GCSE Mathematics Higher Tier Paper 1 Exam Review

This set of flashcards covers the vocabulary, mathematical concepts, and specific problem-solving terms found in the GCSE Mathematics Higher Tier Paper 1 (Non-Calculator) transcript.

GCSE Mathematics Higher Tier Paper 1

A non-calculator assessment with a time allowed of $1$ hour $30$ minutes and a maximum mark of $80$.

Simultaneous equations

A set of equations, such as $2x + 5y = 18$ and $2x + y = 6$, that are solved together to find common values for the variables $x$ and $y$.

Integer inequality

A mathematical statement like $1.07 < 9x < 1.17$ where the variable $x$ must be a whole number.

Density

The mass per unit volume of a substance; in the transcript, a metal solid has a density of $8.5\,g/cm^3$ and a volume of $11\,cm^3$.

Inter-quartile range

A statistical measure representing the spread of the middle $50\%$ of a data set, calculated from a list of numbers such as the $11$ provided values ranging from $2$ to $33$.

Mean mark

The average value of marks for a group; for School A this is stated as $61$ and for School B it is $56$.

Range of marks

The difference between the highest and lowest marks in a set, which is $14$ for School A and $21$ for School B.

Standard form

A method of writing numbers in the form $A \times 10^n$; used in the transcript to express calculations like $0.6 \div 100$ and $40 \times 30 \times 10^5$.

Frequency tree

A diagram used to show how a total (such as $330$ students) is divided into subgroups (Year 10 and Year 11) and further sub-categories (winning a medal).

Translation vector

A column vector in the form $\begin{pmatrix} x \\ y \end{pmatrix}$ that describes the movement of a shape from one position to another on a coordinate grid.

Consecutive cube numbers

Whole numbers that follow each other in the sequence of cubes ($n^3$), denoted as $c$ and $d$ where $c < 4.5^3 < d$.

Isosceles triangle

A triangle with at least two equal sides; triangle $ABC$ in the text is isosceles where side lengths $AC = BC$.

Venn diagram

A diagram using circles to represent sets and their relationships, such as the overlap (intersection) or union of events A and B.

Exact trigonometric values

Precise values for trigonometric functions used in non-calculator calculations, such as $\sin(30^\circ)$, $\cos(45^\circ)$, and $\tan(60^\circ)$.

Surd form

The representation of numbers using roots, such as expressing $\sqrt{44} + \sqrt{99} + \sqrt{275}$ in the simplified form $a\sqrt{n}$.

Graph transformation $y = -f(x)$

A reflection of the original graph of the function $y = f(x)$ in the x-axis.

Graph transformation $y = f(x) + 1$

A vertical translation of the original graph of the function $y = f(x)$ by $1$ unit upwards.

Turning point

The coordinates of the vertex of a curve; for the equation $y = (x - 3)^2 - 8$, it is identified from the completed square form.

Selection without replacement

A probability scenario where an item (such as a black counter) is chosen and not put back, changing the total number of items $n$ for the subsequent selection.