example of a custom form in WordPress using math Captcha plugin by BestWebSoft

gistfile1.php

// shortcode: [demo-form]
function demo_form_shortcode( $atts ) {

	$name    = '';
	$email   = '';
	$company = '';
  
	$errors = array();
	
	if ( isset( $_POST['demo_form_submitted'] )
			&& wp_verify_nonce( $_POST['demo_form_submitted'], 'demo_submission_form' ) ) {
		
		// sanitize posted values
		$name    = sanitize_text_field( $_POST['demo_name'] );
		$email   = sanitize_text_field( $_POST['demo_email'] );
		$company = sanitize_text_field( $_POST['demo_company'] );

		// using Captcha plugin
		if ( function_exists( 'cptch_check_custom_form' ) && cptch_check_custom_form() !== true ) {
			$errors['captcha'] = 'Please complete the CAPTCHA.';
		}

		// validate fields
		if ( empty( $name ) ) {
			$errors['name'] = 'Please enter your name.'; 
		}
		if ( empty( $email ) ) {
			$errors['email'] = 'Please enter your email address.';
		}
		
		if ( ! count( $errors ) ) {
			// do something with submitted data
			return '<div class="success">' .  __( 'Hey, thanks ' . $name . '!', 'yourtextdomain' ) .'</div>';
		}

	}

	// The form
	ob_start();
	?>

	<div id="demo-form">

		<p class="required-notice"><span class="required symbol"></span><?php _e( 'Required Field', 'yourtextdomain' ); ?></p>

		<form id="demo-submission-form" method="post" action="">
			<?php echo wp_nonce_field( 'demo_submission_form', 'demo_form_submitted' ); ?>

			<p class="form-field">
				<label for="demo_name"><?php _e( 'Full Name', 'yourtextdomain' ); ?></label><span class="required symbol"></span>
				<input id="demo_name" class="text" type="text" name="demo_name" value="<?php echo $name; ?>" minlength="2" required>
				<?php if ( isset( $errors['name'] ) ) : ?>
					<span class="error"><label class="error"><?php echo $errors['name']; ?></label></span>
				<?php endif; ?>
			</p>
			
			<p class="form-field">
				<label for="demo_email"><?php _e( 'Email', 'yourtextdomain' ); ?></label>
				<input id="demo_email" class="text email" type="email" name="demo_email" value="<?php echo $email; ?>">
				<?php if ( isset( $errors['email'] ) ) : ?>
					<span class="error"><label class="error"><?php echo $errors['email']; ?></label></span>
				<?php endif; ?>
			</p>

			<p class="form-field">
				<label for="demo_company"><?php _e( 'Company', 'yourtextdomain' ); ?></label>
				<input id="demo_company" class="text" type="text" name="demo_company" value="<?php echo $company; ?>">
			</p>

			<div class="demo-captcha">
				<label for="demo_captcha"><?php _e( 'Captcha', 'yourtextdomain' ); ?></label><span class="required symbol"></span>
				<div class="wrap">
					<?php
						// using Captcha plugin
						if ( function_exists( 'cptch_display_captcha_custom' ) ) {
							?><input type="hidden" name="cntctfrm_contact_action" value="true"><?php
							echo cptch_display_captcha_custom();
						}
					?>
					<?php if ( isset( $errors['captcha'] ) ) : ?>
					<p><label class="error"><?php echo $errors['captcha']; ?></label></p>
					<?php endif; ?>
				</div>
			</div>
			
			<p class="form-field">
				<input type="submit" id="demo_submit" name="demo_submit" value="<?php _e( 'submit', 'yourtextdomain' ); ?>" class="button" validate="required:true" />
			</p>

		</form>

	</div><!-- demo-form -->

	<?php
	$html = ob_get_contents();
	ob_end_clean();
	return $html;

}
add_shortcode( 'demo-form', 'demo_form_shortcode' );

Nice gist but how would you make it work with contact form plugins like the one from Jetpack?

Sorry for the late response. I did not receive any notification.

Jetpack should be running it through Akismet. Are you getting a lot of spam anyway?

This plugin just generates a combination of text and numbers. It's less secure than using an image generator tool. That's my understanding. Are there any alternatives that rely on image-based math captcha?

wp_nonce_field doesn't need to be echoed.