GCSE Maths: Algebra and Equations Flashcards

Question 1

Define Algebraic Expression.

Accepted Answer

A collection of letters and numbers joined by operations, with no equals sign anywhere in it. Because nothing is being equated, an expression can be simplified or evaluated but never solved.

Question 2

What is Term?

Accepted Answer

One separate part of an expression, made of numbers and letters multiplied together and separated from its neighbours by a plus or minus sign.

Question 3

Define Like Terms.

Accepted Answer

Terms carrying exactly the same combination of letters raised to exactly the same powers. Only these may be added or subtracted together, because the letter part stays untouched while the numbers in front combine.

Question 4

What is Identity?

Accepted Answer

A statement that stays true whatever numbers the letters stand for, so it has infinitely many solutions rather than a few. Examiners write it with the three-bar symbol instead of an equals sign.

Question 5

What is Formula?

Accepted Answer

A rule written in algebra that connects two or more quantities, letting you calculate one of them once the others are known. It is stated as an equality and reused with different numbers.

Question 6

Define Subject of a Formula.

Accepted Answer

The single letter standing alone on one side of a formula, with everything else on the other side. Changing the subject means rearranging so a different letter is the one left by itself.

Question 7

Define Inverse Operation.

Accepted Answer

The operation that undoes another one, used to isolate a letter during rearranging. Addition and subtraction undo each other, as do multiplication and division, and squaring and taking the square root.

Question 8

Define Balance Method.

Accepted Answer

The rule that whatever operation you apply to one side of an equation you must apply identically to the other, keeping the two sides equal while the unknown is gradually isolated.

Question 9

Define Common Factor.

Accepted Answer

A number or letter that divides exactly into every term of an expression. Taking the highest one outside a bracket is the first move examiners look for before any other method.

Question 10

Define Difference of Two Squares.

Accepted Answer

The pattern in which one square is subtracted from another, which always splits into two brackets holding the same pair of terms with opposite signs.

Question 11

Define Completed Square Form.

Accepted Answer

A quadratic rewritten as a squared bracket plus a number, in the shape (x + p)² + q. The rewrite exposes the graph's turning point and gives an exact route to the solutions.

Question 12

Define Quadratic Formula.

Accepted Answer

The general solution x = (−b ± √(b² − 4ac)) ÷ 2a, which works on any quadratic written as ax² + bx + c = 0. It is the standard method when no bracket pair can be found.

Question 13

What is Discriminant?

Accepted Answer

The part under the square root sign, b² − 4ac, whose sign tells you how many real solutions a quadratic has: two when positive, one repeated when zero, and none when negative.

Question 14

What is Root?

Accepted Answer

A value of the unknown that makes an equation true, and on a graph the place where the curve meets the horizontal axis. Roots are also called solutions or zeros.

Question 15

Define Turning Point.

Accepted Answer

The single place on a quadratic graph where it stops falling and starts rising, or the reverse. It is the lowest point of a positive curve and the highest point of a negative one.

Question 16

What is Parabola?

Accepted Answer

The smooth U-shaped curve every quadratic graph makes. It opens upwards when the number in front of the squared term is positive and downwards when that number is negative.

Question 17

Define Simultaneous Equations.

Accepted Answer

Two or more equations in two or more unknowns that must all hold at once, so the answer is the pair of values satisfying every equation rather than just one of them.

Question 18

Define Elimination Method.

Accepted Answer

A way of handling two equations by matching the numbers in front of one unknown, then adding or subtracting the equations so that unknown disappears and a single-letter equation is left.

Question 19

Define Substitution Method.

Accepted Answer

A way of handling two equations by rearranging one to make a letter the subject, then replacing that letter in the other equation so only a single unknown remains.

Question 20

What is Index?

Accepted Answer

The small raised number recording how many times a base is multiplied by itself. Its plural is indices, and the laws governing them let powers be combined without writing the multiplication out.

Question 21

Define Negative Index.

Accepted Answer

A power written with a minus sign, which instructs you to take the reciprocal of the positive power rather than to produce a negative answer.

Question 22

Define Fractional Index.

Accepted Answer

A power written as a fraction, where the bottom number gives the root to take and the top number gives the power to raise the result to.

Question 23

Define Strict Inequality.

Accepted Answer

A comparison using the symbols for less than or greater than only, which excludes the boundary value itself. It is drawn on a number line with an open, unshaded circle.

Question 24

Define Solution Set.

Accepted Answer

The complete collection of values that satisfy a statement. For an inequality it is usually an infinite stretch of the number line, described by a range rather than listed one by one.

Question 25

Define Nth Term.

Accepted Answer

A rule in terms of the position number n that generates any entry of a sequence directly, without needing the entries before it. Substituting the position returns that entry.

Question 26

Define Position-to-Term Rule.

Accepted Answer

Another name for a rule that converts a position number straight into the entry sitting at that position, in contrast to a rule that works from the previous entry onwards.

Question 27

Define Term-to-Term Rule.

Accepted Answer

A rule describing how to get from one entry of a sequence to the next one. It needs a starting value to be useful and becomes slow for entries far along the sequence.

Question 28

Define Arithmetic Sequence.

Accepted Answer

A sequence in which the same amount is added or subtracted each time, so the gap between neighbouring entries never changes. Its rule always takes the form of that common gap multiplied by n, plus a number.

Question 29

Define Geometric Sequence.

Accepted Answer

A sequence built by multiplying by the same number each time, called the common ratio. Dividing any entry by the one before it returns that ratio.

Question 30

Define Quadratic Sequence.

Accepted Answer

A sequence whose gaps between entries are themselves changing, but whose gaps between those gaps stay the same. Its rule contains an n² term, and half the constant second difference gives the number in front of n².

Question 31

Define Fibonacci-Type Sequence.

Accepted Answer

A sequence in which each entry is found by adding the two entries immediately before it, so two starting values are needed before it can be continued.

Question 32

Define Function Notation.

Accepted Answer

The shorthand in which a rule is named and the input written in brackets after it, so that writing a number inside the brackets means substituting that number into the rule.

Question 33

Define Inverse Function.

Accepted Answer

The rule that reverses another rule, taking an output back to the input it came from. It is found by writing the rule as an equation and making the input the subject.

Question 34

What is Iteration?

Accepted Answer

A method of approximating a solution by feeding a starting estimate into a rearranged rule, then feeding each answer back in repeatedly until the digits settle to the required accuracy.

Question 35

Define Algebraic Proof.

Accepted Answer

An argument using letters rather than examples to show a statement holds in every case. Marks come from choosing general expressions and finishing with a written conclusion, not from testing numbers.

Question 36

What is Counterexample?

Accepted Answer

One specific case that makes a claim false, which is all that is needed to disprove it. Examples can never prove a claim true, but a single one can settle that it is untrue.

Question 37

Define Algebraic Fraction.

Accepted Answer

A fraction whose top or bottom contains letters. It is simplified by factorising both parts first and cancelling any bracket appearing in each, exactly as numerical fractions cancel shared factors.