
- The rules for combining powers with the same base: add to multiply, subtract to divide, multiply for a power of a power.