Quiz with answer (please recommend me a format of TeX document)

Question

I want to make a quiz using TeX that "looks like"

Problem 1) Let $f(x)=x^2$. Evaluate $f'(1)$.

Problem 2) Let $A$ be a matrix such that
$$A=\begin{bmatrix}3&1\0&1\end{bmatrix}$$ What is the value of $|A|$?

Answer1) 2

Answer2) 3

And I made a TeX file "written as"

\documentclass{article}

\usepackage{amsmath,amssymb}

\newcounter{num}
\newcommand{\prob}{\par\bigskip\bigskip\noindent\refstepcounter{num}\textbf{Problem \arabic{num}) }}
\newcommand{\ans}{\par\bigskip\bigskip\noindent\refstepcounter{num}\textbf{Answer \arabic{num}) }}

\begin{document}
\prob
Let $f(x)=x^2$.
Evaluate $f'(1)$.
 
\prob
Let $A$ be a matrix such that
$$A=\begin{bmatrix}3&1\\0&1\end{bmatrix}.$$
What is the value of $|A|$?

\setcounter{num}{0}

\ans
2
\ans
3
\end{document}

It prints the result pretty well, except for the fact that the problem statements and answers are separated.

I want to type answer 1 just after problem 1, which would prevent many kinds of errors.

How can I fix my code?

Answer 1

With the options answerdelayed of exercise package, you can write the answer near the problem in your code, but print them only when you like with \shipoutAnswer.

I think exercise is the simplest package for exercises, if you find its documentation lengthy, I don't know what you would say of TikZ one! :D

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage[lastexercise,answerdelayed]{exercise}
\renewcommand{\ExerciseName}{Problem}
\renewcommand{\ExerciseHeader}{\noindent\ExerciseName\ \ExerciseHeaderNB)}
\renewcommand{\AnswerName}{Answer}
\renewcommand{\AnswerHeader}{\noindent\AnswerName\ \ExerciseHeaderNB)\ }

\begin{document}
\begin{Exercise}
    Let $f(x)=x^2$.
    Evaluate $f'(1)$.
\end{Exercise}
\begin{Answer}
    2
\end{Answer}
\begin{Exercise}
    Let $A$ be a matrix such that
    \[A=\begin{bmatrix}3&1\\0&1\end{bmatrix}.\]
    What is the value of $|A|$?
\end{Exercise}
\begin{Answer}
    3
\end{Answer}
\shipoutAnswer
\end{document}

Edit: if you prefer commands instead of environments:

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage[lastexercise,answerdelayed]{exercise}
\renewcommand{\ExerciseName}{Problem}
\renewcommand{\ExerciseHeader}{\noindent\ExerciseName\ \ExerciseHeaderNB)}
\renewcommand{\AnswerName}{Answer}
\renewcommand{\AnswerHeader}{\noindent\AnswerName\ \ExerciseHeaderNB)\ }

\newcommand{\prob}[1]{\begin{Exercise}#1\end{Exercise}}
\newcommand{\ans}[1]{\begin{Answer}#1\end{Answer}}

\begin{document}
\prob{Let $f(x)=x^2$.
    Evaluate $f'(1)$.}
\ans{2}
\prob{Let $A$ be a matrix such that
    \[A=\begin{bmatrix}3&1\\0&1\end{bmatrix}.\]
    What is the value of $|A|$?}
\ans{3}
\shipoutAnswer
\end{document}