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Number Toolkit (Edexcel IGCSE Maths A)

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    What is an exponent?

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Cards in this collection (33)

  • What is an exponent?

    An exponent is a power or order used in mathematical expressions to represent repeated multiplication of a base number.

    E.g. In the expression 4 to the power of 5, the 5 is the exponent.

  • What does the symbol ≈ mean?

    The symbol ≈ means approximately equal to.

  • True or False?

    The equals sign (=) is used to show that two expressions are identical.

    False.

    The equals sign (=) is used to show that two expressions are equal, while the identical sign (≡) is used to show that two expressions are identical.

  • What is an inequality?

    An inequality is a statement that compares two quantities in terms of their size using symbols such as >, <, ≥, or ≤.

  • True or False?

    The symbol ± is used to represent two distinct answers.

    True.

    The symbol ± is used to represent two distinct (different) answers, often in quadratic equations.

  • What does this symbol square root of blank end root represent?

    square root of blank end root is the positive square root.

    It represents the positive result when you find perform the opposite (inverse) operation of squaring a number.

    negative square root of blank end root is the negative square root.

  • What do the letters of BIDMAS/BODMAS represent?

    The letters in BIDMAS/BODMAS represent: Brackets, Indices, Division, Multiplication, Addition, Subtraction.

    BIDMAS/BODMAS is an acronym that stands for the order of operations in mathematics.

  • True or False?

    When using BIDMAS/BODMAS on a calculation that only involves addition and subtraction, the calculation should be performed from left to right.

    E.g. table row blank blank cell 2 minus 5 plus 7 minus 3 minus 2 end cell end table

    True.

    When using BIDMAS/BODMAS on a calculation that only involves addition and subtraction, the calculation should be performed from left to right.

    E.g. table row blank blank cell 2 minus 5 plus 7 minus 3 minus 2 end cell end table
    table row blank equals cell negative 3 plus 7 minus 3 minus 2 end cell row blank equals cell 4 minus 3 minus 2 end cell row blank equals cell 1 minus 2 end cell row blank equals cell negative 1 end cell end table

  • True or False?

    When using BIDMAS/BODMAS on a calculation that only involves multiplication and division, the divisions should always be performed first.

    E.g. 3 cross times 8 divided by 2 cross times 9

    False.

    When using BIDMAS/BODMAS on a calculation that only involves multiplication and division, the calculation should be performed from left to right.

    E.g. 3 cross times 8 divided by 2 cross times 9
    equals 24 divided by 2 cross times 9 equals 12 cross times 9 equals 108

  • True or False?

    Multiplying two negative numbers results in a negative value.

    False.

    When multiplying two negative numbers, the result is a positive value.

  • When multiplying a positive and a negative, is the resultant value positive or negative?

    When multiplying a positive and a negative, the result is a negative value.

  • True or False?

    Subtracting a negative number is the same as adding a positive number.

    True.

    Subtracting a negative number is the same as adding a positive number.

  • True or False?

    When finding the square of a negative number, the result is positive.

    True.

    When finding a square of a negative number, the result is positive.

    This is because you are multiplying a negative by a negative, which results in a positive.

  • When finding the cube of a negative number, is the result positive or negative?

    When finding the cube of a negative number, you are multiplying a negative by a negative, by a negative so the final result is a negative.

  • True or False?

    Subtracting a negative from a number will always result in a positive answer.

    False.

    Although subtracting a negative number is equivalent to adding a positive number, the final result will only be positive if the number you are adding it to is large enough.

    For example, the calculation negative 3 minus negative 5 equals 2 but the calculation negative 7 minus negative 5 equals negative 2.

  • True or False?

    open parentheses negative 3 close parentheses squared equals negative 3 squared

    False.

    open parentheses negative 3 close parentheses squared equals negative 3 cross times negative 3 equals 9 but negative 3 squared equals negative open parentheses 3 cross times 3 close parentheses equals negative 9.

    It is always important to put brackets around negative values when you are substituting them into calculations!

  • Define the term currency.

    A currency is a system of money in general use in a particular country or region.

  • True or False?

    Final answers in calculations with money should always be rounded to the nearest integer.

    False.

    You should usually round answers involving money to two decimal places.

    However, you may sometimes be asked to round answers to the nearest integer.

  • True or False?

    Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number, e.g. nearest dollar.

    True.

    Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number.

  • True or False?

    Monetary values given in more than two decimal places within a question should be rounded to two decimal places before doing any calculations.

    False.

    Monetary values given in more than two decimal places should be used in the working.

    They should only be rounded for the final answer.

  • What mathematical operation does the word sum imply?

    The word sum implies that you need to add numbers together.

  • If you are asked to find the difference of two numbers, which operation should you use?

    Subtraction is the mathematical operation of finding the difference between two numbers by taking one number away from another.

  • True or False?

    The word share implies that you need to divide numbers.

    True.

    The word share implies that you need to divide numbers.

  • What mathematical operation is implied by a question asking you to find the product of two or more numbers?

    The word product is often used to imply that you need to multiply two numbers together.

  • How can you perform a division by cancelling common factors in a fraction?

    E.g. 1008 divided by 28

    A division can be treated like a fraction where common factors from both the numerator and denominator can be found and cancelled.

    E.g. 1008 divided by 28 can be written as 1008 over 28

    You can then cancel it to its simplest form by finding common factors, 1008 over 28 equals 504 over 14 equals 252 over 7 equals 36

  • How can estimation be used to check answers when multiplying and dividing with decimals?

    Use estimation to rounding the numbers to integer values, perform the simpler calculation and compare the estimated value with your actual value.

  • How can you use an 'easier' calculation to calculate a decimal division problem?

    E.g. 2.4 divided by 0.08?

    Turn the division into a fraction, e.g. 2.4 divided by 0.08 equals fraction numerator 2.4 over denominator 0.08 end fraction

    Multiply the values by a multiple of 10 to change them to integers,
    e.g. fraction numerator 2.4 cross times 10 over denominator 0.08 cross times 100 end fraction equals 24 over 8

    Simplify the fraction (complete the easier calculation), e.g. 3

    Convert the answer by 'undoing' the initial changes, e.g. fraction numerator 3 cross times 100 over denominator 10 end fraction equals 30

  • True or false?

    a cross times b is the same as b cross times a.

    True.

    a cross times b is the same as b cross times a.

    For example, 5 cross times 0.05 is the same as 0.05 cross times 5.

    It is okay to swap them round.

  • True or false?

    a minus b is the same as b minus a.

    False.

    a minus b is not the same as b minus a.

    For example, 10 minus 2 is not the same as 2 minus 10.

    The first gives 8 but the second gives negative 8.

  • True or false?

    If 6 cross times 17 equals 102 then 17 equals 6 over 102.

    False.

    The correct answer is: if 6 cross times 17 equals 102 then 17 equals 102 over 6.

    That is because a cross times b equals c means b equals c over a (the c stays on the top of the fraction).

  • How would you use the fact that 9 cross times 15 equals 135 to work out 900 cross times 150 ?

    You could write 900 cross times 150 as 9 cross times 10 cross times 10 cross times 15 cross times 10.

    Then bring the 9 and 15 together, giving 9 cross times 15 cross times 10 cross times 10 cross times 10.

    You know that 9 cross times 15 equals 135 so the number above becomes 135 cross times 10 cross times 10 cross times 10.

    Multiplying by ten each time adds an extra zero, so the answer is 135 space 000.

  • True or false?

    If 3 cross times 2 equals 6 then 0.3 cross times 0.2 equals 0.6.

    False.

    0.3 cross times 0.2 is the same as open parentheses 3 divided by 10 close parentheses cross times open parentheses 2 divided by 10 close parentheses.

    This is also the same as open parentheses 3 cross times 2 close parentheses divided by open parentheses 10 cross times 10 close parentheses.

    Alternatively, you can use fractions to see this: 3 over 10 cross times 2 over 10 equals 6 over 100.

    The correct answer is 0.3 cross times 0.2 equals 0.06.

  • What is the first line of working when simplifying fraction numerator 126 over denominator 1.4 end fraction?

    fraction numerator 126 over denominator 1.4 end fraction equals 1260 over 14.

    You multiply the top and bottom of the fraction by 10 to remove the decimal.

    These two fractions are identical, so you can continue working on the second one.

Next:Set Notation & Venn Diagrams

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions

    6. Topic 6

      Percentages

    7. Topic 7

      Compound Interest & Depreciation

    8. Topic 8

      Fractions, Decimals & Percentages

    9. Topic 9

      Rounding, Estimation & Bounds

    10. Topic 10

      Surds

    11. Topic 11

      Using a Calculator

    12. Topic 12

      Ratio Toolkit

    13. Topic 13

      Ratio Problem Solving

    14. Topic 14

      Exchange Rates & Best Buys

    15. Topic 15

      Direct & Inverse Proportion

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Solving Linear Equations

    10. Topic 10

      Solving Quadratic Equations

    11. Topic 11

      Solving Inequalities

    12. Topic 12

      Simultaneous Equations

    13. Topic 13

      Forming & Solving Equations

    1. Topic 1

      Sequences

    2. Topic 2

      Functions

    3. Topic 3

      Coordinate Geometry

    4. Topic 4

      Linear Graphs y = mx + c

    5. Topic 5

      Graphs of Functions

    6. Topic 6

      Estimating Gradients

    7. Topic 7

      Real-Life Graphs

    8. Topic 8

      Graphing Inequalities

    9. Topic 9

      Transformations of Graphs

    10. Topic 10

      Differentiation

    1. Topic 1

      Standard & Compound Units

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing & Constructions

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Right-Angled Triangles - Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Histograms

    3. Topic 3

      Cumulative Frequency Diagrams

    4. Topic 4

      Probability Toolkit

    5. Topic 5

      Probability Diagrams - Venn & Tree Diagrams

    6. Topic 6

      Combined & Conditional Probability