I believe you're in the UK and the Associated Board of the Royal School of Music is probably the most obvious choice of exam board. Their website is
http://www.abrsm.org/?page=exams from which the following was extracted from French Horn Grade 3. (A good music shop would have many of these so that you could browse them - your teacher may have some of them but many of the pieces have changed this term!)
THREE PIECES: one chosen by the candidate from each of the three Lists, A, B and C:
LIST A
1 Byrd The Earl of Salisbury’s Pavan
2 Handel See, the Conqu’ring Hero Comes (from ‘Judas Maccabaeus’) Time Pieces for Horn, Vol. 1, arr. Harris and
3 Schumann Soldiers’ March (from ‘Album for the Young’, Op.68) Skirrow (Associated Board)
4 Weber Theme from ‘Der Freischütz’ Overture
5 Delius La Calinda. No.6 from Going Solo – Horn, arr. Bissill and Campbell (Faber)
6 Dvořák Slavonic Dance. No.3 from Up and Running, arr. Skirrow (Camden Music CM 015/Spartan Press)
7 Anthony Randall Serenade (F/Eb edition: Broadbent & Dunn)
LIST B
1 Delius Lullaby (from ‘5 Piano Pieces’) Time Pieces for Horn, Vol. 1, arr. Harris and Skirrow (Associated Board)
2 Paul Harris Hunt the Horn
3 Ronald Hanmer Suite for Horn: 1st or 2nd movt, Prelude or Waltz (Emerson)
4 Ray Hensher Ragtime Horn. 10 Easy Tunes for Horn, arr. Humphries (Fentone/De Haske)
5 John Lennon and Paul McCartney Yesterday. The Beatles for Horn in F, arr. Mortimer (Editions Marc Reift/MusT)
6 Jim Parker Penguin Parade. Top Line Album for Horn (Brass Wind)
7 Michael Rose Russian Winter Holiday, from ‘Horn on Holiday’ (Associated Board)
8 Thoma Simaku The Blossoming Rose, from ‘Six Albanian Folksongs’ (F/E b edition: Emerson)
LIST C
1 Deborah Calland Keep Moving, from ‘Top Brass’ (Stainer & Bell)
2 Concone Study no.1 (Op.9 no.3) or no.2 (Op.9 no.4) or no.3 (Op.17 no.1). Concone Studies for Horn in F, arr. Ashworth
(Emerson)
3 Peter Lawrance Arietta, from ‘Featuring Melody’ (& brass edition: Brass Wind)
4 Maxime-Alphonse 200 New Studies for Horn, Book 1: no.3 in Eb or no.9 in A minor/major (Leduc/U.M.P.)
5 John Miller Rubic Rumba or The Easy Easy Winners: no.27 or no.31 from ‘Simple Studies for Beginner Brass’ (Faber)
AURAL TESTS FOR THE GRADE
SCALES AND ARPEGGIOS*: from memory, to be played both slurred and tongued in the following keys:
C, E minors (one octave, starting an octave above lowest tonic)
G, A majors; G minor (a twelfth, starting below stave)
Scales: in the above keys (minors in melodic or harmonic form at candidate’s choice)
Chromatic Scale: starting on C (one octave)
Arpeggios: the common chords of the above keys for the ranges indicated
PLAYING AT SIGHT a short piece in simple time within the keys, notes and overall range of the scale requirements
set up to and including this grade. See paragraph k on page 17.
*Published by the Board