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GCSEMathsAQAHigherFlashcards2. AlgebraIntroduction to Algebra

Introduction to Algebra (AQA GCSE Maths)

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  • True or False?

    The expression 4 open parentheses a plus b close parentheses means 4 cross times open parentheses a plus b close parentheses.

    True.

    The expression 4 open parentheses a plus b close parentheses means 4 cross times open parentheses a plus b close parentheses.

  • True or False?

    The expression 3 a b means 3 plus a plus b.

    False.

    The expression 3 a b means 3 cross times a cross times b.

  • True or False?

    The expression f over 2 minus x y means f divided by 2 minus x cross times y.

    True.

    The expression f over 2 minus x y means f divided by 2 minus x cross times y.

  • True or False?

    The expression 2 t squared  means 2 cross times t cross times 2.

    False.

    The expression 2 t squared  means 2 cross times t squared, which is the same as 2 cross times t cross times t.

  • True or False?

    The items in the following list are all examples of terms that you may come across in algebra: y comma space a squared comma space 20 comma space 7 x.

    True.

    y comma space a squared comma space 20 comma space 7 x are all examples of terms that you may come across in algebra.

    A term is either:

    • a letter (variable) on its own, e.g. y,

    • a variable raised to a power, e.g. a squared,

    • a number on its own, e.g. 20,

    • or a number multiplied by a letter, e.g. 7 x.

  • In algebra, what is a variable?

    A variable is a letter that appears in a term.

    E.g. In the expression x squared minus 2 y plus 6, the x and y are both variables.

  • In algebra, what is a constant?

    A constant is a term that is a number only.

    There is no letter (variable) part.

    E.g. In the expression x squared plus 3 x minus 5, the negative 5 is the only constant term.

  • In algebra, what is an expression?

    An expression in algebra is a mathematical statement that does not have an equals sign.

    It can include terms that are combined using operations like addition, subtraction, multiplication, and division.

    E.g. 5 x squared plus y is an algebraic expression.

  • True or False?

    In the expression 4 x cubed plus x squared minus 6, the coefficient of the 4 x cubed term is 3.

    False.

    In the expression 4 x cubed plus x squared minus 6, the coefficient of the 4 x cubed term is not 3.

    In an algebraic expression, the coefficient of a term is the number in front of the letter (variable).

    E.g. In the expression 4 x cubed plus x squared minus 6, the coefficient of the 4 x cubed term is 4.

  • True or False?

    x squared plus 8 x minus 2 is an equation.

    False.

    x squared plus 8 x minus 2 is not an equation.

    An equation in algebra is a mathematical statement with an equals sign between a left-hand side and a right-hand side.

    The equals sign indicates that both sides are equal in value.

  • Define the word formula in algebra.

    A formula in algebra is a rule, definition, or relationship between different quantities, written in shorthand using letters.

    E.g. x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction is the quadratic formula.

  • True or False?

    A formula on its own can be solved.

    False.

    A formula on its own cannot be solved.

    You need to substitute values into the formula to turn it into an equation that can be solved.

    E.g. a squared plus b squared equals c squared cannot be solved unless you know two of the variables.

  • What does substitution mean in algebra?

    Substitution in algebra is the process of replacing letters in a formula with their corresponding numerical values (inputs) in order to calculate an output of the formula.

    E.g. If v equals 3 and a equals negative 5, substituting them into the formula a squared plus 2 v equals t would give open parentheses negative 5 close parentheses plus 2 cross times 3 equals t.

  • True or False?

    When substituting in the number g equals negative 3 you should replace g with open parentheses negative 3 close parentheses, not negative 3.

    True.

    It is important to put brackets around any negative numbers that you substitute into an algebraic expression.

    E.g. Substitute g equals negative 3 into the expression 4 g squared.

    If you use brackets it will give you the correct answer 4 cross times open parentheses negative 3 close parentheses squared equals 4 cross times 9 equals 36.

    If you don't use brackets it will give an incorrect answer 4 cross times negative 3 squared equals 4 cross times negative 9 equals negative 36.

  • True or False?

    You can rearrange a formula first before substituting numbers in.

    True.

    You can rearrange a formula first, before substituting numbers in.

    E.g. A equals l cross times w can be rearranged as l equals A over w if you know the values of Aand w, and want to substitute to find the value of l.

  • True or False?

    It is a good idea to simplify an expression before substituting in values.

    E.g. simplifying the expression 2 a plus 7 t minus 2 open parentheses 5 a plus t close parentheses to 5 t minus 8 a before substitution.

    True.

    It is a good idea to simplify an expression before substituting in values.

    Doing this reduces the number of substitutions you need to do (and the number of errors you could make).

  • True or False?

    Substituting y equals 2 into negative 3 y squared will give open parentheses negative 6 close parentheses squared which is 36.

    False.

    You do not multiply negative 3 by y first. You need to do the power y squared first (from BIDMAS).

    This gives negative 3 cross times 2 squared which simplifies to negative 3 cross times 4 which is negative 12.

  • True or False?

    The term x y is the same as the term y x.

    True.

    The term x y is the same as the term y x, as they both represent x multiplied by y.

    Multiplication can be done in either order.

  • True or False?

    When collecting like terms, 2 x plus 3 y is the same as 5 x y.

    False.

    The terms 2 x and 5 y are not like terms because their letters (variables) are different.

    They cannot be combined, so the expression must be left as 2 x plus 5 y.

  • True or False?

    There are no like terms in the expression 2 x squared minus 2 x plus 2.

    True.

    There are no like terms in the expression 2 x squared minus 2 x plus 2.

    This expression cannot be simplified any further.

  • True or False?

    4 q cubed and negative 8 q open parentheses q squared close parentheses are like terms.

    True.

    4 q cubed and negative 8 q open parentheses q squared close parentheses are like terms as negative 8 q open parentheses q squared close parentheses simplifies to negative 8 q cubed.

Previous:Using a CalculatorNext:Algebraic Roots & Indices

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    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

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    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

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation