Improve Articulation. Articulation is the attack made when playing a note, and examples include: single, double, and triple tonguing. Since jazz depends on swing - the feel of syncopation and momentum ina musical line, becoming proficient with up-beat-accented eighth notes is important. Improve articulation by working out a pattern of slurs and accents within a jazz line. Take two patterns based on the one, two, three and five, and the one, three, five, three scale tones in any key, and combine them at random over a series of eighth notes. Be sure to change accents throughout the exercise, always resolving step-wise within the key.
Learn the relationships of jazz chords and their associated modes. Since the intermediate level is where improvisation proficiency begins, knowing what modes and arpeggios work with each chord type is essential. Practice playing the associated modes and arpeggios with each chord of a jazz tune, which gives you the note knowledge required of jazz trumpet soloists. It's important to flow through the chord changes in all keys.
Knowledge of the common chord progressions used in jazz, such as the II-V-I and various blues progressions, give you the confidence needed to improvise at the intermediate level. The II-V-I progression in the key of C consists of the D minor seventh, G dominant seventh and C major. This is possibly the most common progression in jazz, and the modes used in the key of C are: D dorian, G mixolydian and the C ionian, these being the II-V-I scale tones. Blues requires knowledge of the major and blues scales, and a typical blues progression is the I-IV-V chords and modes of the key.
Listen to your favorite jazz musicians to hear what tricks and techniques they use. Analyze and play transcribed trumpet solos from known jazz trumpeters. Also, play-along recordings are available online, and can be used to practice modes, arpeggios and improvisational lines in the privacy of your home. Although play-along recordings are great learning tools, practicing with fellow jazz musicians is the best learning method at the intermediate level. Other musicians will pass along tips and tricks, and practice with other players will sharpen spontaneous improvisation skills.