Custom post type and taxonomy slug issue

I’m working with custom post types in WordPress and have a question about slugs.

Let’s say that we need to create custom post type Quiz with taxonomy Quiz Category. I’ve used the following code:

// Create and register custom post type quiz
function create_posttype_quiz() {
    $labels = array(
        'name'               => _x( 'Quiz', 'post type general name' ),
        'singular_name'      => _x( 'Quiz', 'post type singular name' ),
        'add_new'            => _x( 'Add New', 'quiz' ),
        'add_new_item'       => __( 'Add New Quiz' ),
        'edit_item'          => __( 'Edit Quiz' ),
        'new_item'           => __( 'New Quiz' ),
        'all_items'          => __( 'All Quiz' ),
        'view_item'          => __( 'View Quiz' ),
        'search_items'       => __( 'Search Quiz' ),
        'not_found'          => __( 'No quiz found' ),
        'not_found_in_trash' => __( 'No quiz found in the Trash' ), 
        'parent_item_colon'  => '',
        'menu_name'          => 'Quizzes'
    );
    $args = array(
        'labels'        => $labels,
        'description'   => 'Holds our quiz and quiz specific data',
        'public'        => true,
        'menu_position' => 5,
        'supports'      => array( 'title', 'editor' ),
        'has_archive'   => true,
        'rewrite' => array('slug' => 'quiz'),
        'show_ui'             => true,
        'show_in_menu'        => true,
        'show_in_nav_menus'   => true,

    );

    register_post_type( 'quiz', $args );    
}
add_action( 'init', 'create_posttype_quiz' );

// Create and register quiz categories
function create_taxonomies_quiz() {
    $labels = array(
        'name'              => _x( 'Quiz Categories', 'taxonomy general name' ),
        'singular_name'     => _x( 'Quiz Category', 'taxonomy singular name' ),
        'search_items'      => __( 'Search Quiz Categories' ),
        'all_items'         => __( 'All Quiz Categories' ),
        'parent_item'       => __( 'Parent Quiz Category' ),
        'parent_item_colon' => __( 'Parent Quiz Category:' ),
        'edit_item'         => __( 'Edit Quiz Category' ), 
        'update_item'       => __( 'Update Quiz Category' ),
        'add_new_item'      => __( 'Add New Quiz Category' ),
        'new_item_name'     => __( 'New Quiz Category' ),
        'menu_name'         => __( 'Quiz Categories' ),
    );
    $args = array(
        'labels' => $labels,
        'hierarchical' => true,
        //'show_admin_column'=> true,
        'rewrite' => array('hierarchical'=>true, 'slug'=>'quizzes', 'with_front'=>false),
    );
    register_taxonomy( 'quiz_category', 'quiz', $args );
}
add_action( 'init', 'create_taxonomies_quiz', 0 );

Everything works fine, I’m able to create and edit quizzes, add them to quiz categories etc. Also, I can access quizzes on frontend, e.g. site.com/quiz/sample-quiz-one, site.com/quiz/sample-quiz-two… and list quizzes in quiz categories, e.g. site.com/quizzes/category-one, site.com/quizzes/category-two…

The problem is that I can’t list quizzes under site.com/quizzes but at site.com/quiz instead. (site.com/quizzes will create page not found error).

Basically, I would like to be able to:

• access a single quiz at url: site.com/quiz/sample-quiz-one
• list all quizzes at site.com/quizzes rather than site.com/quiz.

Is it possible to achieve this without htaccess or any other redirection, but using the code above (maybe some args I’m not aware of)?