GCSE Mathematics practice paper — Foundation tier (50 marks)

\documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage[margin=2cm]{geometry}
\usepackage{amsmath, amssymb}
\usepackage{enumitem}
\usepackage{fancyhdr}

\pagestyle{fancy}
\fancyhf{}
\rhead{Practice paper}
\lhead{GCSE Mathematics --- Foundation tier}
\rfoot{Page \thepage}

\begin{document}

\begin{center}
{\large\bfseries GCSE Mathematics Practice --- Foundation Tier}\\[0.3em]
{\small Time: 90 minutes --- Calculator allowed --- Total: 50 marks}
\end{center}

\noindent\hrulefill

\section*{Question 1 \hfill (5 marks)}

Work out the value of:
\begin{enumerate}[label=\textbf{(\alph*)}]
  \item $\displaystyle \frac{3}{4} + \frac{2}{5}$
  \item $\displaystyle \frac{7}{8} - \frac{1}{6}$
  \item $7 - 3 \times (4 + 1)$
\end{enumerate}

\section*{Question 2 \hfill (6 marks) --- Ratio and proportion}

A recipe uses flour and sugar in the ratio $5 : 2$. To make a cake, $350$\,g of flour are used.

\begin{enumerate}[label=\textbf{(\alph*)}]
  \item How many grams of sugar are needed?
  \item What is the total mass of flour and sugar?
  \item Express the mass of sugar as a percentage of the total mass.
\end{enumerate}

\section*{Question 3 \hfill (8 marks) --- Algebra}

\begin{enumerate}[label=\textbf{(\alph*)}]
  \item Solve $5x - 7 = 23$.
  \item Expand $3(2x - 1) - 2(x + 4)$.
  \item Factorise $x^2 - 6x$.
  \item Make $y$ the subject of $4x + 3y = 12$.
\end{enumerate}

\section*{Question 4 \hfill (10 marks) --- Pythagoras' theorem}

A ladder of length $5$\,m is leant against a vertical wall. The base of the ladder is $1.4$\,m from the wall.

\begin{enumerate}[label=\textbf{(\alph*)}]
  \item Make a clear sketch.
  \item Calculate how high up the wall the ladder reaches. Give your answer to $2$ decimal places.
  \item State one assumption you have made.
\end{enumerate}

\section*{Question 5 \hfill (10 marks) --- Statistics}

The table shows the marks of $25$ students:
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
Mark out of 10 & 4 & 6 & 7 & 9 \\ \hline
Frequency      & 3 & 8 & 9 & 5 \\ \hline
\end{tabular}
\end{center}

\begin{enumerate}[label=\textbf{(\alph*)}]
  \item Find the mode.
  \item Calculate the mean (give your answer to $1$ decimal place).
  \item Find the median.
\end{enumerate}

\section*{Question 6 \hfill (11 marks) --- Probability}

A bag contains $4$ red balls, $3$ blue balls and $5$ green balls. A ball is taken at random.

\begin{enumerate}[label=\textbf{(\alph*)}]
  \item Write down the probability that the ball is blue.
  \item A second ball is taken without replacement. Draw a probability tree showing the outcomes ``red'' versus ``not red'' for both draws.
  \item Calculate the probability that both balls drawn are red.
\end{enumerate}

\end{document}